# Critical behavior at the spatial boundary of a trapped inhomogeneous Bose-Einstein condensate

## TL;DR

This paper studies the critical behavior at the boundary of the Bose-Einstein condensate in inhomogeneous trapped quantum gases, revealing universal scaling laws through numerical simulations of the 3D Bose-Hubbard model.

## Contribution

It demonstrates the critical phenomena at the BEC boundary in inhomogeneous traps and links it to the universality class of the homogeneous transition, supported by numerical evidence.

## Key findings

- Critical behavior occurs at the BEC boundary.
- Scaling behavior is governed by the universality class of the homogeneous transition.
- Numerical simulations confirm the theoretical predictions.

## Abstract

We investigate some aspects of the Bose-Einstein condensation (BEC) of quantum gases in the presence of inhomogeneous conditions. We consider three-dimensional (3D) quantum gases trapped by an external potential when the temperature is sufficiently low to show a BEC phase region around the center of the trap. If the trap is sufficiently large, different phases may coexist in different space regions, when moving from the center of the trap. We show that the quantum gas develops a peculiar critical behavior at the boundary of the BEC region, whose scaling behavior is controlled by the universality class of the homogenous BEC transition. We provide numerical evidence of this phenomenon, for lattice atomic gases modeled by the 3D Bose-Hubbard Hamiltonian.