Quantum many-body systems out of equilibrium: Relaxation, thermalization, and ergodicity breaking

Lately a concept called "recursion method" (also Lanczos method, closely related to the Mori formalism) has received some attention in the context of equilibration in closed quantum systems. This scheme, augmented with the "operator growth hypothesis", allows to obtain information on the actual equilibration dynamics in concrete condensed matter-type quantum systems in the thermodynamic limit. This primarily refers to temporal autocorrelation functions of few body operators at infinite temperature. For example equilibration times or approximations to the full correlation function may be inferred. However the analysis of more involved quantities and/or finite temperatures or chemical potentials appears also feasible. Some introduction will be given, but the focus is on our own (partially published) recent work.

The Sachdev-Ye-Kitaev (SYK) model, has emerged as a powerful tool for exploring the quantum nature of black holes, particularly their residual entropy at zero temperature. In this work, we investigate the role of long-range interactions in a chain of SYK dots with power-law decaying couplings and demonstrate how these interactions can lead to finite residual entropy in the strong non-local case. Indeed, as a function of the interaction range, the black-hole phase, found in the isolated SYK, melts into a long-range Fermi-liquid phase in the weak long-range regime and finally reaches the non Fermi-liquid phase in the purely local case. Our results pave the way to the understanding of the role of the interaction range in black hole thermodynamics and quantum information.

The act of a quantum measurement seems to evade the accessibility of the Schrödinger equation [1]. In this work, we explore whether dynamics resembling quantum measurement can be achieved in a many-body system undergoing unitary time evolution with the Schrödinger equation. For the numerical simulation, we consider an experimentally-realizable, Fermi-Hubbard-inspired model [2] containing a fixed number of environmental particles interacting with a single impurity [3]. A key advantage of this system lies in the high tunability of its parameters, both experimentally and in simulations. To simulate the process of a measurement within the many-body Schrödinger equation, the environmental particles are assumed to act as both a measuring apparatus on the impurity and as the environment in a more conventional sense. We determine the exact quantum mechanical time evolution by diagonalization of mesoscopically sized systems. By tuning the system's parameters, we can investigate two different regimes, being the locally equilibrating and non-equilibrating dynamics. For both of these, we observe clear conditioning of the environment on the impurity's position, and hence, information encoding as required for a measurement. These encoding degrees of freedom are the density fluctuation correlations and the two-body-cumulant. However, contrary to the framework of Quantum Darwinism [4], this encoding does not exhibit any redundancy. This ongoing work provides a case study in analyzing the quantum-to-classical transition within a physically realizable many-body isolated-system model. [1] E. Schwarzhans et al., Phys. Rev. Research 7, 043279, 2025 [2] I. Bloch. Nature physics, 1(1):23–30, 2005 [3] M. Kourehpaz et al., Entropy, 24(12):1740, 2022 [4] W. Zurek. Nature physics, 5(3):181–188, 2009

Classical many-body systems that display slow collective relaxation (the typical example being glass formers) do so due to effective constraints in their dynamics, the simplest manifestation being kinetically constrained models. This approach highlights the relevance of rare events and of the properties of stochastic trajectories. I will review this perspective on slow dynamics, and describe what can be learnt by studying trajectory ensembles using the framework of large deviations. I will also discuss how this way of thinking can extend to quantum systems, highlighting the crossover of ideas and methods between classical and quantum non-equilibrium.

The Mpemba effect, where a system initially farther from equilibrium relaxes faster than one closer to equilibrium, has been extensively studied in classical systems and recently explored in quantum settings. While previous studies of the quantum Mpemba effect (QME) have largely focused on isolated systems with global symmetries, we argue that the QME is ubiquitous in generic, non-integrable many-body systems lacking such symmetries, including U(1) charge conservation, spatial symmetries, and even energy conservation. Using paradigmatic models such as the quantum Ising model with transverse and longitudinal fields, we show that the QME can be understood through the energy density of initial states and their inverse participation ratio in the energy eigenbasis. Our findings provide a unified framework for the QME, linking it with classical thermal relaxation and phenomena such as prethermalization and weak ergodicity breaking.

The present view of modern physics on non-equilibrium dynamics is that generic quantum systems equilibrate or thermalize under rather general conditions, even closed systems under unitary time evolution. The investigation of exceptions thus not only appears attractive, in view of quantum computing where thermalization is a threat it also seems to be necessary. Here, we present aspects of the one-magnon dynamics on the sawtooth chain as well as on the kagome lattice antiferromagnet as an example of a non-equilibrating dynamics due to flat bands. For both systems, localized eigenstates also called localized magnons lead to disorder-free localization and prevent the system from equilibration. This behavior is tunable by modifying the exchange interactions.

I will report on ongoing work towards a proof of many body localization in strongly disordered quantum chains. At the time of writing this abstract, we can prove absence of diffusion, but not yet full localization.

Since von Neumann’s pioneering work, numerous theoretical attempts have been made to understand why laws of thermodynamics emerge from quantum mechanics. Recent advances in measurement and control of isolated quantum many-body systems have enabled experimental tests of such fundamental questions. Inspired by observations of thermalization in ultracold atomic gases and trapped ions, recent studies have focused on identifying the conditions under which isolated quantum systems thermalize, particularly in relation to the Eigenstate Thermalization Hypothesis (ETH). Against this backdrop, we address yet another central issue in thermodynamics: How much work can be extracted from a quantum many-body system? Conventional studies of work extraction from quantum systems [1–3] often assume that arbitrary unitary operations are available for work extraction. This assumption, however, is unrealistic for many-body systems, since such operations in many-body systems generally involve highly nonlocal and $O(N)$-body interactions. Moreover, these conventional results imply that no pure state at finite temperature satisfies the second law of thermodynamics, in apparent contradiction with the ETH which dictates that every energy eigenstate is thermal. In this talk, we resolve this conundrum on the basis of our recently derived upper bound [4] on work extraction from quantum many-body systems. We show that the maximum extractable work, namely the ergotropy, is constrained by the local athermality of the initial state and the local entropy decrease induced by quantum operations. As a consequence, under short-time operations generated by short-range interactions, no work can be extracted from states that are locally thermal. This establishes a special version of the second law of thermodynamics, namely Planck’s principle, for isolated quantum many-body systems. On the other hand, by enlarging the allowed class of operations, work can be extracted even from states that appear thermal. This indicates that thermal equilibrium is not an absolute notion, but should be defined hierarchically according to the class of available operations. We further show that the additional work enabled by two such extensions—long-range interactions and long-time operations—is bounded by differences of entropies that characterize the corresponding levels of this thermodynamic hierarchy [5]. Our findings offer a unified perspective on the emergence of the second law in isolated quantum many-body systems, revealing thermal equilibrium as a hierarchy shaped by the operations one can perform. [1] W. Pusz and S. L. Woronowicz, Passive states and KMS states for general quantum systems, Comm. Math. Phys. 58, 273 (1978). [2] A. Lenard, Thermodynamical proof of the Gibbs formula for elementary quantum systems, J. Stat. Phys. 19, 575 (1978). [3] A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhys. Lett. 67, 565 (2004). [4] A.Hokkyo and M.Ueda, Universal Upper Bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis, Phys. Rev. Lett. 134, 010406 (2025). [5] A.Hokkyo and M.Ueda, in preparation.

We present a single-quench protocol that generates unitary $k$-designs with minimal control. A system first evolves under a random Hamiltonian $H_1$; at a switch time $t_s \geq t_{\mathrm{Th}}$ (the Thouless time), it is quenched to an independently drawn $H_2$ from the same ensemble and then evolves under $H_2$. This single quench breaks residual spectral correlations that prevent strictly time-independent chaotic dynamics from forming higher-order designs. The resulting ensemble approaches a unitary $k$-design using only a single control operation -- far simpler than Brownian schemes with continuously randomized couplings or protocols that apply random quenches at short time intervals. Beyond offering a direct route to Haar-like randomness, the protocol yields an operational, measurement-friendly definition of $t_{\mathrm{Th}}$ and provides a quantitative diagnostic of chaoticity. It further enables symmetry-resolved and open-system extensions, circuit-level single-quench analogs, and immediate applications to randomized measurements, benchmarking, and tomography.

Recent advances in quantum simulations have opened access to the real-time dynamics of lattice gauge theories, providing a new setting to explore how quantum criticality influences thermalization and ergodicity far from equilibrium. Using QuEra's programmable Rydberg atom array, we map out the dynamical phase diagram of the spin-1/2 U(1) quantum link model in one spatial dimension by quenching the fermion mass. We reveal a tunable regime of ergodicity breaking due to quantum many-body scars, manifested as long-lived coherent oscillations that persist across a much broader range of parameters than previously observed, including at the equilibrium phase transition point. We further analyze the electron-positron pairs generated during state preparation via the Kibble-Zurek mechanism, which strongly affect the post-quench dynamics. Our results provide new insights into nonthermal dynamics in lattice gauge theories and establish Rydberg atom arrays as a powerful platform for probing the interplay between ergodicity breaking and quantum criticality.

In the past twenty years, novel nanoscale experimental techniques and theoretical advances grounded in quantum information theory have led to a surge of interest in the quantum and dynamical foundations of thermodynamics and statistical mechanics. Most studies focus on understanding of the mechanisms and time-scales that lead a density matrix to equilibrate and thermalize. Motivated by foundational studies in Geometric Quantum Mechanics and technological needs to characterize quantum ensembles, I have studied a notion of dynamical equilibration and thermalization that goes beyond this, addressing the emergence of equilibrium and non-equilibrium stationary ensembles behind the density matrix. In this talk, I will present a theory to study the dynamics of any quantum ensemble, based on a kinetic theory of quantum states on complex projective spaces. Numerical experiments supporting the theory will illustrate the phenomena discussed.

We consider integrability and non-integrability of quantum spin chains. In this talk, the word integrable/non-integrable stands for the presence/absence of nontrivial local conserved quantities. In the first part, we investigate a striking dichotomy. All quantum spin chains studied so far fall into two extremes: either the system possesses k-local conserved quantities for all k (complete integrability), or it possesses none at all (non-integrability). However, this dichotomy has remained entirely unexplained from a mathematical point of view. In this work, we rigorously prove the dichotomy for several classes of quantum spin chains. For nearest-neighbor, inversion-symmetric spin-1/2 chains, we prove this dichotomy by giving a complete classification into completely integrable and non-integrable models. In particular, we show that all models other than the known integrable models are non-integrable. We also establish the dichotomy for SU(2)-symmetric spin-S chains with arbitrary S. In this setting, we further show that the two cases are distinguished by an extremely simple computable quantity D^3: the model is completely integrable if (D^3=0), and non-integrable otherwise. In the second part, we shed new light on quantum integrability. In the standard approach based on the Yang--Baxter equation, one starts from an R-matrix, and the Hamiltonian is obtained from logarithmic derivatives of the transfer matrix. Therefore, to solve a given Hamiltonian, one has to find a suitable R-matrix by a kind of craftsmanship, and thus it is far from obvious whether such an R-matrix exists. In contrast, we prove that Yang-Baxter solvability can be determined simply by examining a nested commutator of the local Hamiltonian. This criterion, which is equivalent to the Reshetikhin condition, is also the lowest-order nontrivial consequence of the Yang-Baxter equation. Our result therefore reveals a surprising structure: the lowest-order relation already contains the full information of the Yang-Baxter equation.

I will present some recent results on constrained many-body models, focussing on East-type and PXP-type models.

Proving thermalization from the unitary evolution of a closed quantum system is one of the oldest questions in quantum statistical mechanics that remains only partially resolved today [1]. Several lines of research have led to different formulations of the eigenstate thermalization hypothesis, each of which implies thermalization under certain assumptions on the initial state. These assumptions, however, depend sensitively on the precise formulation of the hypothesis. In the core part of this talk [2], we focus on the important case of low-entanglement initial states, which are operationally accessible in many natural physical settings, including experimental studies of thermalization and quantum simulation. We prove thermalization for such states under precise conditions with clear operational significance. More specifically, motivated by the unavoidable finite resolution of physical measurements, we introduce a random energy smoothing of local Hamiltonians that leads to local thermalization whenever the initial state has low entanglement. We then show that this transformation affects neither the local Gibbs state nor, under generic smoothness assumptions on the spectrum, the short-time dynamics. We complement these results by presenting new classical simulation methods for out-of-equilibrium dynamics based on flow techniques [3]. We will also see that random circuits without quantum error correction generate only logarithmically shallow circuit complexity [4]. Finally, we demonstrate that there exist quantum non-equilibrium systems exhibiting no operational signatures of quantum chaos, yet no computationally bounded observer can distinguish them from the Gaussian unitary ensemble, despite the latter displaying the standard hallmarks of quantum chaos [5]. This challenges what can ultimately be learned about out-of-equilibrium physics from experimental data [6]. [1] Nature Physics 11, 124 (2015). [2] Communications Physics 8, 301 (2025). [3] Communications in Mathematical Physics 397, 995 (2023). [4] Nature Physics 22, 751 (2026). [5] arXiv:2410.18196 (2024). [6] Nature Physics 21, 1847 (2025).

In this talk, I present a connection between quantum dynamics in an isolated system and that in an open system. Although the dynamics is unitary in isolated systems, we often observe universal exponential decays of physical quantities in a certain time window. In classical chaos, such exponential decays are characterized by poles of the resolvent of the time evolution operator (or the Hamiltonian) in complex plane, which are known as Ruelle-Pollicott resonances. I will tell you that there is a quantum analogue of the concept of Ruelle-Pollicott resonances in quantum spin systems which are far from the classical limit, and that quantum Ruelle-Pollicott resonances are extracted by investigating weakly dissipative quantum dynamics that is described by the Lindblad equation. I also discuss its implications to the theory of open quantum systems.

Simulation of quantum dynamics is a major potential application of quantum computers. Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In order to characterize the underlying system at such time scales we introduce a novel technique, correlation operator spectroscopy, that relies on time reversed evolution. We demonstrate theoretically that this protocol relying on repeated time-reversal restore sensitivities of quantum observables. Experimentally, using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators. In contrast to dynamics without time reversal, OTOCs are observed to remain sensitive to the underlying dynamics at long time scales.

For a class of translation-invariant free-fermion systems (including those with uniform nearest neighbor hopping) on a $d$-dimensional $L \times \cdots \times L$ hypercubic lattice, we prove that, starting from an arbitrary pure initial state, the system equilibrates with respect to the coarse-grained density within a timescale of order $L$. This scaling is optimal, since there exist initial states whose equilibration requires time of order $L$. Our result establishes $O(L)$ as the equilibration timescale, as is expected in normal macroscopic systems with a conserved quantity, such as total number of particles.

The eigenstate thermalization hypothesis (ETH), introduced by Deutsch and Srednicki, suggests that individual eigenstates of generic quantum many-body systems already encode thermal behavior: Expectation values of local observables agree with those predicted by statistical mechanics. In this talk, we investigate the internal structure of chaotic many-body eigenstates by expanding them in a basis of product eigenstates of two coupled subsystems. Using concepts from random matrix theory, we identify universal features in the resulting expansion coefficients of thermal eigenstates and show how these features give rise to thermal reduced density matrices for small subsystems. We support this analytical picture with numerical results for a nonintegrable spin-1/2 lattice model with local random couplings.

The interaction of nanoscale and quantum systems with their environment can be relatively strong, and alter the equilibrium state. For open quantum systems, explicit expressions of these so-called mean force (MF) equilibrium states have been missing. In this talk I will report on useful analytic expressions of these states, valid for a general quantum system in contact with a bosonic bath [1]. The results are illustrated with the well-known spin-boson model, for which we provide the first classification of coupling regimes, from weak to ultrastrong, and for both the quantum and classical setting [2]. Finally, we will look at thermalization in isolated quantum many-body systems. For the example of a double quantum dot (DQD) coupled to a fermionic chain, I will discuss differences between the thermalization concepts of open and of isolated systems [3]. By considering an initial state suitable for both settings, we will clarify how a local DQD can do both, thermalize in an open sense and not thermalize in an isolated sense, without running into any paradoxes. [1] J.D Cresser, J. Anders, Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State, Phys. Rev. Lett 127, 250601(2021). [2] F. Cerisola, M. Berritta, S. Scali, S.A.R. Horsley, J.D Cresser, J. Anders, Quantum–classical correspondence in spin–boson equilibrium states at arbitrary coupling, New J. of Phys. 26, 053032 (2024). [3] A. Purkayastha, G. Guarnieri, J. Anders, M. Merkli, On the difference between thermalization in open and isolated quantum systems: a case study, SciPost Phys. 19, 136 (2025).

In my talk I will discuss the fate of eigenstates in quantum systems in vicinity of thermal first order phase transition. The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of large systems. In my talk I will show that ETH requires generalization in the presence of thermal first-order phase transitions. I will argue that for energies in the vicinity of the thermal phase transition, eigenstate expectation values do not need to converge to the same thermal value. The system has a regime with coexistence of two classes of eigenstates corresponding to the two branches with distinct expectation values at the same energy density, and another regime with Schrodinger-cat-like eigenstates that are inter-branch superpositions; these two regimes are separated by an eigenstate phase transition. I will also demonstrate extensions of these results to more physical models, and outline how the special structure of eigenstates near first order phase transition can be probed via quench dynamics.

I will address the question of how to describe and study relaxation in unitary quantum or classical systems. While the spectrum of a unitary propagator has no direct relation to dynamic, that of the momentum-resolved truncated propagator does. The leading eigenvalue and the associated eigenvector (the so-called Ruelle-Pollicott resonance) can be used to find conserved operators, including new integrable systems, numerically efficiently study diffusion, or calculate the long timescales present under weak conservation-law breakdown. Via a many-body operator Kolmogorov cascade it also offers a quantum many-body analog of classical chaotic structures responsible for chaos in quantum lattice systems.

I will begin by reviewing a general theory of the approach to thermal equilibrium in macroscopic quantum systems based on certain versions of the eigenstate thermalization hypothesis, or ETH. This line of thought goes back to von Neumann (1929) and was developed further, among others, by Goldstein, Lebowitz, Mastrodonato, Tumulka, and Zanghi (2009), and Tasaki (2016). I will then discuss two concrete examples in which this general scenario can be justified with full mathematical rigor: the two-dimensional Ising model at low temperatures with a small Haar-random perturbation, and the S=1/2 XY chain. The former is an application of a recent general theorem by Roos, Sugimoto, Teufel, Tumulka, and Vogel, while the latter is an improvement, by the same authors and by Hara and Koike, of my earlier result. These examples are illuminating, but they are also rather special. In the first, the perturbation is a wild long-range, super-many-body random interaction; in the second, the model is simply an exactly integrable free-fermion chain. It is highly desirable to understand the full-fledged thermalization that is expected to take place in systems with non-random, short-range, non-integrable Hamiltonians. Of course, this is a formidably difficult problem for humans, at least for now. As a preliminary step toward the future study of time evolution and thermalization in non-integrable systems, I will discuss what is known for the S=1/2 XY chain with a uniform magnetic field in the X-direction. Extending Shiraishi’s breakthrough work from 2019, Yamaguchi, Chiba, and Shiraishi proved that this model has no local conserved quantities except the Hamiltonian. I will describe an ongoing project with Mahiro Futami on a quantified version of this theorem, namely, showing that any translation-invariant operator with finite support width that is orthogonal to the Hamiltonian must evolve nontrivially in time.

In this talk we will theoretically analyse the relaxation dynamics after quenches in quantum systems with competing short- and long-range interactions. We will focus on the case of bosons in lattices and discuss possible implementations in many-body cavity quantum electrodynamics platforms.

The quantum Mpemba effect is a highly counterintuitive phenomenon where a quantum system prepared in an initial state far from equilibrium relaxes to its steady state significantly faster than a state prepared comparatively closer to equilibrium. While this phenomenon has been experimentally observed under engineered dissipation, whether it occurs naturally during the thermalization of quantum systems has remained an open question. In this talk, I will present our experimental demonstration of the quantum Mpemba effect occurring naturally during thermalization of a two qubit system. By considering dipolar relaxation as the dominant decoherence process, we theoretically derive the precise conditions that trigger the Mpemba effect in nuclear spins. After experimentally preparing nuclear spin states dictated by these conditions, we successfully observe the effect as the system thermalizes without any external control. Furthermore, we experimentally verify the genuine quantum Mpemba effect during this process. Our results establish that these anomalous relaxation dynamics are natural features of quantum thermalization and can emerge without the need for bath engineering. Looking ahead, a key challenge is investigating the occurrence of this effect in many-body quantum systems, where the exponential cost of full quantum state tomography presents a primary bottleneck. I will conclude my talk by discussing our recent work on utilizing carefully chosen macroscopic observables to detect the Mpemba effect in larger systems, thereby completely bypassing the need for full state tomography. References : 1. Chatterjee Arijit, Sakil Khan, Sachin Jain, and T. S. Mahesh. "Direct observation of Quantum Mpemba Effect in nuclear spin systems without bath engineering". arXiv preprint arXiv: arXiv:2509.13451 (2025). 2. Pitambar Bagui, Chatterjee Arijit, Bijay Kumar Agarwala "Accelerated relaxation and Mpemba-like effect for operators in open quantum systems" arXiv preprint arXiv: arXiv:2510.24630 (2025). 3. Pitambar Bagui, Chatterjee Arijit, Bijay Kumar Agarwala "Detection of Mpemba effect through good Observables in open quantum systems" arXiv preprint arXiv: arXiv:2512.02709 (2025).

The second law of thermodynamics for adiabatic operations — constraints on state transitions in closed systems under external control — is one of the fundamental principles of thermodynamics. On the other hand, recent studies of thermalization have established that even pure quantum states can represent thermal equilibrium. However, pure quantum states do not satisfy the second law in that they are not passive, i.e., work can be extracted from them if arbitrary unitary operations are allowed. It therefore remains unresolved how thermal equilibrium represented by a pure quantum state can be reconciled with thermodynamics. Here, based on our key quantum-mechanical notions of thermal equilibrium and adiabatic operations, we address the emergence of the second law of thermodynamics in closed quantum many-body systems. We first introduce infinite-observable macroscopic thermal equilibrium (iMATE); a quantum state, including pure states, is said to represent iMATE if the expectation values of all additive observables, which correspond to additive quantities in thermodynamics, agree with their equilibrium values. We also introduce a macroscopic operation as unitary evolution generated by a time-dependent additive Hamiltonian, which is regarded as corresponding to adiabatic operations. Employing these concepts, we show Planck’s principle: no extensive work can be extracted from any quantum state representing iMATE through any macroscopic operations with the operation times independent of the system size. Furthermore, we introduce a quantum-mechanical form of entropy density such that it agrees with thermodynamic entropy density for any quantum state representing iMATE. We then prove the law of increasing entropy: for any initial state representing iMATE, this entropy density cannot be decreased by any macroscopic operations with the operation times independent of the system size, followed by a time-independent relaxation process. Our theory thus proves two different forms of the second law, which are quantum mechanically inequivalent to each other, and demonstrates how thermodynamics emerges from quantum mechanics by adopting macroscopically reasonable classes of observables, equilibrium states, and operations.

With the advent of quantum simulation experiments of lattice gauge theories (LGTs), an open question is the effect of non-Hermiticity on their rich physics. The well-known PXP model, a U(1) LGT with a two-level electric field in one spatial dimension, has become a paradigm of exotic physics in and out of equilibrium. Here, we introduce a non-Hermitian version in which the spin-flip rate differs between the two spin directions. While the naive expectation is that non-Hermiticity might suppress coherent phenomena such as quantum many-body scars, we find that when the facilitating direction of the spin is disfavored, the oscillations are instead \emph{enhanced}, decaying much slower than in the PXP limit. We demonstrate that this can be understood through a similarity transformation that maps our model to the standard PXP model, revealing that the oscillations are enhanced versions of the PXP scars. Our work provides an analytically tractable and conceptually simple example where non-Hermiticity enhances the stability of dynamically non-trivial coherent many-body modes.

Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, reconciling the unitary nature of quantum mechanics with the irreversible entropy growth mandated by the second law of thermodynamics. Despite its ubiquity and significance in fundamental physics, a rigorous mathematical proof for quantum thermalization has remained elusive for several decades, except in certain special cases. In this talk, I will present our recent results showing that quantum thermalization must occur in any qubit system with local interactions, given three conditions: (i) high effective temperature, (ii) translational invariance, and (iii) absence of perfect resonances in the energy spectrum. Unlike previous works, our proof does not break the locality of quantum dynamics nor relies on additional assumptions or empirical models such as the eigenstate thermalization hypothesis (ETH) or random matrix theory. Our results showcase how statistical physics can be understood as an emergent phenomenon, mathematically derived from the first principles of quantum mechanics for a broad class of systems. Nat Commun 17, 75 (2026).

Geometic Floquet theory allows us to unambiguously sort the quasienergy spectrum, and identify a candidate Floquet ground state [PRX 15, 031037]. Exact diagonalization in nonintegrable kicked chains shows that this state can exhibit a many-body average-energy gap, and is weakly entangled. We formulate a variational principle for the Floquet ground state, and use DMRG to approximately find it for system sizes of a few hundred spins. We find indications that the state resists heating and thermalization, contrary to the common expectation that it should heat up to infinite temperature. Moreover, we demonstrate that the state can exhibit both equilibrium (e.g., antiferromagnetic) and nonequilibrium (time crystalline) order, and introduce the notion of stable Floquet ground state order, protected by a finite average-energy gap. DMRG extrapolation results are consistent with a finite gap in the thermodynamic limit. Assuming the gap survives in the thermodynamic limit, we use adiabatic continuation to construct a local parent Floquet Hamiltonian with the Floquet ground state an exact scar eigenstate.

Classically, the phase space Gamma of a system with a macroscopically large number N of particles can be partitioned into subsets Gamma_nu, each comprising the phase points compatible with macro state nu; the Boltzmann entropy of nu is then S_B(nu) = k log vol Gamma_nu. Analogously in quantum mechanics, the Hilbert space H of an N-particle system can be regarded as an orthogonal sum of subspaces H_nu comprising the wave functions compatible with macro state nu, and the quantum Boltzmann entropy is S_{qB}(nu) = k log dim H_nu. Since a general wave function in H is a superposition of contributions from different H_nu, it is not obvious what could even be meant by saying that this kind of entropy increases with time. In my talk, I propose such a meaning and explore the question under which conditions this increase occurs.

We'll discuss a correspondence between temperature and integrability-breaking in classical and quantum many-body systems using geometry and adiabatic transformations. Decreasing temperature, steers chaotic Hamiltonian systems towards an integrable point despite strong integrability-breaking interactions. Subsequently, local observables exhibit slow relaxation dynamics, which violates ergodicity on the approach to this integrable point and is consistent with the well-known KAM regime. The average fidelity susceptibility of stationary states against perturbations, satisfies scaling relations at low temperatures, in close analogy with continuous phase transitions. However, we find that the dynamical exponent encompassing relaxation can be different in low-dimensional quantum and classical systems. Collectively, our results establish temperature as a tunable control parameter for chaos and puts it on equal footing with integrability-breaking perturbations.

The decoherent histories framework is an extension of Feynman's path integral designed to understand which events in an isolated quantum system (a) leave detectable records in the system state and (b) can be simulated by a classical stochastic process. I will start the talk with a review of the framework, highlighting also the connection to out-of-time-order correlators, superdensity matrices and quantum foundations. Then, I will present quantitative results about the emergence of decoherent histories from "first principles" calculations (no ensemble averages, no Markov approximations, etc.). Interestingly, the results can be cast into an Ansatz very similar to the ETH. Finally, if time permits, I will talk about the structure of decoherence from the perspective of quantum state discrimination.

When a classically chaotic system is shaken strongly, its dynamics become turbulent and more chaotic, as it keeps heating up due to the energy transfer from the drive. We showed that the same doesn’t necessarily apply to quantum systems. Strong shaking can produce new kinds of conservation laws which are approximate but stable -- a phenomenon known as dynamical freezing. The mechanism behind the phenomenon has remained elusive to straightforward applications of many-body theory and related intuitions. Our recent results from spectral function analysis are in agreement with the numerical results in some cases, while in others, like the absence of resonant heating, their failure indicates the existence of unknown pieces of the puzzle yet to be discovered.

A quantum quench often consists in the following setup: Some system is initially prepared in an equilibrium state of Hamiltonian $H_g=H-gV$, subject to a (small) parameter change at time $t=0$, and evolves in time with Hamiltonian $H$ for times $t>0$. In such a setup, [1] rigorously established that the relaxation behavior of (the expectation values of) some observable $A$ can be approximated by a series of correlations of $A$ and $V$ in the equilibrium pertaining to $H$. More precisely speaking, it was shown that the approximation is exact up to a finite error independent of the time or system size, and analytical upper bounds are available for many important cases. With this properties, said approximation forms a mighty tool for analytical studies of thermalization and its absence. Taking the paradigmatic XX spin chain model with a magnetic field as an example, it could be shown that the XX model thermalizes whenever it is subject to a homogeneous magnetic field [2]. Turning away from the homogeneous case, it was shown that even one single inhomogeneity in the magnetic field might be sufficient to prevent thermalization [3]. In my presentation, I will briefly introduce the general framework of [1], before presenting the results and implications of [2] and [3] in some detail. [1] P. Reimann and C. Eidecker-Dunkel, Onsager’s regression hypothesis adjusted to quantum systems, Phys. Rev. B 110, 014306 (2024) [2] P. Reimann and C. Eidecker-Dunkel, Thermalization in a simple spin-chain model, Phys. Rev. B 111, 054312 (2025) [3] P. Reimann and C. Eidecker-Dunkel, Absence of thermalization after a local quench and strong violation of the eigenstate thermalization hypothesis, Phys. Rev. B 113, 144304 (2026)

Our understanding of thermalization and chaos in quantum many-body systems largely relies on the statistical properties of the spectrum of the generator of unitary dynamics. The Eigenstate Thermalization Hypothesis (ETH) explains how quantum systems can thermalize by showing that locally individual eigenstates can already encode thermal properties. Similarly, comparing eigenvalue statistics with those of random matrices is a standard tool in the study of quantum chaos. In this talk, we show that these probes of chaos and thermalization are not restricted to quantum systems, since classical dynamics can also be expressed in a unitary framework. By studying the spectrum of classical systems with discrete phase spaces – which is constructed from periodic orbits – we formulate a classical analog of the ETH ansatz and identify the corresponding random matrix universality classes. Finally, we verify our predictions numerically in realistic classical models. Our framework offers a unified perspective on thermalization and chaos across both classical and quantum systems with discrete spectra. In particular, it raises intriguing questions about the relationship between well-established theories of classical and quantum chaos, some of which we briefly discuss.

I present results on the quantum dynamics of a minimal model with spatial structure and local interactions. The model features a time-independent Hamiltonian, in contrast to the widely studied quantum circuits, and is analytically tractable in the limit of large local Hilbert space dimension and weak intersite coupling. In this regime, I show that the energy dynamics are governed by a classical master equation exhibiting diffusive behavior. Furthermore, I demonstrate that the spectral form factor can be expressed exactly in terms of the solution to this master equation, demonstrating how the linear ramp emerges at long times, while locality gives rise to an additional enhancement at short times.