The Gross-Pitaevskii functional with a random background potential and condensation in the single particle ground state

TL;DR

This paper investigates the behavior of the Gross-Pitaevskii ground state in the presence of a random background potential, identifying conditions under which it aligns with the ground state of the background Hamiltonian.

Contribution

It characterizes a specific interaction regime where the Gross-Pitaevskii ground state and the background Hamiltonian ground state asymptotically coincide.

Findings

Identification of a regime where the two ground states align

Asymptotic equivalence of the states in the specified regime

Applicable to both discrete and continuous models

Abstract

For discrete and continuous Gross-Pitaevskii energy functionals with a random background potential, we study the Gross-Pitaevskii ground state. We characterize a regime of interaction coupling when the Gross-Pitaevskii ground state and the ground state of the random background Hamiltonian asymptotically coincide.