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  • 1.
    Andersson, David
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Bengtsson, Ingemar
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Blanchfield, Kate
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Dang, Hoan Bui
    States that are far from being stabilizer states2015Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, nr 34, artikkel-id 345301Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Stabilizer states are eigenvectors of maximal commuting sets of operators in a finite Heisenberg group. States that are far from being stabilizer states include magic states in quantum computation, MUB-balanced states, and SIC vectors. In prime dimensions the latter two fall under the umbrella of minimum uncertainty states (MUSs) in the sense of Wootters and Sussman. We study the correlation between two ways in which the notion of ` far from being a stabilizer state' can be quantified. Two theorems valid for all prime dimensions are given, as well as detailed results for low dimensions. In dimension 7 we identify the MUB-balanced states as being antipodal to the SIC vectors within the set of MUS, in a sense that we make definite. In dimension 4 we show that the states that come closest to being MUS with respect to all of the six stabilizer MUBs are the fiducial vectors for Alltop MUBs.

  • 2.
    Andersson, Ole
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Dumitru, Irina
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Aligned SICs and embedded tight frames in even dimensions2019Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, nr 42, artikkel-id 425302Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Alignment is a geometric relation between pairs of Weyl-Heisenberg SICs, one in dimension d and another in dimension d(d - 2), manifesting a well-founded conjecture about a number-theoretical connection between the SICs. In this paper, we prove that if d is even, the SIC in dimension d(d - 2) of an aligned pair can be partitioned into (d - 2)(2) tight d(2)-frames of rank d(d - 1)/2 and, alternatively, into d(2) tight (d - 2)(2) -frames of rank (d - 1) (d - 2)/2. The corresponding result for odd d is already known, but the proof for odd d relies on results which are not available for even d. We develop methods that allow us to overcome this issue. In addition, we provide a relatively detailed study of parity operators in the Clifford group, emphasizing differences in the theory of parity operators in even and odd dimensions and discussing consequences due to such differences. In a final section, we study implications of alignment for the symmetry of the SIC.

  • 3.
    Andersson, Ole
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Heydari, Hoshang
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    A symmetry approach to geometric phase for quantum ensembles2015Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, nr 48, artikkel-id 485302Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the 'interferometric' geometric phase of Sjqvist et al (2000 Phys. Rev. Lett. 85 2845-9), and for more generally evolving open systems it gives rise to the generalization of the interferometric geometric phase due to Tong et al (2004 Phys. Rev. Lett. 93 080405).

  • 4.
    Andersson, Ole
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Heydari, Hoshang
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Quantum speed limits and optimal Hamiltonians for driven systems in mixed states2014Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 47, nr 21, s. 215301-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Inequalities of Mandelstam-Tamm (MT) and Margolus-Levitin (ML) type provide lower bounds on the time that it takes for a quantum system to evolve from one state into another. Knowledge of such bounds, called quantum speed limits, is of utmost importance in virtually all areas of physics, where determination of the minimum time required for a quantum process is of interest. Most MT and ML inequalities found in the literature have been derived from growth estimates for the Bures length, which is a statistical distance measure. In this paper we derive such inequalities by differential geometric methods, and we compare the quantum speed limits obtained with those involving the Bures length. We also characterize the Hamiltonians which optimize the evolution time for generic finite-level quantum systems.

  • 5. Arutyunov, Gleb
    et al.
    Heinze, Martin
    Medina-Rincon, Daniel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Uppsala University, Sweden .
    Integrability of the eta-deformed Neumann-Rosochatius model2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 3, artikkel-id 035401Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An integrable deformation of the well-known Neumann-Rosochatius system is studied by considering generalised bosonic spinning solutions on the eta-deformed AdS(5) x S-5 background. For this integrable model we construct a 4x4 Lax representation and a set of integrals of motion that ensures its Liouville integrability. These integrals of motion correspond to the deformed analogues of the Neumann-Rosochatius integrals and generalise the previously found integrals for the.-deformed Neumann and (AdS(5) x S-5)(eta) geodesic systems. Finally, we briefly comment on consistent truncations of this model.

  • 6. Arutyunov, Gleb
    et al.
    Heinze, Martin
    Medina-Rincon, Daniel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Uppsala University, Sweden.
    Superintegrability of geodesic motion on the sausage model2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 24, artikkel-id 244002Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Reduction of the eta-deformed sigma model on AdS(5) x S-5 to the two-dimensional squashed sphere (S-2)eta can be viewed as a special case of the Fateev sausage model where the coupling constant v is imaginary. We show that geodesic motion in this model is described by a certain superintegrable mechanical system with four-dimensional phase space. This is done by means of explicitly constructing three integrals of motion which satisfy the sl(2) Poisson algebra relations, albeit being non-polynomial in momenta. Further, we find a canonical transformation which transforms the Hamiltonian of this mechanical system to the one describing the geodesic motion on the usual two-sphere. By inverting this transformation we map geodesics on this auxiliary two-sphere back to the sausage model.

  • 7.
    Bargheer, Till
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Beisert, Niklas
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Loebbert, Florian
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    McLoughlin, Tristan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Conformal anomaly for amplitudes in N=6 superconformal Chern-Simons theory2012Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 47, s. 475402-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Scattering amplitudes in three-dimensional N = 6 Chern-Simons theory are shown to be non-invariant with respect to the free representation of the osp(6 vertical bar 4) symmetry generators. At tree and one-loop level these 'anomalous' terms occur only for non-generic, singular configurations of the external momenta and can be used to determine the form of the amplitudes. In particular we show that the symmetries predict that the one-loop six-point amplitude is non-vanishing and confirm this by means of an explicit calculation using generalized unitarity methods. We comment on the implications of this finding for any putative Wilson loop/amplitude duality in N = 6 Chern-Simons theory.

  • 8.
    Bengtsson, Ingemar
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Blanchfield, Kate
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Campbell, Earl
    Howard, Mark
    Order 3 Symmetry in the Clifford Hierarchy2014Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 47, nr 45, s. 455302-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate the action of Weyl-Heisenberg and Clifford groups on sets of vectors that comprise mutually unbiased bases (MUBs). We consider two distinct MUB constructions, the standard and Alltop constructions, in Hilbert spaces of prime dimension. We show how the standard set of MUBs turns into the Alltop set under the action of an element at the third level of the Clifford hierarchy. We prove that when the dimension is a prime number equal to one modulo three each Alltop vector is invariant under an element of the Clifford group of order 3. The set of all Alltop vectors splits into three different orbits of the Clifford group, and forms a configuration together with the set of all subspaces invariant under an order 3 element of the Clifford group. There is a well-known conjecture that SIC vectors can be found in the eigenspace of order 3 Cliffords. This, combined with a connection between MUB and SIC vectors, suggests our work may provide a clue to the SIC existence problem in these dimensions. We identify Alltop vectors as so-called magic states which appear in the context of fault-tolerant quantum computing. The appearance of distinct Clifford orbits implies an inequivalence between some magic states.

  • 9.
    Bengtsson, Ingemar
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Srivastava, Basudha
    Dimension towers of SICS: II. Some constructions2022Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 55, nr 21, artikkel-id 215302Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A SIC is a maximal equiangular tight frame in a finite dimensional Hilbert space. Given a SIC in dimension d, there is good evidence that there always exists an aligned SIC in dimension d(d - 2), having predictable symmetries and smaller equiangular tight frames embedded in them. We provide a recipe for how to calculate sets of vectors in dimension d(d - 2) that share these properties. They consist of maximally entangled vectors in certain subspaces defined by the numbers entering the d dimensional SIC. However, the construction contains free parameters and we have not proven that they can always be chosen so that one of these sets of vectors is a SIC. We give some worked examples that, we hope, may suggest to the reader how our construction can be improved. For simplicity we restrict ourselves to the case of odd dimensions. 

  • 10. Berkolaiko, Gregory
    et al.
    Kennedy, James B.
    Kurasov, Pavel
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Mugnolo, Delio
    Edge connectivity and the spectral gap of combinatorial and quantum graphs2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 36, artikkel-id 365201Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive a number of upper and lower bounds for the first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge connectivity, i.e. the minimal number of edges which need to be removed to make the graph disconnected. On combinatorial graphs, one of the bounds corresponds to a well-known inequality of Fiedler, of which we give a new variational proof. On quantum graphs, the corresponding bound generalizes a recent result of Band and Levy. All proofs are general enough to yield corresponding estimates for the p-Laplacian and allow us to identify the minimizers. Based on the Betti number of the graph, we also derive upper and lower bounds on all eigenvalues which are 'asymptotically correct', i.e. agree with the Weyl asymptotics for the eigenvalues of the quantum graph. In particular, the lower bounds improve the bounds of Friedlander on any given graph for all but finitely many eigenvalues, while the upper bounds improve recent results of Ariturk. Our estimates are also used to derive bounds on the eigenvalues of the normalized Laplacian matrix that improve known bounds of spectral graph theory.

  • 11. Bern, Zvi
    et al.
    Carrasco, John Joseph
    Chiodaroli, Marco
    Johansson, Henrik
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Uppsala University, Sweden.
    Roiban, Radu
    The SAGEX review on scattering amplitudes Chapter 2: An invitation to color-kinematics duality and the double copy2022Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 55, nr 44, artikkel-id 443003Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    Advances in scattering amplitudes have exposed previously-hidden color-kinematics and double-copy structures in theories ranging from gauge and gravity theories to effective field theories such as chiral perturbation theory and the Born–Infeld model. These novel structures both simplify higher-order calculations and pose tantalizing questions related to a unified framework underlying relativistic quantum theories. This introductory mini-review article invites further exploration of these topics. After a brief introduction to color-kinematics duality and the double copy as they emerge at tree and loop-level in gauge and gravity theories, we present two distinct examples: (1) an introduction to the web of double-copy-constructible theories, and (2) a discussion of the application of the double copy to calculation relevant to gravitational-wave physics.

  • 12. Berntson, Bjorn K.
    et al.
    Klabbers, Rob
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Langmann, Edwin
    Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics2020Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 53, nr 50, artikkel-id 505702Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the half-wave maps (HWM) equation which provides a continuum description of the classical Haldane–Shastry spin chain on the real line. We present exact multi-soliton solutions of this equation. Our solutions describe solitary spin excitations that can move with different velocities and interact in a non-trivial way. We make an ansatz for the solution allowing for an arbitrary number of solitons, each described by a pole in the complex plane and a complex spin variable, and we show that the HWM equation is satisfied if these poles and spins evolve according to the dynamics of an exactly solvable spin Calogero–Moser (CM) system with certain constraints on initial conditions. We also find first order equations providing a Bäcklund transformation of this spin CM system, generalize our results to the periodic HWM equation, and provide plots that visualize our soliton solutions.

  • 13.
    Blanchfield, Kate
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Orbits of mutually unbiased bases2014Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 47, nr 13, artikkel-id 135303Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We express Alltop's construction of mutually unbiased bases as orbits under the Weyl–Heisenberg group in prime dimensions and find a related construction in dimensions 2 and 4. We reproduce Alltop's mutually unbiased bases using abelian subgroups of the Clifford group in prime dimensions, in direct analogy to the well-known construction of mutually unbiased bases using abelian subgroups of the Weyl–Heisenberg group. Finally, we prove three theorems relating to the distances and linear dependencies among different sets of mutually unbiased bases.

  • 14. Borsato, Riccardo
    et al.
    Ohlsson Sax, Olof
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Sfondrini, Alessandro
    Stefanski, Bogdan
    On the spectrum of AdS(3) x S-3 x T-4 strings with Ramond-Ramond flux2016Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 49, nr 41, artikkel-id 41LT03Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We analyze the spectrum of perturbative closed strings on AdS(3) x S-3 x T-4 with Ramond-Ramond flux using integrable methods. By solving the crossing equations we determine the massless and mixed-mass dressing factors of the worldsheet S matrix and derive the Bethe equations. Using these, we construct the underlying integrable spin chain and show that it reproduces the reducible spin chain conjectured at weak coupling in Olof Ohlsson S, Bogdan S Jr and Torrielli A 2013 (arXiv: 1211.1952). We find that the string-theory massless modes are described by gapless excitations of the spin chain. The resulting degeneracy of vacua matches precisely the protected supergravity spectrum found by de Boer.

  • 15. Borsato, Riccardo
    et al.
    Ohlsson Sax, Olof
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Sfondrini, Alessandro
    Stefanski, Bogdan
    Torrielli, Alessandro
    On the dressing factors, Bethe equations and Yangian symmetry of strings on AdS(3) x S-3 x T-42017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 2, artikkel-id 024004Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Integrability is believed to underlie the AdS3/CFT2 correspondence with sixteen supercharges. We elucidate the role of massless modes within this integrable framework. Firstly, we find the dressing factors that enter the massless and mixed-mass worldsheet S matrix. Secondly, we derive a set of all-loop Bethe Equations for the closed strings, determine their symmetries and weak-coupling limit. Thirdly, we investigate the underlying Yangian symmetry in the massless sector and show that it fits into the general framework of Yangian integrability. In addition, we compare our S matrix in the near-relativistic limit with recent perturbative worldsheet calculations of Sundin and Wulff.

  • 16.
    Borsato, Riccardo
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Universidade de Santiago de Compostela, Spain.
    Wulff, Linus
    Marginal deformations of WZW models and the classical Yang-Baxter equation2019Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, nr 22, artikkel-id 225401Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show how so-called Yang-Baxter (YB) deformations of sigma models, based on an R-matrix solving the classical Yang-Baxter equation (CYBE), give rise to marginal current-current deformations when applied to the Wess-Zumino-Witten (WZW) model. For non-compact groups these marginal deformations are more general than the ones usually considered, since they can involve a non-Abelian current subalgebra. We classify such deformations of the AdS(3) x S-3 string.

  • 17.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Carnegie Mellon University, United States of America; Ilia State University, Georgia.
    Quadratic growth during the COVID-19 pandemic: merging hotspots and reinfections2023Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 56, nr 4, artikkel-id 044002Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The existence of an exponential growth phase during early stages of a pandemic is often taken for granted. However, for the 2019 novel coronavirus epidemic, the early exponential phase lasted only for about six days, while the quadratic growth prevailed for forty days until it spread to other countries and continued, again quadratically, but with a shorter time constant. Here we show that this rapid phase is followed by a subsequent slow-down where the coefficient is reduced to almost the original value at the outbreak. This can be explained by the merging of previously disconnected sites that occurred after the disease jumped (nonlocally) to a relatively small number of separated sites. Subsequent variations in the slope with continued growth can qualitatively be explained as a result of reinfections and variations in their rate. We demonstrate that the observed behavior can be described by a standard epidemiological model with spatial extent and reinfections included. Time-dependent changes in the spatial diffusion coefficient can also model corresponding variations in the slope.

  • 18. Budroni, Costantino
    et al.
    Cabello, Adan
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Bell inequalities from variable-elimination methods2012Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 38, s. 385304-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here, we present an alternative method based on a combination of algebraic results on extensions of measures and variable-elimination methods, e. g., the Fourier-Motzkin method. Our method is shown to overcome some of the computational difficulties associated with the hull problem in some non-trivial cases. Moreover, it provides an explanation for the arising of only a finite number of families of Bell inequalities in measurement scenarios where one experimenter can choose between an arbitrary number of different measurements.

  • 19.
    Cabello, Adan
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Danielsen, Lars Eirik
    Lopez-Tarrida, Antonio J.
    Portillo, Jose R.
    Quantum social networks2012Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 28, s. 285101-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce a physical approach to social networks (SNs) in which each actor is characterized by a yes-no test on a physical system. This allows us to consider SNs beyond those originated by interactions based on pre-existing properties, as in a classical SN (CSN). As an example of SNs beyond CSNs, we introduce quantum SNs (QSNs) in which actor i is characterized by a test of whether or not the system is in a quantum state |psi(i)>. We show that QSNs outperform CSNs for a certain task and some graphs. We identify the simplest of these graphs and show that graphs in which QSNs outperform CSNs are increasingly frequent as the number of vertices increases. We also discuss more general SNs and identify the simplest graphs in which QSNs cannot be outperformed.

  • 20.
    Cagnazzo, Alessandra
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Sorokin, Dmitri
    Tseytlin, Arkady A.
    Wulff, Linus
    Semiclassical equivalence of Green-Schwarz and pure-spinor/hybrid formulations of superstrings in AdS(5) x S-5 and AdS(2) x S-2 x T-62013Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 6, s. 065401-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We demonstrate the equivalence between the worldsheet one-loop partition functions computed near classical string solutions in the Green-Schwarz and in the pure-spinor formulations of superstrings in AdS(5) x S-5. While their bosonic sectors are the same in the conformal gauge, their fermionic sectors superficially appear to be very different (first versus second-derivative kinetic terms, presence versus absence of fermionic gauge symmetry). Still, we show that the quadratic fluctuation spectrum of 16 fermionic modes of the pure-spinor formulation is the same as in the Green-Schwarz superstring and the contribution of the extra 'massless' fermionic modes cancels against that of the pure-spinor ghosts. We also provide evidence for a similar semiclassical equivalence between the Green-Schwarz and the hybrid formulations of superstrings in AdS(2) x S-2 x T-6 by studying several particular examples of string solutions.

  • 21.
    Caputa, Pawel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Kyoto University, Japan.
    Kusuki, Yuya
    Takayanagi, Tadashi
    Watanabe, Kento
    Evolution of entanglement entropy in orbifold CFTs2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 24, artikkel-id 244001Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this work we study the time evolution of the Renyi entanglement entropy for locally excited states created by twist operators in the cyclic orbifold (T-2)(n)/Z(n) and the symmetric orbifold (T-2)(n)/S-n. We find that when the square of its compactification radius is rational, the second Renyi entropy approaches a universal constant equal to the logarithm of the quantum dimension of the twist operator. On the other hand, in the non-rational case, we find a new scaling law for the Renyi entropies given by the double logarithm of time log log t for the cyclic orbifold CFT.

  • 22.
    Caputa, Pawel
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Rams, Marek M.
    Quantum dimensions from local operator excitations in the Ising model2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 5, artikkel-id 055002Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Renyi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics.

  • 23. Carugno, Giorgio
    et al.
    Vivo, Pierpaolo
    Coghi, Francesco
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Graph-combinatorial approach for large deviations of Markov chains2022Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 55, nr 29, artikkel-id 295001Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider discrete-time Markov chains and study large deviations of the pair empirical occupation measure, which is useful to compute fluctuations of pure-additive and jump-type observables. We provide an exact expression for the finite-time moment generating function, which is split in cycles and paths contributions, and scaled cumulant generating function of the pair empirical occupation measure via a graph-combinatorial approach. The expression obtained allows us to give a physical interpretation of interaction and entropic terms, and of the Lagrange multipliers, and may serve as a starting point for sub-leading asymptotics. We illustrate the use of the method for a simple two-state Markov chain.

  • 24. Chruściński, Dariusz
    et al.
    Sarbicki, Gniewomir
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Nicolaus Copernicus University, Poland.
    Exposed positive maps: a sufficient condition2012Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 11, artikkel-id 115304Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a sufficient condition for a positive map to be exposed. This is an analogue of a spanning property which guarantees that a positive map is optimal. We analyze a class of decomposable maps for which this condition is also necessary.

  • 25. Cooke, Michael
    et al.
    Dekel, Amit
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Drukker, Nadav
    The Wilson loop CFT: insertion dimensions and structure constants from wavy lines2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 33, artikkel-id 335401Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study operator insertions into the 1/2 BPS Wilson loop in N = 4 SYM theory and determine their two-point coefficients, anomalous dimensions and structure constants. The calculation is done for the first few lowest dimension insertions and relies on known results for the expectation value of a smooth Wilson loop. In addition to the particular coefficients that we calculate, our study elucidates the connection between deformations of the line and operator insertions and between the vacuum expectation value of the line and the CFT data of the insertions.

  • 26.
    de Wijn, A. S.
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Hess, B.
    Fine, B. V.
    Lyapunov instabilities in lattices of interacting classical spins at infinite temperature2013Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 25, s. 254012-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We numerically investigate Lyapunov instabilities for one-, two-and three-dimensional lattices of interacting classical spins at infinite temperature. We obtain the largest Lyapunov exponents for a very large variety of nearest-neighbor spin-spin interactions and complete Lyapunov spectra in a few selected cases. We investigate the dependence of the largest Lyapunov exponents and whole Lyapunov spectra on the lattice size and find that both quickly become size-independent. Finally, we analyze the dependence of the largest Lyapunov exponents on the anisotropy of spin-spin interaction with the particular focus on the difference between bipartite and nonbipartite lattices.

  • 27. Drukker, Nadav
    et al.
    Trancanelli, Diego
    Bianchi, Lorenzo
    Bianchi, Marco S.
    Correa, Diego H.
    Forini, Valentina
    Griguolo, Luca
    Leoni, Matias
    Levkovich-Maslyuk, Fedor
    Nagaoka, Gabriel
    Penati, Silvia
    Preti, Michelangelo
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Probst, Malte
    Putrov, Pavel
    Seminara, Domenico
    Silva, Guillermo A.
    Tenser, Marcia
    Trépanier, Maxime
    Vescovi, Edoardo
    Yaakov, Itamar
    Zhang, Jiaju
    Roadmap on Wilson loops in 3d Chern-Simons-matter theories2020Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 53, nr 17, artikkel-id 173001Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    This is a compact review of recent results on supersymmetric Wilson loops in ABJ(M) and related theories. It aims to be a quick introduction to the state of the art in the field and a discussion of open problems. It is divided into short chapters devoted to different questions and techniques. Some new results, perspectives and speculations are also presented. We hope this might serve as a baseline for further studies of this topic.

  • 28. Frassek, Rouven
    et al.
    Szécsényi, István M.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin2022Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 55, nr 50, artikkel-id 505201Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced Q-operators using the fundamental commutation relations. By acting on Bethe off-shell states and explicitly evaluating the trace in the auxiliary space we compute the eigenvalues of the Q-operators in terms of Bethe roots and show that the unwanted terms vanish if the Bethe equations are satisfied.

  • 29.
    Fremling, Mikael
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Coherent state wave functions on a torus with a constant magnetic field2013Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 27, artikkel-id 275302Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study two alternative definitions of localized states in the lowest Landau level (LLL) on a torus. One definition is to construct localized states, as the projection of the coordinate delta function onto the LLL. Another definition, proposed by Haldane, is to consider the set of functions which have all their zeros at a single point. Since a LLL wave function on a torus, supporting N-phi magnetic flux quanta, is uniquely defined by the position of its N-phi zeros, this defines a set of functions that are expected to be localized around the point maximally far away from the zeros. These two families of localized states have many properties in common with the coherent states on the plane and on the sphere, viz a resolution of unity and a self-reproducing kernel. However, we show that only the projected delta function is maximally localized. Additionally, we show how to project onto the LLL, functions that contain holomorphic derivatives and/or anti-holomorphic polynomials, and apply our methods in the description of hierarchical quantum Hall liquids.

  • 30.
    Fremling, Mikael
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. National University of Ireland, Ireland.
    Success and failure of the plasma analogy for Laughlin states on a torus2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 1, artikkel-id 015201Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate the nature of the plasma analogy for the Laughlin wave function on a torus describing the quantum Hall plateau at nu = 1/q. We first establish, as expected, that the plasma is screening if there are no short nontrivial paths around the torus. We also find that when one of the handles has a short circumference-i.e. the thin-torus limit-the plasma no longer screens. To quantify this we compute the normalization of the Laughlin state, both numerically and analytically. In the thin torus limit, the analytical form of the normalization simplify and we can reconstruct the normalization and analytically extend it back into the 2D regime. We find that there are geometry dependent corrections to the normalization, and this in turn implies that the plasma in the plasma analogy is not screening when in the thin torus limit. Despite the breaking of the plasma analogy in this limit, the analytical approximation is still a good description of the normalization for all tori, and also allows us to compute hall viscosity at intermediate thickness.

  • 31.
    Grøsfjeld, Tobias
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Shapiro, Boris
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Zarembo, Konstantin
    Level crossing in random matrices. II. Random perturbation of a random matrix2019Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, nr 21, artikkel-id 214001Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we study the distribution of level crossings for the spectra of linear families A + lambda B, where A and B are square matrices independently chosen from some given Gaussian ensemble and lambda is a complex-valued parameter. We formulate a number of theoretical and numerical results for the classical Gaussian ensembles and some of their generalisations. Besides, we present intriguing numerical information about the monodromy distribution in case of linear families for the classical Gaussian ensembles of 3 x 3-matrices.

  • 32.
    Guff, Thomas
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Macquarie University, Australia.
    McMahon, Nathan A.
    Sanders, Yuval R.
    Gilchrist, Alexei
    A resource theory of quantum measurements2021Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 54, artikkel-id 225301Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Resource theories are broad frameworks that capture how useful objects are in performing specific tasks. In this paper we devise a formal resource theory quantum measurements, focusing on the ability of a measurement to acquire information. The objects of the theory are equivalence classes of positive operator-valued measures, and the free transformations are changes to a measurement device that can only deteriorate its ability to report information about a physical system. We show that catalysis and purification, protocols that are possible in other resource theories, are impossible in our resource theory for quantum measurements. Standard measures of information gain are shown to be resource monotones, and the resource theory is applied to the task of quantum state discrimination.

  • 33.
    Guica, Monica
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Institut de Physique Théorique, France.
    On correlation functions in J(T)over-bar-deformed CFTs2019Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, nr 18, artikkel-id 184003Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The J (T) over bar deformation, built from the components of the stress tensor and of a U(1) current, is a universal irrelevant deformation of two-dimensional CFTs that preserves the left-moving conformal symmetry, while breaking locality on the right-moving side. Operators in the J (T) over bar -deformed CFT are naturally labeled by the left-moving position and right-moving momentum and transform in representations of the one-dimensional extended conformal group. We derive an all-orders formula for the spectrum of conformal dimensions and charges of the deformed CFT, which we cross-check at leading order using conformal perturbation theory. We also compute the linear corrections to the one-dimensional OPE coefficients and comment on the extent to which the correlation functions in J (T) over bar -deformed CFTs can be obtained from field-dependent coordinate transformations.

  • 34.
    Guica, Monica
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). CEA Saclay, France; Uppsala University, Sweden.
    Levkovich Maslyuk, Fedor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Zarembo, Konstantin
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Uppsala University, Sweden.
    Integrability in dipole-deformed N=4 super Yang-Mills2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 39, artikkel-id 394001Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the null dipole deformation of N = 4 super Yang-Mills theory, which is an example of a potentially solvable 'dipole CFT': a theory that is non-local along a null direction, has non-relativistic conformal invariance along the remaining ones, and is holographically dual to a Schrodinger space-time. We initiate the field-theoretical study of the spectrum in this model by using integrability inherited from the parent theory. The dipole deformation corresponds to a nondiagonal Drinfeld-Reshetikhin twist in the spin chain picture, which renders the traditional Bethe ansatz inapplicable from the very beginning. We use instead the Baxter equation supplemented with nontrivial asymptotics, which gives the full 1-loop spectrum in the sl(2) sector. We show that anomalous dimensions of long gauge theory operators perfectly match the string theory prediction, providing a quantitative test of Schrodinger holography.

  • 35. Harland, Derek
    et al.
    Jäykkä, Juha
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Shnir, Yakov
    Speight, Martin
    Isospinning hopfions2013Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 22, s. 225402-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The problem of constructing internally rotating solitons of fixed angular frequency omega in the Faddeev-Skyrme model is reformulated as a variational problem for an energy-like functional, called pseudoenergy, which depends parametrically on omega. This problem is solved numerically using a gradient descent method, without imposing any spatial symmetries on the solitons, and the dependence of the solitons' energy on omega, and on their conserved total isospin J, studied. It is found that, generically, the shape of a soliton is independent of omega, and that its size grows monotonically with omega. A simple elastic rod model of time-dependent hopfions is developed which, despite having only one free parameter, accounts well for most of the numerical results.

  • 36.
    Hertz, John A.
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Copenhagen, Denmark.
    Roudi, Yasser
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Kavli Institute for Systems Neuroscience and Centre for Neural Computation, NTNU, Norway; Institute for Advanced Study, Princeton, NJ, USA.
    Sollich, Peter
    Path integral methods for the dynamics of stochastic and disordered systems2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 3, artikkel-id 033001Artikkel, forskningsoversikt (Fagfellevurdert)
    Abstract [en]

    We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose/Janssen-De Dominicis-Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.

  • 37.
    Heydari, Hoshang
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    A geometric framework for mixed quantum states based on a Kähler structure2015Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, nr 25, artikkel-id 255301Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we introduce a geometric framework for mixed quantum states based on a Kähler structure. The geometric framework includes a symplectic form, an almost complex structure, and a Riemannian metric that characterize the space of mixed quantum states. We argue that the almost complex structure is integrable. We also in detail discuss a visualizing application of this geometric framework by deriving a geometric uncertainty relation for mixed quantum states. The framework is computationally effective and it provides us with a better understanding of general quantum mechanical systems.

  • 38. Ito, Katsushi
    et al.
    Kondo, Takayasu
    Kuroda, Kohei
    Shu, Hongfei
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    ODE/IM correspondence for affine Lie algebras: a numerical approach2021Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 54, nr 4, artikkel-id 044001Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study numerically the ODE/IM correspondence for untwisted affine Lie algebras associated with simple Lie algebras including exceptional type. We consider the linear problem obtained from the massless limit of that of the modified affine Toda field equation. We found that the Q-functions in integrable models are expressed as the inner product of the solution of the dual linear problem and the subdominant solution of the linear problem. Using Cheng's algorithm to obtain the solution of the linear problem, we can determine efficiently the zeros of the Q-function, which is known to provide the solutions of the Bethe ansatz equations (BAEs). We calculate the zeros numerically, which are shown to agree with the results from the non-linear integral equations (NLIEs) for simply-laced affine Lie algebras including the exceptional type. By the folding procedure of the Dynkin diagrams of simply-laced Lie algebras, we also find the correspondence for the linear problem of the non-simply-laced affine Lie algebras.

  • 39. Ito, Katsushi
    et al.
    Shu, Hongfei
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Tokyo Institute of Technology Tokyo, Japan.
    TBA equations for the Schrödinger equation with a regular singularity2020Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 53, nr 33, artikkel-id 335201Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive the thermodynamic Bethe ansatz (TBA) equations for the Schrödinger equation with an arbitrary polynomial potential and a regular singular (simple and double pole) term. The TBA equations provide a non-trivial generalization of the ODE/IM correspondence and also give a solution for the Riemann-Hilbert problem in the exact WKB method. We study the TBA equations in detail for the linear and the harmonic oscillator potentials together with inverse and centrifugal terms. As an application, we also compute numerically the Voros spectrum for these potentials using the Bohr-Sommerfeld quantization condition.

  • 40.
    Krishnamurthy, Supriya
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Smith, Eric
    Solving moment hierarchies for chemical reaction networks2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 42, artikkel-id 425002Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The study of chemical reaction networks (CRN's) is a very active field. Earlier well-known results (Feinberg 1987 Chem. Enc. Sci. 42 2229, Anderson et al 2010 Bull. Math. Biol. 72 1947) identify a topological quantity called deficiency, for any CRN, which, when exactly equal to zero, leads to a unique factorized steady-state for these networks. No results exist however for the steady states of non-zero-deficiency networks. In this paper, we show how to write the full moment-hierarchy for any non-zero-deficiency CRN obeying mass-action kinetics, in terms of equations for the factorial moments. Using these, we can recursively predict values for lower moments from higher moments, reversing the procedure usually used to solve moment hierarchies. We show, for non-trivial examples, that in this manner we can predict any moment of interest, for CRN's with non-zero deficiency and non-factorizable steady states.

  • 41.
    Kurasov, Pavel
    Stockholms universitet.
    Response to "Comment on 'On the Coulomb potential in one dimension' " by W.Fisher, H.Leschke and P.Muller1997Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121Artikkel i tidsskrift (Fagfellevurdert)
  • 42.
    Kurasov, Pavel
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Malenova, G.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Naboko, S.
    Spectral gap for quantum graphs and their edge connectivity2013Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 27, s. 275309-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The spectral gap for Laplace operators on metric graphs and the relation between the graph's edge connectivity is investigated, in particular what happens to the gap if an edge is added to (or deleted from) a graph. It is shown that, in contrast to discrete graphs, the connection between the connectivity and the spectral gap is not one-to-one. The size of the spectral gap depends not only on the topology of the metric graph but on its geometric properties as well. It is shown that adding sufficiently large edges as well as cutting away sufficiently small edges leads to a decrease of the spectral gap. Corresponding explicit criteria are given.

  • 43.
    Kurasov, Pavel
    et al.
    Stockholms universitet.
    Nowaczyk, Marlena
    Lunds universitet.
    Inverse spectral problem for quantum graphs2005Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121Artikkel i tidsskrift (Fagfellevurdert)
  • 44.
    Kurasov, Pavel
    et al.
    Stockholms universitet.
    Stenberg, Fredrik
    On the inverse scattering problem on branching graphs2002Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121Artikkel i tidsskrift (Fagfellevurdert)
  • 45.
    Larson, Jonas
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Irish, Elinor K.
    Some remarks on 'superradiant' phase transitions in light-matter systems2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 17, artikkel-id 174002Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we analyze properties of the phase transition that appears in a set of quantum optical models; Dicke, Tavis-Cummings, quantum Rabi, and finally the Jaynes-Cummings model. As the light-matter coupling is increased into the deep strong coupling regime, the ground state turns from vacuum to become a superradiant state characterized by both atomic and photonic excitations. It is pointed out that all four transitions are of the mean-field type, that quantum fluctuations are negligible, and hence these fluctuations cannot be responsible for the corresponding vacuum instability. In this respect, these are not quantum phase transitions. In the case of the Tavis-Cummings and Jaynes-Cummings models, the continuous symmetry of these models implies that quantum fluctuations are not only negligible, but strictly zero. However, all models possess a non-analyticity in the ground state in agreement with a continuous quantum phase transition. As such, it is a matter of taste whether the transitions should be termed quantum or not. In addition, we also consider the modifications of the transitions when photon losses are present. For the Dicke and Rabi models these non-equilibrium steady states remain critical, while the criticality for the open Tavis-Cummings and Jaynes-Cummings models is completely lost, i. e. in realistic settings one cannot expect a true critical behaviour for the two last models.

  • 46.
    Lim, Soon Hoe
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Anomalous thermodynamics in homogenized generalized Langevin systems2021Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 54, nr 15, artikkel-id 155001Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study functionals, such as heat and work, along trajectories of a class of multi-dimensional generalized Langevin systems in various limiting situations that correspond to different level of homogenization. These are the situations where one or more of the inertial time scale(s), the memory time scale(s) and the noise correlation time scale(s) of the systems are taken to zero. We find that, unless one restricts to special situations that do not break symmetry of the Onsager matrix associated with the fast dynamics, it is generally not possible to express the effective evolution of these functionals solely in terms of trajectory of the homogenized process describing the system dynamics via the widely adopted Stratonovich convention. In fact, an anomalous term is often needed for a complete description, implying that convergence of these functionals needs more information than simply the limit of the dynamical process. We trace the origin of such impossibility to area anomaly, thereby linking the symmetry breaking and area anomaly. This hold important consequences for many nonequilibrium systems that can be modeled by generalized Langevin equations. Our convergence results hold in a strong pathwise sense.

  • 47.
    Léna, Corentin
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Serio, Andrea
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Concrete method for recovering the Euler characteristic of quantum graphs2020Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 53, nr 27, artikkel-id 275201Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Trace formulas play a central role in the study of spectral geometry and in particular of quantum graphs. The basis of our work is the result by Kurasov which links the Euler characteristic χ of metric graphs to the spectrum of their standard Laplacian. These ideas were shown to be applicable even in an experimental context where only a finite number of eigenvalues from a physical realization of quantum graph can be measured. In the present work we analyse sufficient hypotheses which guarantee the successful recovery of χ. We also study how to improve the efficiency of the method and in particular how to minimise the number of eigenvalues required. Finally, we compare our findings with numerical examples-surprisingly, just a few dozens of eigenvalues can be enough.

  • 48. Mahdifar, Ali
    et al.
    Mirza, Behrouz
    Roknizadeh, Rasoul
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Two-dimensional isotropic harmonic oscillator on a time-dependent sphere2012Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 46, s. 465301-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we investigate a two-dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a fluctuating background, transition probabilities per unit time are obtained. Transitions are possible if the energy eigenvalues of the oscillator E-i and frequencies of the fluctuating background omega(n) satisfy the following two simple relations: E-j similar or equal to E-i - (h) over bar omega(n) (stimulated emission) and E-j similar or equal to E-i + (h) over bar omega(n) (absorption). This indicates that a background fluctuating at a frequency of omega(n) interacts with the oscillator as a quantum field of the same frequency. We believe this result is also applicable for an arbitrary quantum system defined on a fluctuating maximally symmetric background.

  • 49.
    Majidzadeh Garjani, Babak
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Ardonne, Eddy
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Anyon chains with pairing terms2017Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 13, artikkel-id 135201Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we introduce a one-dimensional model of $su(2)_k$ anyons in which the number of anyons can uctuate by means of a pairing term. The model can be tuned to a point at which one can determine the exact zero-energy ground states, in close analogy to the spin-1 AKLT model. We also determine the points at which the model is integrable and determine the behavior of the model at these integrable points. 

  • 50.
    Majidzadeh Garjani, Babak
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Estienne, B.
    Ardonne, Eddy
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    On the particle entanglement spectrum of the Laughlin states2015Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, nr 28, artikkel-id 285205Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The study of the entanglement entropy and entanglement spectrum has proven to be very fruitful in identifying topological phases of matter. Typically, one performs numerical studies of finite-size systems. However, there are few rigorous results in this regard. We revisit the problem of determining the rank of the 'particle entanglement spectrum' (PES) of the Laughlin states. We reformulate the problem into a problem concerning the ideal of symmetric polynomials that vanish under the formation of several clusters of particles. We introduce an explicit generating set of this ideal, and we prove that polynomials in this ideal have a total degree that is bounded from below. We discuss the difficulty in proving the same bound on the degree of any of the variables, which is necessary to determine the rank of the PES.

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