# On the finite-size effects in two segregated Bose-Einstein condensates restricted by a hard wall

## TL;DR

This paper investigates finite-size effects in two segregated Bose-Einstein condensates confined by a hard wall, analyzing boundary conditions, stability, and phase transitions using the Gross-Pitaevskii equations within the double-parabola approximation.

## Contribution

It identifies all possible boundary conditions and their effects on condensate stability and phase transitions, highlighting the stability of Neumann BC and the wetting transitions from Robin and Dirichlet BCs.

## Key findings

- Neumann boundary condition yields a stable ground state.
- Robin and Dirichlet boundary conditions lead to unstable states.
- Wetting phase transitions occur from the unstable states, with Robin BC being more favorable.

## Abstract

The finite-size effects in two segregated Bose-Einstein condensates (BECs) restricted by a hard wall is studied by means of the Gross-Pitaevskii equations in the double-parabola approximation (DPA). Starting from the consistency between the boundary conditions (BCs) imposed on condensates in confined geometry and in the full space, we find all possible BCs together with the corresponding condensate profiles and interface tensions. We discover two finite-size effects: a) The ground state derived from the Neumann BC is stable whereas the ground states derived from the Robin and Dirichlet BCs are unstable. b) Thereby, there equally manifest two possible wetting phase transitions originating from two unstable states. However, the one associated with the Robin BC is more favourable because it corresponds to a smaller interface tension.