Exact Thermodynamics For Weakly Interacting Normal-Phase Quantum Gases: Equations of State For All Partial Waves

TL;DR

This paper derives exact equations of state for weakly interacting quantum gases across all partial waves, extending known thermodynamics beyond s-wave interactions and providing tools for ultracold atom experiments.

Contribution

It provides the first systematic closed-form thermodynamic expressions for arbitrary partial wave interactions in weakly interacting quantum gases.

Findings

Derived equations of state for all partial waves

Analyzed thermodynamic quantities like contact and compressibility

Enhanced thermometry methods for ultracold gases

Abstract

While the thermodynamics for bosonic systems with weak $s$-wave interactions has been known for decades, a general and systematic extension to higher partial waves has not yet been reported. We provide closed-form expressions for the equations of state for weakly interacting systems with arbitrary partial waves in the normal phase. Thermodynamics, including contact, loss rate, and compressibility, are derived over the entire temperature regime. Our results offer an improved thermometer for ultracold atoms and molecules with weak high-partial wave interactions.