The forces on a single interacting Bose-Einstein condensate

TL;DR

This paper investigates the boundary conditions and phase transitions of a single Bose-Einstein condensate confined between slabs, analyzing forces like surface tension and Casimir force in different statistical ensembles.

Contribution

It demonstrates ensemble-dependent boundary conditions and phase transitions in a confined Bose-Einstein condensate using the double parabola approximation.

Findings

Ground state with Robin BC is favored in GCE.

System transitions from Robin to Dirichlet BC in CE depending on slab separation.

First-order phase transition observed in the ground state.

Abstract

Using double parabola approximation for a single Bose-Einstein condensate confined between double slabs we proved that in grand canonical ensemble (GCE) the ground state with Robin boundary condition (BC) is favored, whereas in canonical ensemble (CE) our system undergoes from ground state with Robin BC to the one with Dirichlet BC in small-$L$ region and vice versa for large-$L$ region and phase transition in space of the ground state is the first order. The surface tension force and Casimir force are also considered in both CE and GCE in detail.