Contribuições ao estudo do Movimento Browniano Quântico induzido por flutuações quânticas de vácuo em teorias escalares

Abstract

According to Quantum Field Theory, matter and its interactions are described by fundamental structures called fields, which permeate the entire Universe. A fundamental characteristic of quantum fields is that they always fluctuate. In this sense, the concepts of vacuum according to the classical and quantum field theory perspectives is totally different. The first associates the vacuum with a state of complete emptiness. On the other hand, the second viewpoint suggests that, in fact, the (quantum) vacuum corresponds to a chaotic structure, in constant agitation and filled by quantum vacuum fluctuations, resulting from the creation and annihilation of virtual particles. The real existence of these fluctuations is a well-established fact. It is known that they give rise a physical phenomena, such as the Casimir effect and Lamb shift. Another, more recent, effect is the stochastic motion that point particles can obtain due to the influence of these quantum vacuum fluctuations of the fields (e.g. electromagnetic and scalar). This phenomenon is known in the literature as quantum Brownian motion or induced quantum Brownian motion (IQBM), in reference to the classical Brownian Motion that a particle performs, when it is suspended in a fluid with a finite temperature. This is the central theme of this thesis. After a brief review of the necessary formalism and previous calculations of the positive frequency Wightman functions, we study the IQBM in three different scenarios. Following a a la Langevin approach, in the first part of the work, we calculate the velocity dispersion of a particle in a Bose-Einstein condensate with disclination, which simulates the vacuum of an expanding universe of Friedmann-Lemaitre-Robertson-Walker (FLRW) with the presence of a cosmic string. In general, unlike what is found in the literature, we observe anisotropies in the velocity dispersions due to the influence of disclination. In the second scenario, we study the influences of two one-dimensional confinement mechanisms on the IQBM of a particle coupled to a massless scalar field in Minkowski spacetime. In the first case, aiming complement (and transcend) a parallel observed in the literature, between the IQBM by electromagnetic and scalar fields, we investigated the IQBM of a particle in the presence of two perfectly reflecting planes under Dirichlet, Neumann and mixed conditions. In the second case, we study the effects of a one-dimensional compactification with a quasiperiodic condition. In each situation, the velocity and positions dispersions are calculated, observing the existence of anisotropies and that the parameter related to confinement (distance between planes and compactification lengh) works as a natural scale for the system. Finally, we analyze the IQBM of a particle coupled to a massless scalar field in a curved spacetime. In view of technical difficulties, we consider Einstein’s universe, a simplified version of curved spacetime, which corresponds to the static FLRW universe with positive curvature constant. In this latest study, all dispersion components for the physical momentum, as well as for the physical lengths, are equal, indicating a manifestation of the isotropy and homogeneity properties of the universe model.