A measure of chaos from eigenstate thermalization hypothesis
- URL: http://arxiv.org/abs/2401.13633v1
- Date: Wed, 24 Jan 2024 18:01:49 GMT
- Title: A measure of chaos from eigenstate thermalization hypothesis
- Authors: Nilakash Sorokhaibam
- Abstract summary: Eigenstate thermalization hypothesis is a detailed statement of the matrix elements of few-body operators in energy eigenbasis of a chaotic Hamiltonian.
We propose that the exponent ($gamma>0$) is a measure of quantum chaos.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Eigenstate thermalization hypothesis is a detailed statement of the matrix
elements of few-body operators in energy eigenbasis of a chaotic Hamiltonian.
Part of the statement is that the off-diagonal elements fall exponential for
large energy difference. We propose that the exponent ($\gamma>0$) is a measure
of quantum chaos. Smaller $\gamma$ implies more chaotic dynamics. The chaos
bound is given by $\gamma=\beta/4$ where $\beta$ is the inverse temperature. We
give analytical argument in support of this proposal. The slower exponential
fall also means that the action of the operator on a state leads to higher
delocalization in energy eigenbasis. Numerically we compare two chaotic
Hamiltonians - SYK model and chaotic XXZ spin chain. Using the new measure, we
find that the SYK model becomes maximally chaotic at low temperature which has
been shown rigorously in previous works. The new measure is more readily
accessible compare to other measures using numerical methods.
Related papers
- Kubo-Martin-Schwinger relation for energy eigenstates of SU(2)-symmetric quantum many-body systems [41.94295877935867]
We show that non-Abelian symmetries may alter conventional thermodynamics.<n>This work helps extend into nonequilibrium physics the effort to identify how non-Abelian symmetries may alter conventional thermodynamics.
arXiv Detail & Related papers (2025-07-09T19:46:47Z) - Numerical evidence for the non-Abelian eigenstate thermalization hypothesis [41.94295877935867]
The eigenstate thermalization hypothesis (ETH) explains how generic quantum many-body systems thermalize internally.
We prove analytically that the non-Abelian ETH exhibits a self-consistency property.
arXiv Detail & Related papers (2024-12-10T19:00:01Z) - Two types of quantum chaos: testing the limits of the Bohigas-Giannoni-Schmit conjecture [0.8287206589886881]
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.
arXiv Detail & Related papers (2024-11-12T21:10:04Z) - 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) - Scattering Neutrinos, Spin Models, and Permutations [42.642008092347986]
We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with $N$ degrees of freedom.
These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to $N$, non-trivial eigenvalues.
arXiv Detail & Related papers (2024-06-26T18:27:15Z) - On stability of k-local quantum phases of matter [0.4999814847776097]
We analyze the stability of the energy gap to Euclids for Hamiltonians corresponding to general quantum low-density parity-check codes.
We discuss implications for the third law of thermodynamics, as $k$-local Hamiltonians can have extensive zero-temperature entropy.
arXiv Detail & Related papers (2024-05-29T18:00:20Z) - High-Temperature Gibbs States are Unentangled and Efficiently Preparable [22.397920564324973]
We show that thermal states of local Hamiltonians are separable above a constant temperature.
This sudden death of thermal entanglement upends conventional wisdom about the presence of short-range quantum correlations in Gibbs states.
arXiv Detail & Related papers (2024-03-25T15:11:26Z) - Average entanglement entropy of midspectrum eigenstates of
quantum-chaotic interacting Hamiltonians [0.0]
We show that the magnitude of the negative $O(1)$ correction is only slightly greater than the one predicted for random pure states.
We derive a simple expression that describes the numerically observed $nu$ dependence of the $O(1)$ deviation from the prediction for random pure states.
arXiv Detail & Related papers (2023-03-23T18:00:02Z) - Brownian Axion-like particles [11.498089180181365]
We study the non-equilibrium dynamics of a pseudoscalar axion-like particle (ALP) weakly coupled to degrees of freedom in thermal equilibrium.
Time evolution is determined by the in-in effective action which we obtain to leading order in the (ALP) coupling.
We discuss possible cosmological consequences on structure formation, the effective number of relativistic species and birefringence of the cosmic microwave background.
arXiv Detail & Related papers (2022-09-16T00:35:04Z) - On parametric resonance in the laser action [91.3755431537592]
We consider the selfconsistent semiclassical Maxwell--Schr"odinger system for the solid state laser.
We introduce the corresponding Poincar'e map $P$ and consider the differential $DP(Y0)$ at suitable stationary state $Y0$.
arXiv Detail & Related papers (2022-08-22T09:43:57Z) - Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
arXiv Detail & Related papers (2022-07-28T17:58:59Z) - Thermalization of many many-body interacting SYK models [0.0]
We investigate the non-equilibrium dynamics of complex Sachdev-Ye-Kitaev (SYK) models in the $qrightarrowinfty$ limit.
A single SYK $qrightarrowinfty$ Hamiltonian for $tgeq 0$ is a perfect thermalizer in the sense that the local Green's function is instantaneously thermal.
arXiv Detail & Related papers (2021-11-16T18:10:20Z) - Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear
$\sigma$-model with $\theta=\pi$ term [17.494746371461694]
We perform a tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $sigma$-model with $theta=pi$ term.
Within the Hamiltonian formulation, this field theory emerges as the finite-temperature partition function of a modified quantum rotor model decorated with magnetic monopoles.
arXiv Detail & Related papers (2021-09-23T12:17:31Z) - Energy of a free Brownian particle coupled to thermal vacuum [0.0]
Experimentalists have come to temperatures very close to absolute zero at which physics that was once ordinary becomes extraordinary.
We study the simplest open quantum system, namely, a free quantum Brownian particle coupled to thermal vacuum.
arXiv Detail & Related papers (2020-03-30T15:44:04Z)
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.