Tamm's surface states and Bose-Einstein condensation

TL;DR

This paper investigates how an energy gap in a 3D Bose gas affects its thermodynamic properties, revealing increased critical temperature, a discontinuity in specific heat, and recovering ideal gas results when the gap vanishes.

Contribution

It provides explicit formulas for thermodynamic quantities of a 3D Bose gas with an energy gap, highlighting the effects of the gap on phase transition properties.

Findings

Critical temperature increases with the energy gap.

Specific heat exhibits a jump-discontinuity for non-zero gaps.

Results reduce to ideal Bose gas when the gap approaches zero.

Abstract

We calculate and discuss the effects on the thermodynamic properties of a 3D Bose gas caused by a gap $\Delta$ in the energy of the particles constituting the gas that without the gap behaves like an ideal Bose gas. Explicit formulae with arbitrary $\Delta$ values are discussed for: the critical temperature which increases as the gap grows; the condensate fraction; the internal energy; and the constant-volume specific heat found to possess a jump-discontinuity for any $\Delta$ different from zero. Three dimensional infinite ideal Bose gas results are recovered when we the energy gap goes to zero.