Finite temperature and dissipative corrections to the Gross-Pitaevskii equation from $\lambda\Phi^4$ one loop contributions

TL;DR

This paper derives a generalized Gross-Pitaevskii equation incorporating finite temperature and dissipative effects from one-loop quantum corrections in a scalar field theory, aiming to better understand Bose-Einstein condensate phase transitions.

Contribution

It introduces a relativistic finite-temperature Gross-Pitaevskii-like equation derived from quantum field theory, including thermodynamic and viscosity effects, for the first time.

Findings

Generalized Gross-Pitaevskii equation at finite temperature

Expressions for thermodynamic and viscosity properties

Potential insights into BEC phase transitions from quantum field theory

Abstract

Starting with a scalar field in a thermal bath and using the one loop quantum correction potential, we rewrite the Klein-Gordon equation in its thermodynamical representation and study the behavior of this scalar field due to temperature variations in the equations of motion. We find the generalization of a Gross-Pitaevskii like equation for a relativistic Bose gas with finite temperature, the corresponding thermodynamic and viscosity expressions, and an expression for the postulate of the first law of the thermodynamics for this BECs. We also propose that the equations obtained might help to explain at some level the phase transition of a Bose-Einstein Condensate in terms of quantum field theory in a simple way.