arXiv subjects

C. Romaniega

Publications and source records attributed to C. Romaniega.

5 recordsLinked to original sources

arXiv2022

Casimir self-energy of a δ-δ' sphere

We extend previous work on the vacuum energy of a massless scalar field in the presence of singular potentials. We consider a single sphere denoted by the so-called "delta-delta prime" interaction. Contrary to the Dirac delta potential, we find a nontrivial one-parameter family of potentials such that the regularization procedure gives an unambiguous result for the Casimir self-energy. The procedure employed is based on the zeta function regularization and the cancellation of the heat kernel coefficient a_2. The results obtained are in agreement with particular cases, such as the Dirac delta or Robin and Dirichlet boundary conditions.

hep-th↗

arXiv2021

Casimir-Lifshitz pressure on cavity walls

We extend our previous work on the electromagnetic Casimir-Lifshitz interaction between two bodies when one is contained within the other. We focus on the fluctuation-induced pressure acting on the cavity wall, which is assumed to be spherical. This pressure can be positive or negative depending on the response functions describing the bodies and the medium filling the cavity. However, we find that, under general hypotheses, the sign is independent of the geometry of the configuration. This result is based on the representation of the Casimir-Lifshitz energy in terms of transition operators. In particular, we study the components of these operators related to inside scattering amplitudes, adapting the invariant imbedding procedure to this unfamiliar scattering setup. We find that our main result is in agreement with the Dzyaloshinskii-Lifshitz-Pitaevskii result, which is obtained as a limiting case.

quant-ph↗

arXiv2021

Repulsive Casimir-Lifshitz pressure in closed cavities

We consider the interaction pressure acting on the surface of a dielectric sphere enclosed within a magnetodielectric cavity. We determine the sign of this quantity regardless of the geometry of the cavity for systems at thermal equilibrium, extending the Dzyaloshinskii-Lifshitz-Pitaevskii result for homogeneous slabs. As in previous theorems regarding Casimir-Lifshitz forces, the result is based on the scattering formalism. In this case the proof follows from the variable phase approach of electromagnetic scattering. With this, we present configurations in which both the interaction and the self-energy contribution to the pressure tend to expand the sphere.

quant-ph↗

arXiv2020

An approximation to the Woods-Saxon potential based on a contact interaction

We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial $δ$-$δ'$ contact interaction at the well edge. This contact potential is defined by appropriate matching conditions for the radial functions, thereby fixing a self adjoint extension of the non-singular Hamiltonian. Since this model admits exact solutions for the wave function, we are able to characterize and calculate the number of bound states. We also extend some well-known properties of certain spherically symmetric potentials and describe the resonances, defined as unstable quantum states. Based on the Woods-Saxon potential, this configuration is implemented as a first approximation for a mean-field nuclear model. The results derived are tested with experimental and numerical data in the double magic nuclei $^{132}$Sn and $^{208}$Pb with an extra neutron.

nucl-th↗

arXiv2018

Hyperspherical ${δ\text{-}δ^\prime}$ potentials

The spherically symmetric potential $a \,δ(r-r_0)+b\,δ' (r-r_0)$ is generalised for the $d$-dimensional space as a characterisation of a unique selfadjoint extension of the free Hamiltonian. For this extension of the Dirac delta, the spectrum of negative, zero and positive energy states is studied in $d\geq 2$, providing numerical results for the expectation value of the radius as a function of the free parameters of the potential. Remarkably, only if $d=2$ the $δ$-$δ'$ potential for arbitrary $a>0$ admits a bound state with zero angular momentum.

math-ph↗