q-Deformed Gross Pitaevskii Equation

TL;DR

This paper derives a q-deformed Gross Pitaevskii equation for bosonic condensates obeying deformed statistics, extending the standard GPE to systems with non-standard quantum statistics at low temperatures.

Contribution

The paper introduces a q-deformed GPE derived from a Hamiltonian approach, applicable to bosonic systems with deformed statistics, expanding the theoretical framework of condensate dynamics.

Findings

Derivation of the q-deformed GPE from a Hamiltonian formalism

Applicable to low-temperature systems with deformed quantum statistics

Shows the dynamics resemble those of Bose-Einstein condensates under deformation

Abstract

We derive the Gross Pitaevskii equation (GPE) for condensate of bosons obeying deformed statistics under external potential and inter-particle interaction. First, we obtain the well-known Schrodinger equation. Using a suitable Hamiltonian for condensate phase and minimizing the free energy of the system, we find out the $q$- deformed GPE. Thus, at very low temperature, where the dynamics of excited-occupation level can be neglected, the dynamics of a deformed statistics system can be described by the GPE, similar to the Bose-Einstein condensate.