An Adiabatic Theorem for the Gross-Pitaevskii Equation

TL;DR

This paper establishes an adiabatic theorem for the non-autonomous Gross-Pitaevskii equation with a weak trap, assuming the potential decays at infinity and has a single bound state, advancing understanding of quantum dynamics in such systems.

Contribution

It provides a rigorous proof of an adiabatic theorem for the Gross-Pitaevskii equation under specific conditions on the external potential, which was previously unaddressed.

Findings

Proves adiabatic behavior for the Gross-Pitaevskii equation with a weak trap

Shows the external potential's decay and bound state conditions are sufficient

Enhances theoretical understanding of quantum systems with time-dependent potentials

Abstract

We prove an adiabatic theorem for the non-autonomous Gross-Pitaevskii equation in the case of a weak trap. More precisely, we assume that the external potential decays suitably at infinity and admits exactly one bound state.