Timescales of quantum and classical chaotic spin models evolving toward equilibrium

• URL: http://arxiv.org/abs/2307.05681v2
• Date: Thu, 22 Feb 2024 03:19:32 GMT
• Title: Timescales of quantum and classical chaotic spin models evolving toward equilibrium
• Authors: Fausto Borgonovi, Felix M. Izrailev, Lea F. Santos
• Abstract summary: We investigate the quench dynamics of a strongly chaotic lattice with $L$ interacting spins. By analyzing both the classical and quantum dynamics, we identify and elucidate the two mechanisms of the relaxation process.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the quench dynamics of a one-dimensional strongly chaotic lattice with $L$ interacting spins. By analyzing both the classical and quantum dynamics, we identify and elucidate the two mechanisms of the relaxation process of these systems: one arises from linear parametric instability and the other from nonlinearity. We demonstrate that the relaxation of the single-particles energies (global quantity) and of the onsite magnetization (local observable) is primarily due to the first mechanism, referred to as linear chaos. Our analytical findings indicate that both quantities, in the classical and quantum domain, relax at the same timescale, which is independent of the system size. The physical explanation for this behavior lies in the conservation of the $L$ spin angular momenta. We argue that observables with a well-defined classical limit should conform to this picture and exhibit a finite relaxation time in the thermodynamic limit. In contrast, the evolution of the participation ratio, which measures how the initial state spreads in the many-body Hilbert space and has no classical limit, indicates absence of relaxation in the thermodynamic limit.

Related papers

• Primordial power spectrum from an objective collapse mechanism: The simplest case [0.0]
  In this work we analyze the physical origin of the primordial inhomogeneities during the inflation era. We incorporate an objective collapse mechanism based on the Continuous Spontaneous Localization (CSL) model. We obtain a primordial spectrum that has the same distinctive features as the standard one, which is consistent with the observations from the Cosmic Microwave Background.
  arXiv  Detail & Related papers  (2024-11-07T15:54:20Z)
• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM) By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Non-equilibrium dynamics of charged dual-unitary circuits [44.99833362998488]
  interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the centre of an intense multidisciplinary research effort. We show that one can introduce a class of solvable states, which extends that of generic dual unitary circuits. In contrast to the known class of solvable states, which relax to the infinite temperature state, these states relax to a family of non-trivial generalised Gibbs ensembles.
  arXiv  Detail & Related papers  (2024-07-31T17:57:14Z)
• On the Conditions for a Quantum Violent Relaxation [0.0]
  We study the dynamics of generic many-body systems with two-body, all-to-all, interactions in the thermodynamic limit. We show that, in order for violent relaxation to occur very specific conditions on the spectrum of the mean-field effective Hamiltonian have to be met. Our results demonstrate how, even in the mean-field regime, quantum effects have a rather dramatic impact on the dynamics.
  arXiv  Detail & Related papers  (2023-12-22T15:33:26Z)
• Observation of many-body dynamical localization [12.36065516066796]
  We present evidence for many-body dynamical localization for the Lieb-Liniger version of the many-body quantum kicked rotor. Our results shed light on the boundary between the classical, chaotic world and the realm of quantum physics.
  arXiv  Detail & Related papers  (2023-12-21T14:24:50Z)
• Non-equilibrium quantum probing through linear response [41.94295877935867]
  We study the system's response to unitary perturbations, as well as non-unitary perturbations, affecting the properties of the environment. We show that linear response, combined with a quantum probing approach, can effectively provide valuable quantitative information about the perturbation and characteristics of the environment.
  arXiv  Detail & Related papers  (2023-06-14T13:31:23Z)
• Rotor/spin-wave theory for quantum spin models with U(1) symmetry [0.0]
  We show that the zero mode corresponds exactly to a U(1) quantum rotor, related to the Anderson tower of states expected in systems showing symmetry breaking in the thermodynamic limit. This picture leads to an approximate separation of variables between rotor and spin-wave ones, which allows for a correct description of the ground-state and low-energy physics.
  arXiv  Detail & Related papers  (2023-03-01T10:04:11Z)
• Quantum-classical correspondence of strongly chaotic many-body spin models [0.0]
  We study the quantum-classical correspondence for systems with interacting spin-particles that are strongly chaotic in the classical limit. Our analysis of the Lyapunov spectra reveals that the largest Lyapunov exponent agrees with the Lyapunov exponent. In the quantum domain, our analysis of the Hamiltonian matrix in a proper representation allows us to obtain the conditions for the onset of quantum chaos.
  arXiv  Detail & Related papers  (2022-11-18T19:00:01Z)
• Dynamics of mixed quantum-classical spin systems [0.0]
  Mixed quantum-classical spin systems have been proposed in spin chain theory, organic chemistry, and, more recently, spintronics. Here, we present a fully Hamiltonian theory of quantum-classical spin dynamics that appears to be the first to ensure an entire series of consistency properties.
  arXiv  Detail & Related papers  (2022-10-03T14:53:46Z)
• 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)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)

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.