Virial theorems for trapped cold atoms

TL;DR

This paper derives a general virial theorem applicable to quantum particles with various interactions in external potentials, providing insights into trapped cold atom systems across different interaction regimes.

Contribution

It introduces a comprehensive virial theorem for cold atoms with zero-range and finite-range interactions, including effects like Efimov states and Feshbach resonances.

Findings

Trapping potential energy exhibits an inflection point at unitarity during adiabatic variation of scattering length.

Virial theorems are extended to multiple interaction scenarios relevant to cold atom experiments.

Provides theoretical tools for analyzing energy relations in trapped cold atom systems.

Abstract

We present a general virial theorem for quantum particles with arbitrary zero-range or finite-range interactions in an arbitrary external potential. We deduce virial theorems for several situations relevant to trapped cold atoms: zero-range interactions with and without Efimov effect, hard spheres, narrow Feshbach resonances, and finite-range interactions. If the scattering length $a$ is varied adiabatically in the BEC-BCS crossover, we find that the trapping potential energy as a function of $1/a$ has an inflexion point at unitarity.