Ground State Energy of Mean-field Model of Interacting Bosons in Bernoulli Potential

TL;DR

This paper analyzes the ground state energy of interacting bosons in a Bernoulli potential, establishing conditions for delocalization and deriving asymptotic energy behavior in large systems with weak interactions.

Contribution

It provides a new criterion for delocalization and asymptotic formulas for ground state energy in a mean-field bosonic system with randomness.

Findings

Delocalization condition depends on particle number and interaction strength.

Asymptotic ground state energy per particle derived for large systems with small coupling.

Methods describe the ground state shape in specific random potential realizations.

Abstract

This paper explores a system of interacting `soft core' bosons in the Gross-Pitaevskii mean-field approximation in a random Bernoulli potential. First, a condition for delocalization of the ground state wave function is proved which depends on the number of particles and interaction strength. Using this condition, asymptotics for ground state energy per particle are derived in the large system limit for small values of the coupling constant. Our methods directly describe the shape of the ground state in a given realization of the random potential.