Movimento browniano quântico induzido por flutuações de vácuo de um campo escalar não massivo sob condições de Dirichlet

Abstract

In this work, we investigate the Brownian motion of a charged particle induced by fluctuations in the scalar field vacuum in scalar quantum field theory. To introduce the subject, we start with the classical description of Brownian motion, where particles move randomly due to collisions with other particles. In quantum field theory, Brownian motion is described by induced Brownian motion, which arises from fluctuations in the ground state of a quantum field, such as the scalar field. To better understand this phenomenon, it is necessary to comprehend the quantum theory of the scalar field and the associated two-point function, known as the Wightman function. In this regard, we review induced Brownian motion in (1+1)-dimensional Minkowski spacetime under Dirichlet boundary conditions applied to a massless scalar field. Then, motivated by the (1+1)-dimensional case, we study induced Brownian motion in (3+1) dimensions under Dirichlet conditions applied to a massless scalar field, but with the charged particle located between two perfectly reflecting parallel planes. In both scenarios, the Langevin equation is solved, and the particle’s position and velocity dispersions are obtained. Finally, we present graphs illustrating the behavior of the dispersions in the velocity and position of the charged particle, discussing important divergences present in the results and the validity range of the studied model.