Quantum vacuum energy in cavities: from singular interactions to magnetodielectrics
- Autores: César Romaniega Sancho
- Directores de la Tesis: Luis Miguel Nieto (dir. tes.), Inés Cavero Peláez (codir. tes.), Jose María Muñoz Castañeda (codir. tes.)
- Lectura: En la Universidad de Valladolid ( España ) en 2023
- Idioma: inglés
- Tribunal Calificador de la Tesis: Javier Negro Vadillo (presid.), Manuel Asorey Carballeira (secret.), Irina Pirozhenko (voc.)
- Programa de doctorado: Programa de Doctorado en Física por la Universidad de Valladolid
- Materias:
- Enlaces
- Tesis en acceso abierto en: UVADOC
- Resumen
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.
