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Exponentially fast dynamics of chaotic many-body systems
Fausto Borgonovi1,2, Felix M Izrailev3,4, Lea F Santos5
1Dipartimento di Matematica e Fisica and Interdisciplinary Laboratories for Advanced Materials Physics, Università Cattolica, via Musei 41, 25121 Brescia, Italy.
Physical Review. E
|February 21, 2019
Summary
The number of quantum states involved in isolated systems grows exponentially after a perturbation. This growth rate relates to system dynamics and eventually saturates in finite systems.
Area of Science:
- Quantum mechanics
- Statistical physics
- Quantum chaos
Background:
- Understanding the dynamics of isolated quantum systems after a quench is crucial.
- The delocalization of eigenstates in the energy shell plays a key role in quantum evolution.
Purpose of the Study:
- To analytically and numerically demonstrate the time evolution of many-body states in isolated quantum systems after a quench.
- To investigate the relationship between the growth rate of participating states and system properties like the local density of states width (Γ).
Main Methods:
- Analytical derivations and numerical simulations were employed.
- The study analyzed two-body random interaction models of bosons and dynamical models of interacting spin-1/2 particles.
Main Results:
- The number of participating many-body states increases exponentially with time, governed by the local density of states width (Γ).
- This exponential growth is linked to Kolmogorov-Sinai entropy in systems with classical limits.
- Saturation of this growth occurs in finite systems on a timescale significantly larger than ℏ/Γ.
Conclusions:
- The findings provide a theoretical framework for understanding quantum state dynamics after a quench.
- Numerical results validate the analytical predictions, offering insights into quantum thermalization and chaos.
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