Theory of Irreversibility in Quantum Many-Body Systems
arXiv:2501.06183 · doi:10.1103/82f6-qdyd
Abstract
We address the longstanding challenge in quantum many-body theory of reconciling unitary dynamics with irreversible relaxation. In classical chaos, the unitary evolution operator develops Ruelle-Pollicott (RP) resonances inside the unit circle in the continuum limit, leading to mixing. In the semiclassical limit, chaotic single-particle quantum systems relax with the same RP resonances. In contrast, the theory of quantum many-body RP resonances and their link to irreversibility remain underdeveloped. Here, we relate the spectral form factor to the sum of autocorrelation functions and, in generic many-body lattice systems without conservation laws, argue that all quantum many-body RP resonances converge inside the unit disk, highlighting the role of nonunitary and the thermodynamic limit. While we conjecture this picture to be general, we analytically prove the emergence of irreversibility in the random phase model (RPM), a paradigmatic Floquet quantum circuit model, in the limit of large local Hilbert space dimension. To this end, we couple it to local environments and compute the exact time evolution of autocorrelation functions, the dissipative form factor, and out-of-time-order correlation functions (OTOCs). Although valid for any dissipation strength, we then focus on weak dissipation to clarify the origin of irreversibility in unitary systems. When the dissipationless limit is taken after the thermodynamic limit, the unitary quantum map develops an infinite tower of decaying RP resonances -- chaotic systems display so-called anomalous relaxation. We also show that the OTOC in the RPM can undergo a two-stage relaxation and that during the second stage, the approach to the stationary value is again controlled by the leading RP resonance. [See the paper for the full abstract.]
25 pages, 7 figures. v2: references added. v3: minor corrections, as published
References in corpus (52)
- Many body localization and thermalization in quantum statistical mechanics
- A bound on chaos
- Many-body localization, thermalization, and entanglement
- Chaos and complexity by design
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Semiclassical Foundation of Universality in Quantum Chaos
- Chaos, Complexity, and Random Matrices
- Spectral statistics in spatially extended chaotic quantum many-body systems
- Periodic-Orbit Theory of Universality in Quantum Chaos
- Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
- Many-body quantum chaos: Analytic connection to random matrix theory
- Onset of Random Matrix Behavior in Scrambling Systems
- Spectral statistics and many-body quantum chaos with conserved charge
- Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
- Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems
- Local pairing of Feynman histories in many-body Floquet models
- Chaos and Complexity of quantum motion
- Thermofield dynamics: Quantum Chaos versus Decoherence
- Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems
- Many-body delocalisation as symmetry breaking
- Lindbladian dissipation of strongly-correlated quantum matter
- Random Lindblad Dynamics
- Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos
- Universal spectral form factor for chaotic dynamics
- Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving
- Quantum fingerprints of classical Ruelle-Pollicot resonances
- Many-body quantum chaos and emergence of Ginibre ensemble
- Operator backflow and the classical simulation of quantum transport
- Dynamical quantum phase transitions in SYK Lindbladians
- Spectral Properties of Disordered Interacting Non-Hermitian Systems
- Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom
- Classical decays in decoherent quantum maps
- Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
- Many-Body Quantum Chaos and Space-time Translational Invariance
- Classical versus Quantum Time Evolution of Densities at Limited Phase-Space Resolution
- Solvable non-Hermitian skin effect in many-body unitary dynamics
- Spectral properties of noisy classical and quantum propagators
- Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
- Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
- Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries
- Spectral properties and classical decays in quantum open systems
- Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
- Robustness of quantum chaos and anomalous relaxation in open quantum circuits
- Exact universal bounds on quantum dynamics and fast scrambling
- Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
- Quantum Chaos and Coherence: Random Parametric Quantum Channels
- An exactly solvable dissipative spin liquid
- Operator dynamics in Floquet many-body systems
- Quantum and Classical Dynamics with Random Permutation Circuits
- Purity decay rate in random circuits with different configurations of gates
- Two-step relaxation in local many-body Floquet systems
- Classical nonlinear response of a chaotic system: Langevin dynamics and spectral decomposition
Cited by in corpus (6)
- Ruelle-Pollicott resonances of diffusive U(1)-invariant qubit circuits
- Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems
- Impact of quantum coherence on the dynamics and thermodynamics of quenched free fermions coupled to a localized defect
- Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
- Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
- On the modeling of irreversibility by relaxator Liouville dynamics