Exponentially fast dynamics in the Fock space of chaotic many-body systems

We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of states participating in the evolution after a quench increases exponentially in time, provided the eigenstates are delocalized in the energy shell. The rate of the exponential gr...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Borgonovi, Fausto, Izrailev, Felix M, Santos, Lea F
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.02.2018
Subjects
Bosons
Eigenvectors
Interaction models
Mathematical models
Particle spin
Online AccessGet full text

Cover

More Information
Summary:We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of states participating in the evolution after a quench increases exponentially in time, provided the eigenstates are delocalized in the energy shell. The rate of the exponential growth is defined by the width \(\Gamma\) of the local density of states (LDOS) and is associated with the Kolmogorov-Sinai entropy for systems with a well defined classical limit. In a finite system, the exponential growth eventually saturates due to the finite volume of the energy shell. We estimate the time scale for the saturation and show that it is much larger than \(1/\Gamma\). Numerical data obtained for a two-body random interaction model of bosons and for a dynamical model of interacting spin-1/2 particles show excellent agreement with the analytical predictions.
ISSN:2331-8422
DOI:10.48550/arxiv.1802.08265