Exponentially fast dynamics of chaotic many-body systems

Abstract

We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of many-body 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 $\hslash /\Gamma$. 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.

11 pages, 5 figures (as published)

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Simulations of Information Transport in Spin Chains
• Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
• Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge
• Thermalization in one- plus two-body ensembles for dense interacting boson systems
• Phase-space characterization of complexity in quantum many-body dynamics
• Localized Thermal States

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