Exact Quantum Decay of an Interacting Many-Particle System: the Calogero-Sutherland model

TL;DR

This paper presents an exact analysis of quantum decay in a one-dimensional Bose gas with inverse-square interactions, revealing a power-law decay influenced by particle number and interaction strength, and linking decay behavior to many-particle state reconstruction.

Contribution

It provides the first exact solution for quantum decay dynamics in the Calogero-Sutherland model, connecting decay exponents to interaction parameters and initial state reconstruction.

Findings

Decay exhibits quadratic then power-law behavior over time.

Power-law exponent depends on particle number and interaction strength.

Decay is nonexponential due to many-particle state reconstruction.

Abstract

The exact quantum decay of a one-dimensional Bose gas with inverse-square interactions is presented. The system is equivalent to a gas of particles obeying generalized exclusion statistics. We consider the expansion dynamics of a cloud initially confined in a harmonic trap that is suddenly switched off. The decay is characterized by analyzing the fidelity between the initial and the time-evolving states, also known as the survival probability. It exhibits early on a quadratic dependence on time that turns into a power-law decay, during the course of the evolution. It is shown that the particle number and the strength of interactions determine the power-law exponent in the latter regime, as recently conjectured. The nonexponential character of the decay is linked to the many-particle reconstruction of the initial state from the decaying products.