Effective potential for the second virial coefficient at Feshbach resonance

TL;DR

This paper investigates the relationship between quantum and classical second virial coefficients near Feshbach resonance, revealing a scale-invariant inverse square potential and proposing experimental tests via isothermal compressibility measurements.

Contribution

It establishes an exact mapping from quantum to classical second virial coefficients at Feshbach resonance, introducing a scale-independent inverse square potential.

Findings

Quantum and classical virial coefficients are exactly connected near resonance.

A scale-invariant inverse square potential describes the classical second virial coefficient.

Proposes measuring isothermal compressibility to test the theoretical predictions.

Abstract

In a recent paper entitled "High temperature expansion applied to fermions near Feshbach resonance" (Phys. Rev. Lett. 92, 160404 (2004)), Ho and Muller have demonstrated a remarkable similarity between its high and low temperature properties at resonance. The quantum second virial coefficient plays a crucial role in their analysis, and has a universal value at resonance. In this paper, we explore the connection between the quantum and classical second virial coefficients, and show that near a Feshbach resonance, an exact mapping from the quantum to classical form is possible. This gives rise to a scale independent inverse square potential for the classical second virial coefficient. It is suggested that it may be tested by measuring the isothermal compressibility of the gas on the repulsive side of the resonance.