Average Equilibration Time for Gaussian Unitary Ensemble Hamiltonians

• URL: http://arxiv.org/abs/2603.28587v1
• Date: Mon, 30 Mar 2026 15:35:04 GMT
• Title: Average Equilibration Time for Gaussian Unitary Ensemble Hamiltonians
• Abstract summary: We study equilibration times in closed quantum systems using the framework of equilibration as dephasing.<n>We find that the equilibration time decreases with system size and timescales in the thermodynamic limit.<n>This unphysical result indicates that the true equilibration timescale of realistic chaotic many-body systems must be dominated by physical features not captured by random matrix ensembles.
• Score: 35.18016233072556
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding equilibration times in closed quantum systems is essential for characterising their approach to equilibrium. Chaotic many-body systems are paradigmatic in this context: they are expected to thermalise according to the eigenstate thermalisation hypothesis and exhibit spectral properties well described by random matrix theory (RMT). While RMT successfully captures spectral correlations, its ability to provide quantitative predictions for equilibration timescales has remained largely unexplored. Here, we study equilibration within RMT using the framework of equilibration as dephasing, focusing on closed systems whose Hamiltonians are drawn from the Gaussian unitary ensemble (GUE). We derive an analytical expression that approximates the average equilibration time of the GUE and show that it is independent of both the initial state and the choice of observable, a consequence of the rotational invariance of the GUE. Numerical simulations confirm our analytical expression and demonstrate that our approximation is in close agreement with the true average equilibration time of the GUE. We find that the equilibration time decreases with system size and vanishes in the thermodynamic limit. This unphysical result indicates that the true equilibration timescale of realistic chaotic many-body systems must be dominated by physical features not captured by random matrix ensembles -- the GUE in particular.

Related papers

• Monitored free fermions under periodic driving [42.078441758883635]
  We investigate periodically driven free-fermionic systems subjected to monitoring of the local particle density.<n>We use the nonlinear sigma-model (NLSM) to explain the long-wavelength physics of the time-dependent Hamiltonian.<n>Our results provide a unified analytical and numerical framework for understanding the effects of monitoring in time-modulated fermionic systems.
  arXiv  Detail & Related papers  (2026-08-22T08:10:12Z)
• Symmetry Constrained Quantum Error Mitigation for the Schwinger Model [39.146761527401424]
  We exploit the parity and fermion-number symmetries of a gauge theory under depolarising noise.<n>We investigate symmetry verification under digital quantum simulation.
  arXiv  Detail & Related papers  (2026-08-21T13:49:11Z)
• Identifiable learning of dissipative dynamics [25.409059056398124]
  We introduce I-OnsagerNet, a neural framework that learns dissipative dynamics directly from trajectories.<n>I-OnsagerNet extends the Onsager principle to guarantee that the learned potential is obtained from the stationary density.<n>Our approach enables us to calculate the entropy production and to quantify irreversibility, offering a principled way to detect and quantify deviations from equilibrium.
  arXiv  Detail & Related papers  (2025-10-28T07:57:14Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Finite-time quantum equilibration for continuous variables [0.0]
  We develop the theory of Quantum Equilibration for the case of infinite-dimensional systems.<n>The main goal of this paper will be to propose a framework to extend the results obtained by Short in.
  arXiv  Detail & Related papers  (2024-12-01T22:11:45Z)
• Equilibration of Isolated Systems: investigating the role of coarse-graining on the initial state magnetization [1.9926435972281176]
  equilibration may be affected by a lack of resolution, or coarse-graining, in the magnetization of the initial state. We show that the level of equilibration of an initial state with a coarse, not well-defined magnetization is different from the level of an initial state with well-defined magnetization. Our study highlights the crucial role of initial state preparation in the equilibration dynamics of quantum systems.
  arXiv  Detail & Related papers  (2023-05-19T20:05:53Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• Thermal equilibrium in Gaussian dynamical semigroups [77.34726150561087]
  We characterize all Gaussian dynamical semigroups in continuous variables quantum systems of n-bosonic modes which have a thermal Gibbs state as a stationary solution. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices.
  arXiv  Detail & Related papers  (2022-07-11T19:32:17Z)
• Simultaneous Transport Evolution for Minimax Equilibria on Measures [48.82838283786807]
  Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures. By adding entropic regularization, our main result establishes global convergence towards the global equilibrium.
  arXiv  Detail & Related papers  (2022-02-14T02:23:16Z)
• Relaxation of non-integrable systems and correlation functions [0.0]
  We investigate early-time equilibration rates of observables in closed many-body quantum systems. We find evidence for this coincidence when the initial conditions are sufficiently generic, or typical. Our findings are confirmed by proving that these different timescales coincide for dynamics generated by Haar-random Hamiltonians.
  arXiv  Detail & Related papers  (2021-12-17T12:34:34Z)
• Equilibration of Non-Markovian Quantum Processes in Finite Time Intervals [0.0]
  Quantum processes are shown, within finite time intervals and for finite dimensional time Hamiltonians, to be close to a corresponding stationary equilibrium process. This dictates conditions on time scales at when the multitime statistics of any arbitrary non-equilibrium quantum process look equilibrium on average.
  arXiv  Detail & Related papers  (2021-12-02T10:18:36Z)
• Universal Quantum Fluctuation-Dissipation Relation for Systems Far From Equilibrium [3.0965505512285967]
  We present a general nonequilibrium Fluctuation-Dissipation Theorem (FDT) for quantum Markovian processes where the detailed-balance condition is violated. Apart from the fluctuations, the relaxation involves extra correlation that is governed by the quantum curl flux emerged in the far-from-equilibrium regime. Our results have the advantage of and exceed the scope of the fluctuation-dissipation relation in the perturbative and near equilibrium regimes.
  arXiv  Detail & Related papers  (2021-01-28T06:12:08Z)
• Quantum relaxation in a system of harmonic oscillators with time-dependent coupling [0.0]
  We analyze the relaxation of nonequilibrium initial distributions for a system of coupled one-dimensional harmonic oscillators. We show that in general the system studied here tends to equilibrium, but the relaxation can be retarded depending on the values of the parameters.
  arXiv  Detail & Related papers  (2020-07-06T12:57:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.