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arXiv:2305.05494 · Physical review. B./Physical review. B

Thermal bath effects in quantum quenches within quantum critical regimes

Francesco Tarantelli, Ettore Vicari

Published Jul 14, 2023• 4 citations
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Abstract

We address the out-of-equilibrium dynamics arising from quantum-quench (QQ) protocols (instantaneous changes of the Hamiltonian parameters) in many-body systems within their quantum critical regime and in contact with (homogeneously coupled) thermal baths. We consider two classes of QQ protocols. In one of them, the thermal bath is used to prepare the initial finite-temperature Gibbs state; then, after quenching, the thermal bath is removed and the dynamics of the system is unitary. We also address a more complex QQ protocol where the thermal bath is not removed after quenching, thus the quantum evolution is also driven by the interaction with the bath, which may be described by appropriate master equations for the density matrix of the system, where a further relevant time scale, or inverse decay rate, characterizes the system-bath coupling. Under these QQ protocols, the critical system develops out-of-equilibrium scaling behaviors, which extend those for isolated critical systems, by introducing further scaling variables proportional to the temperature of the thermal bath and the decay rate of the system-bath interactions. These out-of-equilibrium scaling behaviors are checked by analyzing QQ protocols within fermionic Kitaev wires, or equivalently quantum Ising chains, supplemented with a particular modelization of thermal bath that guarantees the asymptotic thermalization within the Lindblad master equation for the dynamics of open systems.

DOI
10.1103/physrevb.108.035128

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Thermalization and Out-of-Equilibrium Dynamics in Open Quantum Many-Body Systems

Michael Buchhold

Thermalization, the evolution of an interacting many-body system towards a thermal Gibbs ensemble after initialization in an arbitrary non-equilibrium state, is currently a phenomenon of great interest, both in theory and experiment. As the time evolution of a quantum system is unitary, the proposed mechanism of thermalization in quantum many-body systems corresponds to the so-called eigenstate thermalization hypothesis (ETH) and the typicality of eigenstates. Although this formally solves the contradiction of thermalizing but unitary dynamics in a closed quantum many-body system, it does neither make any statement on the dynamical process of thermalization itself nor in which way the coupling of the system to an environment can hinder or modify the relaxation dynamics. 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For frequencies below the photon loss rate, the dissipation takes over and the system shows the universal behavior of a dissipative spin glass, with a characteristic spectral density $\\mathcal{A}(\\omega)\\sim\\sqrt{\\omega}$. On the other hand, for frequencies above the loss rate, the system retains the universal behavior of a zero temperature, quantum spin glass. Remarkably, at the glass transition, the two subsystems of spins and photons thermalize to a joint effective temperature, even in the presence of photon loss. This thermalization is a consequence of the strong spin-photon interactions, which favor detailed balance in the system and detain photons from escaping the cavity. In the thermalized system, the features of the spin glass are mirrored onto the photon degrees of freedom, leading to an emergent photon glass phase. Exploiting the inherent photon loss of the cavity, we make predictions of possible measurements on the escaping photons, which contain detailed information of the state inside the cavity and allow for a precise, non-destructive measurement of the glass state. As a further set of non-equilibrium systems, we consider one-dimensional quantum fluids driven out of equilibrium, whose universal low energy theory is formed by the so-called Luttinger Liquid description, which, due to its large degree of universality, is of intense theoretical and experimental interest. A set of recent experiments in research groups in Vienna, Innsbruck and Munich have probed the non-equilibrium time-evolution of one-dimensional quantum fluids for different experimental realizations and are pushing into a time regime, where thermalization is expected. From a theoretical point of view, one-dimensional quantum fluids are particular interesting, as Luttinger Liquids are integrable and therefore, due to an infinite number of constants of motion, do not thermalize. The leading order correction to the quadratic theory is irrelevant in the sense of the renormalization group and does therefore not modify static correlation functions, however, it breaks integrability and will therefore, even if irrelevant, induce a completely different non-equilibrium dynamics as the quadratic Luttinger theory alone. In this thesis, we derive for the first time a kinetic equation for interacting Luttinger Liquids, which describes the time evolution of the excitation densities for arbitrary initial states. The resonant character of the interaction makes a straightforward derivation of the kinetic equation, using Fermi\'s golden rule, impossible and we have to develop non-perturbative techniques in the Keldysh framework. We derive a closed expression for the time evolution of the excitation densities in terms of self-energies and vertex corrections. Close to equilibrium, the kinetic equation describes the exponential decay of excitations, with a decay rate $\\sigma^R=\\mbox{Im}\\Sigma^R$, determined by the self-energy at equilibrium. However, for long times $\\tau$, it also reveals the presence of dynamical slow modes, which are the consequence of exactly energy conserving dynamics and lead to an algebraic decay $\\sim\\tau^{-\\eta\\sub{D}}$ with $\\eta_D=0.58$. The presence of these dynamical slow modes is not contained in the equilibrium Matsubara formalism, while they emerge naturally in the non-equilibrium formalism developed in this thesis. In order to initialize a one-dimensional quantum fluid out of equilibrium, we consider an interaction quench in a model of interacting, dispersive fermions in Chap.~\\ref{sec:Quench}. In this scenario, the fermionic interaction is suddenly changed at time $t=0$, such that for $t>0$ the system is not in an eigenstate and therefore undergoes a non-trivial time evolution. For the quadratic theory, the stationary state in the limit $t\\rightarrow\\infty$ is a non-thermal, or prethermal, state, described by a generalized Gibbs ensemble (GGE). The GGE takes into account for the conservation of all integrals of motion, formed by the eigenmodes of the Hamiltonian. On the other hand, in the presence of non-linearities, the final state for $t\\rightarrow\\infty$ is a thermal state with a finite temperature $T>0$. . The spatio-temporal, dynamical thermalization process can be decomposed into three regimes: A prequench regime on the largest distances, which is determined by the initial state, a prethermal plateau for intermediate distances, which is determined by the metastable fixed point of the quadratic theory and a thermal region on the shortest distances. The latter spreads sub-ballistically $\\sim t^{\\alpha}$ in space with $0<\\alpha<1$ depending on the quench. Until complete thermalization (i.e. for times $t<\\infty$), the thermal region contains more energy than the prethermal and prequench region, which is expressed in a larger temperature $T_{t}>T_{\\infty}$, decreasing towards its final value $T_{\\infty}$. As the system has achieved local detailed balance in the thermalized region, energy transport to the non-thermal region can only be performed by the macroscopic dynamical slow modes and the decay of the temperature $T_{t}-T_{\\infty}\\sim t^{-\\eta\\sub{D}}$ again witnesses the presence of these slow modes. The very slow spreading of thermalization is consistent with recent experiments performed in Vienna, which observe a metastable, prethermal state after a quench and only observe the onset of thermalization on much larger time scales. As an immediate indication of thermalization, we determine the time evolution of the fermionic momentum distribution after a quench from non-interacting to interacting fermions. For this quench scenario, the step in the Fermi distribution at the Fermi momentum $k\\sub{F}$ decays to zero algebraically in the absence of a non-linearity but as a stretched exponential (the exponent being proportional to the non-linearity) in the presence of a finite non-linearity. This can serve as a proof for the presence or absence of the non-linearity even on time-scales for which thermalization can not yet be observed. Finally, we consider a bosonic quantum fluid, which is driven away from equilibrium by permanent heating. The origin of the heating is atomic spontaneous emission of laser photons, which are used to create a coherent lattice potential in optical lattice experiments. This process preserves the system\'s $U(1)$-invariance, i.e. conserves the global particle number, and the corresponding long-wavelength description is a heated, interacting Luttinger Liquid, for which phonon modes are continuously populated with a momentum dependent rate $\\partial_tn_q\\sim\\gamma |q|$. In the dynamics, we identify a quasi-thermal regime for large momenta, featuring an increasing time-dependent effective temperature. In this regime, due to fast phonon-phonon scattering, detailed balance has been achieved and is expressed by a time-local, increasing temperature. The thermal region emerges locally and spreads in space sub-ballistically according to $x_t\\sim t^{4/5}$. For larger distances, the system is described by an non-equilibrium phonon distribution $n_q\\sim |q|$, which leads to a new, non-equilibrium behavior of large distance observables. For instance, the phonon decay rate scales universally as $\\gamma_q\\sim |q|^{5/3}$, with a new non-equilibrium exponent $\\eta=5/3$, which differs from equilibrium. This new, universal behavior is guaranteed by the $U(1)$ invariant dynamics of the system and is insensitive to further subleading perturbations. The non-equilibrium long-distance behavior can be determined experimentally by measuring the static and dynamic structure factor, both of which clearly indicate the exponents for phonon decay, $\\eta=5/3$ and for the spreading of thermalization $\\eta_T=4/5$. Remarkably, even in the presence of this strong external drive, the interactions and their aim to achieve detailed balance are strong enough to establish a locally emerging and spatially spreading thermal region. The physical setups in this thesis do not only reveal interesting and new dynamical features in the out-of-equilibrium time evolution of interacting systems, but they also strongly underline the high degree of universality of thermalization for the classes of models studied here. May it be a system of coupled spins and photons, where the photons are pulled away from a thermal state by Markovian photon d

•Jun 29, 2015•1 citation
We address the out-of-equilibrium dynamics arising from quantum-quench (QQ) protocols (instantaneous changes of the Hamiltonian parameters) in many-body systems within their quantum critical regime and in contact with (homogeneously coupled) thermal baths. We consider two classes of QQ protocols. In one of them, the thermal bath is used to prepare the initial finite-temperature Gibbs state; then, after quenching, the thermal bath is removed and the dynamics of the system is unitary. We also address a more complex QQ protocol where the thermal bath is not removed after quenching, thus the quantum evolution is also driven by the interaction with the bath, which may be described by appropriate master equations for the density matrix of the system, where a further relevant time scale, or inverse decay rate, characterizes the system-bath coupling. Under these QQ protocols, the critical system develops out-of-equilibrium scaling behaviors, which extend those for isolated critical systems, by introducing further scaling variables proportional to the temperature of the thermal bath and the decay rate of the system-bath interactions. These out-of-equilibrium scaling behaviors are checked by analyzing QQ protocols within fermionic Kitaev wires, or equivalently quantum Ising chains, supplemented with a particular modelization of thermal bath that guarantees the asymptotic thermalization within the Lindblad master equation for the dynamics of open systems.
We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models we consider fermionic wires subject to dissipative interactions at the boundaries, associated with pumping or loss of particles. They are induced by couplings with a Markovian baths, so that the evolution of the system density matrix can be described by a Lindblad master equation. We study the quantum evolution arising from variations of the Hamiltonian and dissipation parameters, starting at t=0t=0t=0 from the ground state of the Hamiltonian at, or close to, the critical point. Two different dynamic regimes emerge: (i) an early-time regime for times $t\ensuremath{\sim}L$, where the competition between coherent and incoherent drivings develops a dynamic finite-size scaling, obtained by extending the scaling framework describing the coherent critical dynamics of the closed system, to allow for the boundary dissipation; and (ii) a large-time regime for $t\ensuremath{\sim}{L}^{3}$ whose dynamic scaling describes the late quantum evolution leading to the $t\ensuremath{\rightarrow}\ensuremath{\infty}$ stationary states.
We investigate the quantum dynamics generated by quantum quenches (QQs) of the Hamiltonian parameters in many-body systems, focusing on protocols that cross first-order and continuous quantum transitions, both in finite-size systems and in the thermodynamic limit. As a paradigmatic example, we consider the quantum Ising chain in the presence of homogeneous transverse (ggg) and longitudinal (hhh) magnetic fields. This model exhibits a continuous quantum transition (CQT) at g=gcg=g_cg=gc​ and h=0h=0h=0, and first-order quantum transitions (FOQTs) driven by hhh along the line h=0h=0h=0 (g<gcg<g_cg<gc​). In the integrable limit h=0h=0h=0, the system can be mapped onto a quadratic fermionic theory; however, any nonvanishing longitudinal field breaks integrability and the spectrum of the resulting Hamiltonian is generally expected to enter a chaotic regime. We analyze QQs in which the longitudinal field is suddenly changed from a negative value hi<0h_i < 0hi​<0 to a positive value hf>0h_f>0hf​>0. We focus on values of hfh_fhf​ such that the spectrum of the post-QQ Hamiltonian H(g,hf)H(g,h_f)H(g,hf​) lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of ggg, finding qualitatively distinct behaviors for g>gcg > g_cg>gc​ (where the chain is in the disordered phase), for g=gcg = g_cg=gc​ (QQ across the CQT), and for g<gcg<g_cg<gc​ (QQ across the FOQT line).
We address the out-of-equilibrium dynamics of many-body systems subject to time-dependent round-trip protocols across quantum and classical (thermal) phase transitions. They are realized by slowly changing one relevant parameter www across its critical point wc=0{w}_{c}=0wc​=0, linearly in time with a large timescale ts{t}_{s}ts​, from wi<0{w}_{i}<0wi​<0 to wf>0{w}_{f}>0wf​>0 and then back to wi<0{w}_{i}<0wi​<0, thus entailing multiple passages through the critical point. Analogously to the one-way Kibble-Zurek protocols across a critical point, round-trip protocols develop dynamic scaling behaviors at both classical and quantum transitions put forward within renormalization-group frameworks. The scaling scenario is analyzed within some paradigmatic models undergoing quantum and classical transitions belonging to the two-dimensional Ising universality class, such as one-dimensional quantum Ising models and fermionic wires, and two-dimensional classical Ising models (supplemented with a purely relaxational dynamics). While the dynamic scaling frameworks are similar for classical and quantum systems, substantial differences emerge due to the different nature of their dynamics, which is purely relaxational for classical systems (implying thermalization in the large-time limit at fixed model parameters), and unitary in the case of quantum systems. In particular, when the critical point separates two gapped (short-ranged) phases and the extreme value wf>0{w}_{f}>0wf​>0 is kept fixed in the large-ts{t}_{s}ts​ limit of the round-trip protocol, we observe hysteresislike scenarios in classical systems, while quantum systems do not apparently develop a sufficiently robust scaling limit along the return way, due to the presence of rapidly oscillating relative phases among the relevant quantum states.
We study the scaling behavior of the relaxation dynamics to thermal equilibrium when a quantum system is near the quantum critical point. In particular, we investigate systems whose relaxation dynamics is described by a Lindblad master equation. We find that the universal scaling behavior not only appears in the equilibrium stage at the long-time limit but also manifests in the nonequilibrium relaxation process. While the critical behavior is dictated by the low-lying energy levels of the Hamiltonian, the dissipative part in the Lindblad equation also plays important roles in two aspects: First, the dissipative part makes the high-energy levels decay fast, after which the universal behavior controlled by the low-lying modes emerges. Second, the dissipation rate gives rise to a time scale that affects the scaling behavior. We confirm our theory by solving the Lindblad equation for the one-dimensional transverse-field Ising model.
We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter ggg driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of ggg around the critical value gc{g}_{c}gc​, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of ggg. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest-neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular, the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.
Thermalization, the evolution of an interacting many-body system towards a thermal Gibbs ensemble after initialization in an arbitrary non-equilibrium state, is currently a phenomenon of great interest, both in theory and experiment. As the time evolution of a quantum system is unitary, the proposed mechanism of thermalization in quantum many-body systems corresponds to the so-called eigenstate thermalization hypothesis (ETH) and the typicality of eigenstates. Although this formally solves the contradiction of thermalizing but unitary dynamics in a closed quantum many-body system, it does neither make any statement on the dynamical process of thermalization itself nor in which way the coupling of the system to an environment can hinder or modify the relaxation dynamics. In this thesis, we address both the question whether or not a quantum system driven away from equilibrium is able to relax to a thermal state, which fulfills detailed balance, and if one can identify universal behavior in the non-equilibrium relaxation dynamics. As a first realization of driven quantum systems out of equilibrium, we investigate a system of Ising spins, interacting with the quantized radiation field in an optical cavity. For multiple cavity modes, this system forms a highly entangled and frustrated state with infinite correlation times, known as a quantum spin glass. In the presence of drive and dissipation, introduced by coupling the intra-cavity radiation field to the photon vacuum outside the cavity via lossy mirrors, the quantum glass state is modified in a universal manner. For frequencies below the photon loss rate, the dissipation takes over and the system shows the universal behavior of a dissipative spin glass, with a characteristic spectral density mathcalA(omega)simsqrtomega\\mathcal{A}(\\omega)\\sim\\sqrt{\\omega}mathcalA(omega)simsqrtomega. On the other hand, for frequencies above the loss rate, the system retains the universal behavior of a zero temperature, quantum spin glass. Remarkably, at the glass transition, the two subsystems of spins and photons thermalize to a joint effective temperature, even in the presence of photon loss. This thermalization is a consequence of the strong spin-photon interactions, which favor detailed balance in the system and detain photons from escaping the cavity. In the thermalized system, the features of the spin glass are mirrored onto the photon degrees of freedom, leading to an emergent photon glass phase. Exploiting the inherent photon loss of the cavity, we make predictions of possible measurements on the escaping photons, which contain detailed information of the state inside the cavity and allow for a precise, non-destructive measurement of the glass state. As a further set of non-equilibrium systems, we consider one-dimensional quantum fluids driven out of equilibrium, whose universal low energy theory is formed by the so-called Luttinger Liquid description, which, due to its large degree of universality, is of intense theoretical and experimental interest. A set of recent experiments in research groups in Vienna, Innsbruck and Munich have probed the non-equilibrium time-evolution of one-dimensional quantum fluids for different experimental realizations and are pushing into a time regime, where thermalization is expected. From a theoretical point of view, one-dimensional quantum fluids are particular interesting, as Luttinger Liquids are integrable and therefore, due to an infinite number of constants of motion, do not thermalize. The leading order correction to the quadratic theory is irrelevant in the sense of the renormalization group and does therefore not modify static correlation functions, however, it breaks integrability and will therefore, even if irrelevant, induce a completely different non-equilibrium dynamics as the quadratic Luttinger theory alone. In this thesis, we derive for the first time a kinetic equation for interacting Luttinger Liquids, which describes the time evolution of the excitation densities for arbitrary initial states. The resonant character of the interaction makes a straightforward derivation of the kinetic equation, using Fermi\'s golden rule, impossible and we have to develop non-perturbative techniques in the Keldysh framework. We derive a closed expression for the time evolution of the excitation densities in terms of self-energies and vertex corrections. Close to equilibrium, the kinetic equation describes the exponential decay of excitations, with a decay rate sigmaR=mboxImSigmaR\\sigma^R=\\mbox{Im}\\Sigma^RsigmaR=mboxImSigmaR, determined by the self-energy at equilibrium. However, for long times tau\\tautau, it also reveals the presence of dynamical slow modes, which are the consequence of exactly energy conserving dynamics and lead to an algebraic decay simtau−etasubD\\sim\\tau^{-\\eta\\sub{D}}simtau−etasubD with etaD=0.58\\eta_D=0.58etaD​=0.58. The presence of these dynamical slow modes is not contained in the equilibrium Matsubara formalism, while they emerge naturally in the non-equilibrium formalism developed in this thesis. In order to initialize a one-dimensional quantum fluid out of equilibrium, we consider an interaction quench in a model of interacting, dispersive fermions in Chap.~\\ref{sec:Quench}. In this scenario, the fermionic interaction is suddenly changed at time t=0t=0t=0, such that for t>0t>0t>0 the system is not in an eigenstate and therefore undergoes a non-trivial time evolution. For the quadratic theory, the stationary state in the limit trightarrowinftyt\\rightarrow\\inftytrightarrowinfty is a non-thermal, or prethermal, state, described by a generalized Gibbs ensemble (GGE). The GGE takes into account for the conservation of all integrals of motion, formed by the eigenmodes of the Hamiltonian. On the other hand, in the presence of non-linearities, the final state for trightarrowinftyt\\rightarrow\\inftytrightarrowinfty is a thermal state with a finite temperature T>0T>0T>0. . The spatio-temporal, dynamical thermalization process can be decomposed into three regimes: A prequench regime on the largest distances, which is determined by the initial state, a prethermal plateau for intermediate distances, which is determined by the metastable fixed point of the quadratic theory and a thermal region on the shortest distances. The latter spreads sub-ballistically simtalpha\\sim t^{\\alpha}simtalpha in space with 0<alpha<10<\\alpha<10<alpha<1 depending on the quench. Until complete thermalization (i.e. for times t<inftyt<\\inftyt<infty), the thermal region contains more energy than the prethermal and prequench region, which is expressed in a larger temperature Tt>TinftyT_{t}>T_{\\infty}Tt​>Tinfty​, decreasing towards its final value TinftyT_{\\infty}Tinfty​. As the system has achieved local detailed balance in the thermalized region, energy transport to the non-thermal region can only be performed by the macroscopic dynamical slow modes and the decay of the temperature Tt−Tinftysimt−etasubDT_{t}-T_{\\infty}\\sim t^{-\\eta\\sub{D}}Tt​−Tinfty​simt−etasubD again witnesses the presence of these slow modes. The very slow spreading of thermalization is consistent with recent experiments performed in Vienna, which observe a metastable, prethermal state after a quench and only observe the onset of thermalization on much larger time scales. As an immediate indication of thermalization, we determine the time evolution of the fermionic momentum distribution after a quench from non-interacting to interacting fermions. For this quench scenario, the step in the Fermi distribution at the Fermi momentum ksubFk\\sub{F}ksubF decays to zero algebraically in the absence of a non-linearity but as a stretched exponential (the exponent being proportional to the non-linearity) in the presence of a finite non-linearity. This can serve as a proof for the presence or absence of the non-linearity even on time-scales for which thermalization can not yet be observed. Finally, we consider a bosonic quantum fluid, which is driven away from equilibrium by permanent heating. The origin of the heating is atomic spontaneous emission of laser photons, which are used to create a coherent lattice potential in optical lattice experiments. This process preserves the system\'s U(1)U(1)U(1)-invariance, i.e. conserves the global particle number, and the corresponding long-wavelength description is a heated, interacting Luttinger Liquid, for which phonon modes are continuously populated with a momentum dependent rate partialtnqsimgamma∣q∣\\partial_tn_q\\sim\\gamma |q|partialt​nq​simgamma∣q∣. In the dynamics, we identify a quasi-thermal regime for large momenta, featuring an increasing time-dependent effective temperature. In this regime, due to fast phonon-phonon scattering, detailed balance has been achieved and is expressed by a time-local, increasing temperature. The thermal region emerges locally and spreads in space sub-ballistically according to xtsimt4/5x_t\\sim t^{4/5}xt​simt4/5. For larger distances, the system is described by an non-equilibrium phonon distribution nqsim∣q∣n_q\\sim |q|nq​sim∣q∣, which leads to a new, non-equilibrium behavior of large distance observables. For instance, the phonon decay rate scales universally as gammaqsim∣q∣5/3\\gamma_q\\sim |q|^{5/3}gammaq​sim∣q∣5/3, with a new non-equilibrium exponent eta=5/3\\eta=5/3eta=5/3, which differs from equilibrium. This new, universal behavior is guaranteed by the U(1)U(1)U(1) invariant dynamics of the system and is insensitive to further subleading perturbations. The non-equilibrium long-distance behavior can be determined experimentally by measuring the static and dynamic structure factor, both of which clearly indicate the exponents for phonon decay, eta=5/3\\eta=5/3eta=5/3 and for the spreading of thermalization etaT=4/5\\eta_T=4/5etaT​=4/5. Remarkably, even in the presence of this strong external drive, the interactions and their aim to achieve detailed balance are strong enough to establish a locally emerging and spatially spreading thermal region. The physical setups in this thesis do not only reveal interesting and new dynamical features in the out-of-equilibrium time evolution of interacting systems, but they also strongly underline the high degree of universality of thermalization for the classes of models studied here. May it be a system of coupled spins and photons, where the photons are pulled away from a thermal state by Markovian photon d