RT info:eu-repo/semantics/doctoralThesis
T1 Quantum vacuum energy in cavities: from singular interactions to magnetodielectrics
A1 Romaniega Sancho, César
A2 Universidad de Valladolid. Escuela de Doctorado
K1 Física matemática
K1 Mathematical Physics
K1 Física Matemática
K1 2212.12 Teoría Cuántica de Campos
AB This thesis presents an analysis of the Casimir-Lifshitz effect for configurations of two objects, being one of them contained within the other. The first of the two parts of this work is devoted to the construction and study of a particular family of potentials that will be used for mimicking the bodies. The aim is to employ a potential simple enough for obtaining some nontrivial analytical results. This will help us to gain some insight in the properties of the quantum vacuum for these systems and thus be able to present general results for more realistic systems. To that end, we use a generalization of the Dirac $\delta$, the so-called $\delta$-$\delta'$ interaction, extending the one-dimensional definition to spherical systems for spatial dimension $d\geq2$. The definition is based on constructing self-adjoint extensions of the original Hamiltonian. We perform a study of the domain and spectrum of the resulting operator, indicating some possible applications in quantum mechanics, in particular within the context of mean-field nuclear models.  For this reason, we add {nonsingular} potentials to the  $\delta$-$\delta'$ interaction such as the spherical well and a Coulombic term, suitable to describe neutron and proton energy levels. We show that general features of the low-energy states can be obtained, indicating how these singular interactions can be used as a first approximation for real physical systems in certain contexts.The second part of the thesis is devoted to the proper study of the vacuum energy in cavity configurations. The main goal is to expand the analysis of the Casimir effect to this kind of configurations, establishing some general results on the sign of the energy and pressure. Thus, we first study a massless scalar field in the presence of two concentric $\delta$-$\delta'$ spheres. For computing the pressure on the spheres, the interaction energy between them and the self-energy should be considered. On this basis, we first study the interaction between the spheres employing the TGTG representation. The interaction energy is known to be free of divergences. However, this is not  the case for the self-energy. In order to regularize this quantity we employ the zeta function regularization method. Studying the structure of the divergences we find a one-parameter family of potentials in which the self-energy and self-pressure are unambiguously defined. The latter is based on the cancellation of the heat kernel coefficient $a_2$, so no renormalization procedure is needed. Bearing in mind the results obtained for the interaction energy for the scalar field, some general results for the electromagnetic field are obtained {also employing the TGTG representation}. In particular, we consider two different configurations: a dielectric sphere enclosed within an arbitrarily shaped magnetodielectric cavity and a  dielectric object with a spherical cavity in which another arbitrarily shaped magnetodielectric object is enclosed. For the latter, some new results in classical scattering theory for experiments in which source and detector are inside an object are presented. As for the scalar field, the self-energy is also considered when computing the total pressure. In this case, for one of the few configurations in which the self-energy is unambiguously defined for material bodies, a dilute dielectric ball.
YR 2021
FD 2021
LK https://uvadoc.uva.es/handle/10324/60184
UL https://uvadoc.uva.es/handle/10324/60184
LA eng
NO Escuela de Doctorado
DS UVaDOC
RD 22-dic-2024