Quantum instabilities in the system of identical bosons

TL;DR

This paper analyzes the quantum instabilities in systems of identical bosons using Bogoliubov transformations, highlighting how nonlinear interactions influence instability rates, with implications for Bose-Einstein condensates.

Contribution

It establishes a connection between quantum and classical stability theories and explores how nonlinear interactions affect instability rates in bosonic systems.

Findings

Instability rates are suppressed by strong repulsive or attractive interactions.

Weak attraction significantly increases the instability rate.

Quantum instability analysis can inform Bose-Einstein condensate behavior.

Abstract

The quantum instability of the mean-field theory for identical bosons is shown to be described by an appropriate Bogoliubov transformation. A connection between the quantum and classical linear stability theories is indicated. It is argued that the instability rate in a system of identical bosons must be strongly affected by the nonlinear terms (interactions). In the case of the repulsive interactions or strong attractive interactions the instability rate is suppressed. On the other hand, a weak attraction significantly enhances the instability rate. The results can have applications in the field of Bose-Einstein condensates of dilute quantum gases.