Casimir Effect in systems in and out of Equilibrium

This thesis consists on two separate parts. In the first part, we discuss about the nature of the Casimir effect as the response of a fluctuant medium to the breakdown of the translation symmetry because the presence of intrusions in that medium. To do so, we present a dynamical approximation of Casimir effect, which generalizes Casimir effect studies to out of equilibrium steady states. The equilibrium known case is recovered as a particular case, including the case of electromagnetic (EM) Casimir effect generated because of quantum fluctuations. This formalism also allows us to define (and calculate) the variance of Casimir forces. In the second part of this thesis, by the use of a Multiscattering formalism, we study the nature of the multibody Casimir effect. We demonstrate that the Casimir force and energy between two spheres in presence of a plate (perfect metal objects all of them) is non-monotonous with the distance between spheres and between sphere and plate. We derive the Pairwise Summation Approximation (PSA) of the EM field from this multiscattering formalism for generalized dielectrics, including magnetic responses and Topological Insulators as an example of magnetoelectric couplings. We also study the nonmonotonous behavior of the entropy with the temperature for a system of two perfect metal spheres and describes the Casimir energy between non-parallel cylinders, a geometry not studied until now to our knownledge.Comment: Ph.D. Thesis, 10 chapters, 231 pages and 33 figures. University Complutense of Madrid, Spain, 28th October 201

Dirac fermion time-Floquet crystal: manipulating Dirac points

We demonstrate how to control the spectra and current flow of Dirac electrons in both a graphene sheet and a topological insulator by applying either two linearly polarized laser fields with frequencies $\omega$ and $2\omega$ or a monochromatic (one-frequency) laser field together with a spatially periodic static potential(graphene/TI superlattice). Using the Floquet theory and the resonance approximation, we show that a Dirac point in the electron spectrum can be split into several Dirac points whose relative location in momentum space can be efficiently manipulated by changing the characteristics of the laser fields. In addition, the laser-field controlled Dirac fermion band structure -- Dirac fermion time-Floquet crystal -- allows the manipulation of the electron currents in graphene and topological insulators. Furthermore, the generation of dc currents of desirable intensity in a chosen direction occurs when applying the bi-harmonic laser field which can provide a straightforward experimental test of the predicted phenomena.Comment: 9 pages, 7 figures, version that will appear in Phys. Rev.

Effect of Curvature and Confinement on the Casimir-Polder Interaction

Modifications of Casimir-Polder interactions due to confinement inside a cylindrical cavity and due to curvature in- and outside the cavity are studied. We consider a perfectly conducting cylindrical shell with a single particle (atom or macroscopic sphere) located next to its interior or exterior surface, or two atoms placed inside the shell. By employing the scattering approach, we obtain the particle-cavity interaction and the modification of the two-particle interaction due to the cavity. We consider both retardation and thermal effects. While for the atoms a dipole description is sufficient, for the macroscopic sphere we sum (numerically) over many multipole fluctuations to compute the interaction at short separations. In the latter limit we compare to the proximity approximation and a gradient expansion and find agreement. Our results indicate an confinement induced suppression of the force between atoms. General criteria for suppression and enhancement of Casimir interactions due to confinement are discussed.Comment: 13 pages, 11 figure

Three-body Casimir effects and non-monotonic forces

Casimir interactions are not pair-wise additive. This property leads to collective effects that we study for a pair of objects near a conducting wall. We employ a scattering approach to compute the interaction in terms of fluctuating multipoles. The wall can lead to a non-monotonic force between the objects. For two atoms with anisotropic electric and magnetic dipole polarizabilities we demonstrate that this non-monotonic effect results from a competition between two- and three body interactions. By including higher order multipoles we obtain the force between two macroscopic metallic spheres for a wide range of sphere separations and distances to the wall.Comment: 4 pages, 4 figure