Large momentum part of fermions with large scattering length

TL;DR

This paper establishes a universal relation linking the large-momentum tail of fermions with large scattering length to the derivative of energy, applicable across temperatures, scattering lengths, and even in few-body systems.

Contribution

It introduces a universal formula connecting the $1/k^4$ tail magnitude to the adiabatic derivative of energy with respect to inverse scattering length, extending to various conditions.

Findings

The $1/k^4$ tail magnitude equals the adiabatic energy derivative times a constant.

The relation holds at any temperature and for any large scattering length.

Connections between the tail and energy change rates during dynamic scattering length sweeps.

Abstract

It is well known that the momentum distribution of the two-component Fermi gas with large scattering length has a tail proportional to $1/k^4$ at large $k$. We show that the magnitude of this tail is equal to the adiabatic derivative of the energy with respect to the reciprocal of the scattering length, multiplied by a simple constant. This result holds at any temperature (as long as the effective interaction radius is negligible) and any large scattering length; it also applies to few-body cases. We then show some more connections between the $1/k^4$ tail and various physical quantities, in particular the rate of change of energy in a DYNAMIC sweep of the inverse scattering length.