Thermalization is an elusive phenomenon in quantum mechanics. Since according to the AdS/CFT correspondence, a thermal state in the boundary CFT is dual to a black hole in the bulk spacetime, thermalization in the CFT is dual to black hole formation in AdS. Thus, understanding quantum thermalization is likely a key component in understanding the information paradox---the contradiction between QFT and general relativity occurring when a black hole seemingly erases the information of whatever went into creating it.

(Apparent) thermalization in QFT can be investigated by imposing a quench, i.e., a sudden change of some parameter of the theory, and subsequently studying the equilibration process. In this thesis we aim to gain understanding of quantum thermalization by investigating the late-time quench dynamics of a simple free field theory, namely the $O(N)$ vector model. Since the theory is integrable, ``true'' thermalization will not occur but an approximate thermalization. We use different probes such as the effective density matrix and the spectral density function to investigate the extent to which the (pure) state ``looks'' thermal and how this deviates from conventional thermality.

Linear response theory is an incredibly powerful calculation tool. We apply this framework in quantum field theory to a variety of models originated from distinct areas in theoretical physics and for different reasons. In the context of black hole holography, we consider a quench model where we investigate effective thermalization as well as the boundary signal of the so called evanescent modes which indicate the presence of a black hole like object in the bulk. The problem of quantum thermalization plays a central role within the holographic duality between thermal states in the boundary field theory and black hole like objects in the bulk. However, quantum thermalization is also an interesting question in itself from a fundamental point of view and with that motivation we continue to explore this phenomenon further. Inspired by recent progress in understanding how operators in quantum field theories thermalize, which occurs even when considering integrable models, we investigate the so called operator thermalization hypothesis. We focus on gauge theories at finite temperature with a large number of fields which present a phase transition between the low-temperature and high-temperature regimes. In particular, these theories are the so called vector model and the adjoint matrix model. Last, within the common background of linear response theory we investigate transport properties in a family of Weyl semimetal systems. Concretely, we develop a general analytic method to compute the magneto-optical conductivity of these systems in the presence of an external magnetic field aligned with the tilt of the spectrum.

Thermalization is an elusive phenomenon in quantum mechanics. Since according to the AdS/CFT correspondence, a black hole in the bulk spacetime is dual to a thermal state in the boundary CFT, thermalization in the CFT is dual to black hole formation in AdS. Thus, understanding quantum thermalization is likely a key component in understanding the information paradox—the contradiction between QFT and general relativity occurring when a black hole seemingly erases the information of whatever went into creating it.

In this thesis we investigate different aspects of quantum thermalization in simple field theories that have conjectured holographic duals, or more specifically, free large N singlet models. Since such theories are free and hence integrable, thermalization is more subtle but nevertheless appears in different forms. We investigate the late-time quench dynamics of a version of the O(N) vector model with probes such as the effective density matrix and the spectral density function. We refine an operator thermalization hypothesis and explore its consequences in different spacetime dimensions in general large N singlet models. We also discuss the prospect of using thermal mixing in the boundary theory as a diagnostic of strong gravity in the bulk.

Linear response theory is a powerful calculation tool in quantum field theory. We apply this framework to a variety of models originating from distinct areas in theoretical physics and for different reasons. In the context of black hole holography, we consider a quench model where we investigate effective thermalization, as well as the boundary signal of so-called evanescent modes which indicate the presence of a black hole-like object in the bulk. The problem of quantum thermalization plays a central role within the holographic duality between thermal states in the boundary field theory and black hole-like objects in the bulk. However, quantum thermalization is also an interesting question in itself from a fundamental point of view. Inspired by recent progress in understanding how operators in quantum field theories thermalize, which occurs even when considering integrable models, we investigate the so-called operator thermalization hypothesis. We focus on gauge theories at finite temperature with a large number of fields which present a phase transition between the low-temperature and high-temperature regimes. In a separate application of linear response theory, we investigate transport properties in a family of Weyl semimetal systems. Concretely, we develop a general analytic method to compute the magneto-optical conductivity of these systems in the presence of an external magnetic field aligned with the tilt of the spectrum. Last, we examine non-Hermitian Weyl-like systems as potential analogue black hole models and suggest a specific parity-time-symmetric dissipative Hamiltonian displaying analogue Hawking radiation.