Quantum Brownian motion induced by an inhomogeneous tridimensional space and a \(S^1\times R^3\) topological space-time

In this paper we investigate the Quantum Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless scalar field in (3 + 1)-dimensional Minkowski spacetime with distinct conditions (Dirichlet, Neumann, mixed and quasiperiodic). The modes of the field are confined and co...

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Bibliographic Details
Published in:arXiv.org 2023-04
Main Authors: Ferreira, Éwerton J B, Guedes, Eliza M B, Herondy F Santana Mota
Format: Article
Language:English
Subjects:
Brownian motion
Dirichlet problem
Dispersions
Mathematical analysis
Minkowski space
Scalars
Online Access:Get full text
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Summary:In this paper we investigate the Quantum Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless scalar field in (3 + 1)-dimensional Minkowski spacetime with distinct conditions (Dirichlet, Neumann, mixed and quasiperiodic). The modes of the field are confined and compactified to a finite length region, which consequently provides a natural measure scale for the system. Useful expressions for the Wightman function have been obtained, which allow us to calculate analytical expressions for the velocity dispersion in all condition cases considered. We also obtain expressions for the velocity dispersion in the short and late time regimes. Finally, we exhibit some graphs in order to show the behavior of the velocity dispersions, discussing important divergencies that are present in our results.
ISSN:2331-8422
DOI:10.48550/arxiv.2301.05934