The Gross-Pitaevskii equation for a infinite square-well with a delta-function barrier

TL;DR

This paper analytically solves the Gross-Pitaevskii equation for a double-well potential with a delta-function barrier, revealing symmetric and asymmetric solutions, their bifurcations, and stability properties.

Contribution

It provides new analytical and numerical solutions for the Gross-Pitaevskii equation in a double-well potential with a delta barrier, including bifurcation analysis and stability considerations.

Findings

Existence of symmetric and asymmetric solutions

Bifurcation of solutions depending on interaction type

Preliminary stability analysis of states

Abstract

The Gross-Pitaevskii equation is solved by analytic methods for an external double-well potential that is an infinite square well plus a $\delta$-function central barrier. We find solutions that have the symmetry of the non-interacting Hamiltonian as well as asymmetric solutions that bifurcate from the symmetric solutions for attractive interactions and from the antisymmetric solutions for repulsive interactions. We present a variational approximation to the asymmetric state as well as an approximate numerical approach. Stability of the states is briefly considered.