Quantum Brownian motion induced by a scalar field in Einstein universe under Dirichlet and Neumann boundary conditions

TL;DR

This study investigates how boundary conditions in an Einstein universe affect the quantum Brownian motion of a particle caused by vacuum fluctuations of a scalar field, revealing anisotropic effects and divergences.

Contribution

It provides new analytical expressions for the renormalized momentum dispersion of a particle in Einstein universe with Dirichlet and Neumann boundary conditions, highlighting boundary-induced anisotropy.

Findings

Distinct dispersions for different momentum components due to boundary conditions

Loss of homogeneity and isotropy in the particle’s motion

Presence of divergences related to universe's compactness and boundary effects

Abstract

In this paper, the Quantum Brownian motion of a point particle induced by the quantum vacuum fluctuations of a real massless scalar field in Einstein universe under Dirichlet and Neumann boundary conditions is studied. Using the Wightman functions, general expressions for the renormalized dispersion of the physical momentum are derived. Distinct expressions are found for the dispersion associated with each component of the particle physical momentum, indicating that the global properties of homogeneity and isotropy of space are lost, as a consequence of the introduced boundary conditions. Divergences also arise and are related to the compact nature of Einstein universe and the introduced boundary conditions.