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
- Time-dependent Neural Galerkin Method for Quantum Dynamics [42.81677042059531]
We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle.
We showcase the method's effectiveness simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D.
Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches.
arXiv Detail & Related papers (2024-12-16T13:48:54Z) - Real-time dynamics of false vacuum decay [49.1574468325115]
We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential.
We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
arXiv Detail & Related papers (2023-10-06T12:44:48Z) - Motivating semiclassical gravity: a classical-quantum approximation for
bipartite quantum systems [0.0]
We derive a "classical-quantum" approximation scheme for a broad class of bipartite quantum systems.
In this approximation, one subsystem evolves via classical equations of motion with quantum corrections, and the other subsystem evolves quantum mechanically.
arXiv Detail & Related papers (2023-06-01T18:05:33Z) - 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) - Out-of-equilibrium dynamics arising from slow round-trip variations of
Hamiltonian parameters across quantum and classical critical points [0.0]
We address the out-of-equilibrium dynamics of many-body systems subject to slow time-dependent round-trip protocols across quantum and classical (thermal) phase transitions.
We consider protocols where one relevant parameter w is slowly changed across its critical point wc = 0, linearly in time with a large time scale ts.
arXiv Detail & Related papers (2022-05-17T13:27:32Z) - 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) - Quantum-classical entropy analysis for nonlinearly-coupled
continuous-variable bipartite systems [0.0]
We investigate the behavior of classical analogs arising upon the removal of interference traits.
By comparing the quantum and classical entropy values, it is shown that, instead of entanglement production, such entropies rather provide us with information.
arXiv Detail & Related papers (2021-11-19T11:39:15Z) - 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) - Semi-classical quantisation of magnetic solitons in the anisotropic
Heisenberg quantum chain [21.24186888129542]
We study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain.
Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves.
arXiv Detail & Related papers (2020-10-14T16:46:11Z) - Equivalence of approaches to relational quantum dynamics in relativistic
settings [68.8204255655161]
We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector.
We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
arXiv Detail & Related papers (2020-07-01T16:12:24Z) - Quantum vs classical dynamics in a spin-boson system: manifestations of
spectral correlations and scarring [0.0]
We compare the classical and quantum evolutions of the Dicke model in its regular and chaotic domains.
We identify features of the long-time dynamics that are purely quantum and discuss their impact on equilibration times.
In the case of maximal quantum ergodicity, our results are analytical and show that quantum equilibration takes longer than classical equilibration.
arXiv Detail & Related papers (2020-02-06T19:00:05Z)
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.