Quantum corrections to the thermodynamic potential of interacting Bosons in a trap

TL;DR

This paper analytically calculates quantum corrections to the thermodynamic potential of a confined weakly interacting Bose gas at finite temperature, highlighting their significance for finite-size effects in large systems.

Contribution

It introduces a systematic $ abla$ expansion method to compute quantum corrections for confined Bosons, providing explicit analytical results for a 3D harmonic trap.

Findings

Quantum corrections are convergent when $kT$ exceeds energy level spacing.

Quantum corrections diminish as particle number increases.

Finite size effects are influenced by quantum corrections.

Abstract

We calculate the quantum corrections of the thermodynamic quantities of a system of confined Bosons at finite temperature. Systematically quantum corrections are written in a series of $\hbar$, which is convergent when $kT$ is much larger than the spacing between energy levels of the system. We apply this method to calculate analytically the thermodynamic potential of a weakly interacting Bose-gas confined in 3-d harmonic oscillator potential. For large number of particles, quantum corrections become small, and contribute to the finite size corrections to scaling.