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arXiv:1609.08518 · Physical review. B./Physical review. B

Universal long-time behavior of aperiodically driven interacting quantum systems

Zi Cai, Claudius Hubig, Ulrich Schollwöck

Published Aug 9, 2017• 9 citations
arXivHTMLPDF

Abstract

Understanding the collective dynamics in many-particle systems is of important significance in nonequilibrium physics. In this paper, we systematically study the long-time behavior in stochastically driven interacting quantum systems. We find that even though the stochastic forces will inevitably drive a system into a featureless steady state, the asymptotic behavior to approach the steady state can be highly nontrivial and exhibits rich universal dynamics due to the interplay between the stochastic driving and quantum many-body effects. Special attention is devoted to the effect of the mode-coupling perturbations, which may have important consequence for the long-time dynamics of the stochastically driven quantum many-body systems.

DOI
10.1103/physrevb.96.054303

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Understanding the collective dynamics in many-particle systems is of important significance in nonequilibrium physics. In this paper, we systematically study the long-time behavior in stochastically driven interacting quantum systems. We find that even though the stochastic forces will inevitably drive a system into a featureless steady state, the asymptotic behavior to approach the steady state can be highly nontrivial and exhibits rich universal dynamics due to the interplay between the stochastic driving and quantum many-body effects. Special attention is devoted to the effect of the mode-coupling perturbations, which may have important consequence for the long-time dynamics of the stochastically driven quantum many-body systems.
Does a closed quantum many-body system that is continually driven with a time-dependent Hamiltonian finally reach a steady state? This question has only recently been answered for driving protocols that are periodic in time, where the long-time behavior of the local properties synchronizes with the drive and can be described by an appropriate periodic ensemble. Here, we explore the consequences of breaking the time-periodic structure of the drive with additional aperiodic noise in a class of integrable systems. We show that the resulting unitary dynamics leads to new emergent steady states in at least two cases. While any typical realization of random noise causes eventual heating to an infinite-temperature ensemble for all local properties in spite of the system being integrable, noise that is self-similar in time leads to an entirely different steady state (which we dub the ``geometric generalized Gibbs ensemble'') that emerges only after an astronomically large time scale. To understand the approach to the steady state, we study the temporal behavior of certain coarse-grained quantities in momentum space that fully determine the reduced density matrix for a subsystem with size much smaller than the total system. Such quantities provide a concise description for any drive protocol in integrable systems that are reducible to a free-fermion representation.
Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown.Here we present a systematic study of these interplays in the case of driven Hubbard chains subject to a variety of interaction (from non-interacting to strongly correlated) and dynamical regimes (from sudden quench to quasi-adiabatic), and discuss which effects all these ingredients have on the work extraction and entropy production.As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting.We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy production, even when many-body correlations are significant.
In this Letter, we study the mean-field dynamics of a general class of many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter m(t)∼t^{-χ} with an exponent χ=1/3 that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states, and even the driving protocols. It is shown that such a dynamical universality class can be understood as a consequence of a diffusive process with a time-dependent diffusion coefficient which is determined self-consistently during the evolution. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.
Long-range interacting models exhibit rich dynamical phenomena driven by deviations from collective descriptions. This work extends the study of these models to open quantum systems, focusing on the complex interplay between nonlocal interactions and local dissipation. The results demonstrate that the impact of long-range interactions on relaxation is twofold: they mitigate the impact of noises by stabilizing ferromagnetic domains and reducing local fluctuation, yet simultaneously accelerate memory loss by indirectly exposing each spin to a broader environment. While strong dissipation drives the system into glassy, range-insensitive relaxation, the results in weak dissipation regime reveal rich state-dependent dynamics. Specifically, long-range collective behaviors protect the early-stage coherence of systems quenched from polarized states, whereas they actively accelerate the relaxation of staggered configurations. Furthermore, nonlocal interactions continue to drive memory decorrelation even in the near-steady stages of a dissipative quench. These findings offer timely theoretical insights for the design, control, and calibration of analog quantum simulators operating with long-range interactions.
We study nonequilibrium dynamics of integrable and nonintegrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate rrr, that project the system to its initial state. We show that the steady-state density matrix of a nonintegrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite rrr. Consequently a generic observable $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{O}$, whose expectation value receives a contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite rrr. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles characterized by rrr. We also study the spread of particle density of a noninteracting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.