Efeitos de flutuações quânticas de vácuo de campos escalares em observáveis físicos em espaços-tempo com topologia não trivial - Farias, Klecio Emanuel Lima de (2022)
In the present thesis, we consider the effects of quantum vacuum fluctuations of scalar fields as a consequence of space-time with non-trivial topology, boundary conditions and temperature corrections. The first physical system we investigate is that of a charged scalar field whose quantum modes propagate in a conical spacetime, such as cosmic string or disclination. The scalar field is also subject to a quasi-periodic condition that generalizes the well-known periodic and anti-periodic conditions widely used in literature. In this sense, we calculate exact and closed analytical expressions for the two-point Wightman function, for the vacuum expected value (VEV) of the scalar field squared, as well as for the VEV of all components of the energy-momentum tensor. Furthermore, we also consider the VEV of the current density induced by the system in question and obtained that the only non-zero component is the azimuthal one. Finally, we analyze particular cases for the obtained expressions assuming specific values for the parameters associated with the conical space-time and quasi-periodicity [1]. A second physical system considered is that of a classical liquid, which may effectively be described in terms of its quantized sound vibrations, that is, in terms of phonons. In the effective description considered, the phonons are characterized by a non-massive real scalar field that obeys an effective Klein-Gordon equation, with the speed of light replaced by the speed of sound. Thus, we consider two scenarios to analyze the propagation of sound modes. The first one is the Minkowski space-time, where the real scalar field is subject to Dirichlet, Neumann and mixed boundary conditions applied to one and two parallel planes. In the other scenario, we take into account that the quantized modes of the scalar field propagate in the space-time describing the conical topology of the cosmic string, or declination, and obey a quasi-periodic boundary condition. Thus, in each scenario, we obtain closed analytical expressions for the two-point function and the renormalized mean square density fluctuation of the liquid. We point out specific characteristics of this physical observable by plotting its graphs [2]. To complement the analysis of the phonon system, as a generalization of the work conducted in Ref. [2], we have studied now quantum fluctuations, at finite temperature, of a classical liquid induced by the conical topology of a cosmic string, or disclination, as well as by a quasi-periodic boundary condition. In this context, we consider again a phonon field representing quantum excitations of the liquid density. The real scalar field describing quantum excitations obeys an effective Klein-Gordon equation with the speed of sound replaced by the speed of light. We obtain closed analytic expressions for the Hadamard thermal function and, consequently, for the fluctuations of the renormalized mean square density of the liquid along with thermodynamic quantities such as internal energy, free energy, total energy and entropy densities. We also discuss some limiting cases, including low and high-temperature regimes and situations in which there is either conical space-time or quasi-periodicity [3].