Exact scaling transform for a unitary quantum gas in a time dependent harmonic potential

TL;DR

This paper derives an exact mathematical transformation describing the time evolution of a unitary quantum gas confined in a three-dimensional harmonic trap with time-dependent parameters, enhancing understanding of its dynamics.

Contribution

It introduces an exact gauge and scaling transform for the dynamics of a unitary quantum gas in a time-dependent harmonic potential.

Findings

Exact solution for the gas's evolution in a time-dependent trap

Application of the Fermi pseudo-potential model

Provides a theoretical framework for experimental analysis

Abstract

A unitary quantum gas is a gas of quantum particles with a binary interaction of infinite scattering length and negligible range. It has been produced in recent experiments with gases of fermionic atoms by means of a Feshbach resonance. Using the Fermi pseudo-potential model for the atomic interaction, we show that the time evolution of such a gas in an isotropic three-dimensional time dependent harmonic trap is exactly given by a gauge and scaling transform.