Chaos in effective classical and quantum dynamics

TL;DR

This paper compares classical and quantum dynamics of N-component phi^4 oscillators, revealing that chaos present in classical systems is suppressed in quantum systems due to quantum fluctuations altering orbit structures.

Contribution

It demonstrates how quantum corrections modify the effective dynamics, reducing chaos by removing hyperbolic fixed points in the quantum case.

Findings

Classical systems exhibit chaos for all external field values.

Quantum systems show strong suppression of chaos.

Quantum fluctuations alter orbit structures, reducing chaos.

Abstract

We investigate the dynamics of classical and quantum N-component phi^4 oscillators in the presence of an external field. In the large N limit the effective dynamics is described by two-degree-of-freedom classical Hamiltonian systems. In the classical model we observe chaotic orbits for any value of the external field, while in the quantum case chaos is strongly suppressed. A simple explanation of this behaviour is found in the change in the structure of the orbits induced by quantum corrections. Consistently with Heisenberg's principle, quantum fluctuations are forced away from zero, removing in the effective quantum dynamics a hyperbolic fixed point that is a major source of chaos in the classical model.