Infinite Statistics and the Gross Pitaevskii Equation

TL;DR

This paper explores the behavior of a system obeying infinite statistics, clarifying its inability to undergo condensation and deriving a Gross Pitaevskii-like equation for its dynamics at low temperatures.

Contribution

It derives a Gross Pitaevskii-like equation for infinite statistics systems, extending the understanding of quantum gases beyond Bose-Einstein statistics.

Findings

Infinite statistics systems cannot undergo condensation.

The derived equation describes low-temperature dynamics similar to Bose-Einstein condensates.

Provides a theoretical framework for infinite statistics in quantum gases.

Abstract

We clarify that an ideal gas obeying infinite statistics cannot undergo condensation. Then we derive the dynamic equation for an identical particle system obeying infinite statistics under external potential and inter-particle interaction. The derivation utilizes the Hamiltonian written in terms of the number operators and the transition number operators. At a very low temperature, where one can discard the dynamics of the excited occupation level, the dynamic of an infinite statistics system can be described by the Gross Pitaevskii equation, similar to the Bose-Einstein case.