Isobar of an ideal Bose gas within the grand canonical ensemble

TL;DR

This paper analyzes the isobar of an ideal Bose gas in a finite system, deriving precise temperature corrections and revealing zigzag behavior in the temperature-volume plane, with results validated numerically and consistent with prior canonical ensemble studies.

Contribution

It provides exact formulas for supercooling and superheating temperatures with finite-size corrections, and uncovers the zigzag pattern of the isobar for large particle numbers.

Findings

Finite-size corrections to Bose-Einstein condensation temperature.

Zigzag behavior of the isobar on the temperature-volume plane.

Quantitative agreement with canonical ensemble results within 0.1%.

Abstract

We investigate the isobar of an ideal Bose gas confined in a cubic box within the grand canonical ensemble, for a large yet finite number of particles, N. After solving the equation of the spinodal curve, we derive precise formulae for the supercooling and the superheating temperatures which reveal an N^{-1/3} or N^{-1/4} power correction to the known Bose-Einstein condensation temperature in the thermodynamic limit. Numerical computations confirm the accuracy of our analytical approximation, and further show that the isobar zigzags on the temperature-volume plane if N is greater than or equal to 14393. In particular, for the Avogadro's number of particles, the volume expands discretely about 10^5 times. Our results quantitatively agree with a previous study on the canonical ensemble within 0.1% error.