Multipulse phases in k-mixtures of Bose-Einstein condensates

TL;DR

This paper proves the existence of multi-pulse phase-separated solutions in k-component Bose-Einstein condensates modeled by coupled nonlinear Schrödinger equations, revealing how components separate into many domains as competition increases.

Contribution

It establishes the existence of positive radial solutions and describes their multi-pulse phase separation behavior in the large competition limit.

Findings

Components separate into many pulses as competition grows.

Pulse locations are linked to oscillations of scalar solutions.

The results provide a theoretical basis for phase separation in Bose-Einstein condensates.

Abstract

For a competitive system of k coupled nonlinear Schroedinger equations we prove the existence, when the competition parameter is large, of positive radial solutions on R^N. We show that, when the competition parameter goes to infinity, the profile of each component separates, in many pulses, from the others. Moreover, we can prescribe the location of such pulses in terms of the oscillations of the changing-sign solutions of the scalar nonlinear Schroedinger equation. Within an Hartree-Fock approximation, this provides a theoretical indication of phase separation into many nodal domains for the k-mixtures of Bose-Einstein condensates.