Quantum Brownian motion for a particle in analog expanding cosmologies in the presence of disclination

TL;DR

This paper investigates the quantum Brownian motion of a scalar particle in an analog expanding cosmology modeled by a Bose-Einstein condensate, analyzing phonon dynamics and velocity dispersions in a curved spacetime with a disclination.

Contribution

It provides exact solutions for scalar field modes in an analog cosmological spacetime with disclination, and computes the particle's velocity dispersion in this setting.

Findings

Exact solutions for scalar field modes in the analog spacetime.

Analysis of velocity dispersion showing consistency with theoretical expectations.

Graphical results illustrating the effects of disclination and expansion on particle motion.

Abstract

In this paper we study the quantum brownian motion of a scalar point particle in the analog Friedman-Robertson-Walker spacetime in the presence of a disclination, in a condensed matter system. The analog spacetime is obtained as an effective description of a Bose-Einstein condensate in terms of quantum excitations of sound waves, named phonons. The dynamics of the phonons is described by a massless real scalar field whose modes are also subjected to a quasi-periodic condition. In this sense, we find exact solutions for the real scalar field in this scenario and calculate the two-point function which makes possible to analyze the mean squared velocity dispersion of the particle in all directions. We, thus, analyze some interesting particular cases and show some graphs where it is possible to see the consistency of our results.