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

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.