The Paradox of Bose-Einstein Condensation

TL;DR

This paper clarifies the paradox of Bose-Einstein condensation by showing it involves multiple low-lying states rather than solely the ground state, resolving the apparent contradiction between macroscopic phenomena and microscopic occupancy.

Contribution

It provides a simple derivation demonstrating that Bose-Einstein condensation occurs into multiple low-lying states, not just the ground state, resolving a longstanding paradox.

Findings

Bose-Einstein condensation involves multiple low-lying states.

The derivation clarifies the macroscopic phenomena associated with BEC.

The paradox is resolved by understanding the distribution of particles across states.

Abstract

The paradox of Bose-Einstein condensation is that phenomena such as the $\lambda$-transition heat capacity and superfluid flow are macroscopic, whereas the occupancy of the ground state is microscopic. This contradiction is resolved with a simple derivation for ideal bosons that shows Bose-Einstein condensation is into multiple low-lying states, not just the ground state.