Related papers: Thermalization rates and quantum Ruelle-Pollicott resonances: insights from operator hydrodynamics

Thermalization rates and quantum Ruelle-Pollicott resonances: insights from operator hydrodynamics

URL: http://arxiv.org/abs/2409.17251v1
Date: Wed, 25 Sep 2024 18:07:46 GMT
Title: Thermalization rates and quantum Ruelle-Pollicott resonances: insights from operator hydrodynamics
Authors: Carolyn Zhang, Laimei Nie, Curt von Keyserlingk,
Abstract summary: We derive a relationship between exponential decay rate $overlineg$ and the operator spreading properties of a local unitary evolution. Our calculations are based on analytical results for random unitary circuits, but we argue that similar results hold for ergodic Floquet systems.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: In thermalizing many-body quantum systems without conservation laws such as ergodic Floquet and random unitary circuits, local expectation values are predicted to decay to their equilibrium values exponentially quickly. In this work we derive a relationship between said exponential decay rate $\overline{g}$ and the operator spreading properties of a local unitary evolution. A hydrodynamical picture for operator spreading allows us to argue that, for random unitary circuits, $\overline{g}$ is encoded by the leading eigenvalue of a dynamical map obtained by enriching unitary dynamics with dissipation, in the limit of weak dissipation. We argue that the size of the eigenvalue does not depend on the details of this weak dissipation (given mild assumptions on properties of the ergodic dynamics), so long as it only suppresses large operators significantly. Our calculations are based on analytical results for random unitary circuits, but we argue that similar results hold for ergodic Floquet systems. These conjectures are in accordance with existing results which numerically obtain quantum many-body analogues of classical Ruelle-Pollicott resonances [T. Prosen J. Phys. A: Math. Gen. 35 L737 (2002), T. Mori, arXiv:2311.10304] by studying unitary evolutions subject to weak dissipation.

Related papers

Thermalization and hydrodynamic long-time tails in a Floquet system [0.0]
We investigate whether classical hydrodynamic field theories can predict the long-time dynamics of many-particle quantum systems. Based on a field theoretical analysis and symmetry arguments, we map each operator in the spin model to corresponding fields in hydrodynamics. We illustrate these findings by studying the time evolution of all 255 Hermitian operators which can be defined on four neighboring sites.
arXiv Detail & Related papers (2024-10-21T16:47:33Z)
Spectral gaps of local quantum channels in the weak-dissipation limit [0.0]
We consider the dynamics of generic chaotic quantum many-body systems with no conservation laws, subject to weak bulk dissipation. The generator of these dissipative dynamics, a quantum channel $mathcalE$, retains a nonzero gap as the dissipation strength $gamma to 0$ if the thermodynamic limit is taken first. We argue that the gap in the $gamma to 0$ limit can change nonanalytically as one tunes the parameters of the unitary dynamics.
arXiv Detail & Related papers (2024-09-25T18:00:07Z)
Quantum space-time Poincaré inequality for Lindblad dynamics [15.031583573428481]
We derive explicit and constructive exponential decay estimates for the convergence in the noncommutative $L2$-norm. Our analysis relies on establishing a quantum analog of space-time Poincar'e inequalities. A number of concrete examples are provided as applications of our theoretical results.
arXiv Detail & Related papers (2024-06-13T13:43:41Z)
Eigenstate correlations, the eigenstate thermalization hypothesis, and quantum information dynamics in chaotic many-body quantum systems [0.0]
We consider correlations between eigenstates specific to spatially extended systems and that characterise entanglement dynamics and operator spreading. The correlations associated with scrambling of quantum information lie outside the standard framework established by the eigenstate thermalisation hypothesis (ETH) We establish the simplest correlation function that captures these correlations and discuss features of its behaviour that are expected to be universal at long distances and low energies.
arXiv Detail & Related papers (2023-09-22T16:28:15Z)
A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits [37.84307089310829]
Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit. Despite their promise, the trainability of these algorithms is hindered by barren plateaus. We present a general Lie algebra that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits.
arXiv Detail & Related papers (2023-09-17T18:14:10Z)
Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation [14.746754599760562]
We revisit the dissipaton equation of motion theory and establish an equivalent dissipatons-embedded quantum master equation (DQME) The DQME supplies a direct approach to investigate the statistical characteristics of dissipatons and thus the physically supporting hybrid bath modes. Numerical demonstrations are carried out on the electron transfer model, exhibiting the transient statistical properties of the solvation coordinate.
arXiv Detail & Related papers (2023-03-19T14:14:46Z)
Quantum Lyapunov exponent in dissipative systems [68.8204255655161]
The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems. We study the interplay between these two processes. The OTOC decay rate is closely related to the classical Lyapunov.
arXiv Detail & Related papers (2022-11-11T17:06:45Z)
Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z)
Nontrivial damping of quantum many-body dynamics [0.0]
We show that a nontrivial damping in the Schr"odinger picture can emerge if the dynamics in the unperturbed system possesses rich features. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain.
arXiv Detail & Related papers (2021-03-11T12:58:39Z)
Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit [0.0]
We investigate the interplay between unitary dynamics after a quantum quench and localized dissipation in a noninteracting fermionic chain. In particular, we consider the effect of gain and loss processes, for which fermions are added and removed incoherently. For strong dissipation the coherent dynamics of the system is arrested, which is a manifestation of the celebrated quantum Zeno effect.
arXiv Detail & Related papers (2021-03-09T19:16:31Z)
Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
arXiv Detail & Related papers (2020-07-20T18:00:02Z)

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