Quantum Instability

TL;DR

This paper explores how classical instabilities manifest in quantum systems, demonstrating that quantum systems can exhibit instability-like behavior through wave function cascades and spectrum complexity.

Contribution

It reveals the conditions under which quantum systems can display instabilities analogous to classical linear instabilities, using three-wave interactions as an example.

Findings

Quantum systems can exhibit instability through wave function cascades.

Unstable quantum systems have richer spectra and longer recurrence times.

Conditions for quantum instability are characterized.

Abstract

The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a unitary quantum description. Using the example of three-wave interactions, we describe how a time-independent, finite-dimensional quantum system, which is Hermitian with all real eigenvalues, can give rise to a linear instability corresponding to that in the classical system. We show that the instability is realized in the quantum theory as a cascade of the wave function in the space of occupation number states, and an unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system. The conditions for quantum instability are described.