# Phase transition in a Rabi coupled two-component Bose-Einstein condensate

## TL;DR

This paper investigates the phase transition behavior of a two-component Bose-Einstein condensate with Rabi coupling, analyzing asymptotic behaviors and limiting cases as interaction strength varies.

## Contribution

It provides new mathematical estimates and limiting problems for the wave functions of the condensate under different interaction regimes.

## Key findings

- Asymptotic estimates for wave functions in strong and weak interaction limits
- Derivation of limiting problems for the condensate system
- Insights into the phase transition behavior under Rabi coupling

## Abstract

This paper deals with the study of the phase transition of the wave functions of a segregated two-component Bose-Einstein condensate under Rabi coupling. This yields a system of two coupled ODE's where the Rabi coupling is linear in the other wave function and acts against segregation. We prove estimates on the asymptotic behaviour of the wave functions, as the strength of the interaction gets strong or weak. We also derive limiting problems in both cases.