Scaling law for the size dependence of a finite-range quantum gas

TL;DR

This paper develops a scaling law for finite-range quantum gases, linking size dependence to thermodynamic accuracy and free energy response, extending previous surface interaction methods to dense quantum systems.

Contribution

It introduces a new approximate size-dependence scaling law for finite-range quantum gases and relates it to free energy response, expanding the applicability of surface interaction criteria.

Findings

Derived an approximate size-scaling law for finite-range quantum gases.

Established the equivalence of the criterion to free energy response analysis.

Confirmed the criterion's complementarity to simulation-based estimates.

Abstract

In a recent work [Reible et al., Phys. Rev. Res. 5, 023156, 2023], it has been shown that the mean particle-particle interaction across an ideal surface that divides a system into two parts, can be employed to estimate the size dependence for the thermodynamic accuracy of the system. In this work we propose its application to systems with finite range interactions that models a dense quantum gases and derive an approximate size-dependence scaling law. In addition, we show that the application of the criterion is equivalent to the determination of a free energy response to a perturbation. The latter result confirms the complementarity of the criterion to other estimates of finite-size effects based on direct simulations and empirical structure or energy convergence criteria.