Two types of quantum chaos: testing the limits of the Bohigas-Giannoni-Schmit conjecture

• URL: http://arxiv.org/abs/2411.08186v1
• Date: Tue, 12 Nov 2024 21:10:04 GMT
• Title: Two types of quantum chaos: testing the limits of the Bohigas-Giannoni-Schmit conjecture
• Authors: Javier M. Magan, Qingyue Wu,
• Abstract summary: There are two types of quantum chaos: eigenbasis chaos and spectral chaos. The Bohigas-Giannoni-Schmit conjecture asserts a direct relationship between the two types of chaos for quantum systems with a chaotic semiclassical limit. We study the Poissonian ensemble associated with the Sachdev-Ye-Kitaev (SYK) model.
• Score: 0.8287206589886881
• License:
• Abstract: There are two types of quantum chaos: eigenbasis chaos and spectral chaos. The first type controls the early-time physics, e.g. the thermal relaxation and the sensitivity of the system to initial conditions. It can be traced back to the Eigenstate Thermalization Hypothesis (ETH), a statistical hypothesis about the eigenvectors of the Hamiltonian. The second type concerns very late-time physics, e.g. the ramp of the Spectral Form Factor. It can be traced back to Random Matrix Universality (RMU), a statistical hypothesis about the eigenvalues of the Hamiltonian. The Bohigas-Giannoni-Schmit (BGS) conjecture asserts a direct relationship between the two types of chaos for quantum systems with a chaotic semiclassical limit. The BGS conjecture is challenged by the Poissonian Hamiltonian ensembles, which can be used to model any quantum system displaying RMU. In this paper, we start by analyzing further aspects of such ensembles. On general and numerical grounds, we argue that these ensembles can have chaotic semiclassical limits. We then study the Poissonian ensemble associated with the Sachdev-Ye-Kitaev (SYK) model. While the distribution of couplings peaks around the original SYK model, the Poissonian ensemble is not $k$-local. This suggests that the link between ETH and RMU requires of physical $k$-locality as an assumption. We test this hypothesis by modifying the couplings of the SYK Hamiltonian via the Metropolis algorithm, rewarding directions in the space of couplings that do not display RMU. The numerics converge to a $k$-local Hamiltonian with eigenbasis chaos but without spectral chaos. We finally comment on ways out and corollaries of our results.

Related papers

• D-commuting SYK model: building quantum chaos from integrable blocks [7.876232078364128]
  We study the spectrum of this model analytically in the double-scaled limit. For finite $d$ copies, the spectrum is close to the regular SYK model in UV but has an exponential tail $eE/T_c$ in the IR. We propose the existence of a new phase around $T_c$, and the dynamics should be very different in two phases.
  arXiv  Detail & Related papers  (2024-11-19T19:00:06Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. Even with sublinear barriers, we use Feynman-Kac techniques to lift classical to quantum ones establishing tight lower bound $T_mathrmmix = 2Omega(nalpha)$.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Quantum Chaos on Edge [36.136619420474766]
  We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension. While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
  arXiv  Detail & Related papers  (2024-03-20T11:31:51Z)
• Projected state ensemble of a generic model of many-body quantum chaos [0.0]
  The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design.
  arXiv  Detail & Related papers  (2024-02-26T19:00:00Z)
• String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory [0.0]
  We study the Hamiltonian lattice Yang-Mills theory based on spin networks. We study quantum scars in a nonabelian gauge theory.
  arXiv  Detail & Related papers  (2023-05-10T07:45:43Z)
• Quantum dissipation and the virial theorem [22.1682776279474]
  We study the celebrated virial theorem for dissipative systems, both classical and quantum. The non-Markovian nature of the quantum noise leads to novel bath-induced terms in the virial theorem. We also consider the case of an electrical circuit with thermal noise and analyze the role of non-Markovian noise in the context of the virial theorem.
  arXiv  Detail & Related papers  (2023-02-23T13:28:11Z)
• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model [0.0]
  Spectral rigidity in Hermitian quantum chaotic systems signals the presence of dynamical universal features at timescales that can be much shorter than the Heisenberg time. We study the analog of this timescale in many-body non-Hermitian quantum chaos by a detailed analysis of long-range spectral correlators.
  arXiv  Detail & Related papers  (2022-11-03T08:45:19Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)
• Isospectral twirling and quantum chaos [0.0]
  We show that the most important measures of quantum chaos like frame potentials, scrambling, Loschmidt echo, and out-of-time correlators (OTOCs) can be described by the unified framework of the isospectral twirling. We show that, by exploiting random matrix theory, these measures of quantum chaos clearly distinguish the finite time profiles of probes to quantum chaos.
  arXiv  Detail & Related papers  (2020-11-11T19:01:08Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

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.