arXiv subjects
Publications and source records attributed to Luigi Rosa.
We study the influence of Casimir energy on the critical field of a superconducting film, and we show that by this means it might be possible to directly measure, for the first time, the variation of Casimir energy that accompanies the superconducting transition. It is shown that this novel approach may also help clarifying the long-standing controversy on the contribution of TE zero modes to the Casimir energy in real materials.
Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral representation of photon Green functions, we link them to the evaluation of integrals involving Gamma-functions. Eventually, the full asymptotic expansion of the Feynman photon Green function at small values of the world function, as well as its explicit dependence on the gauge parameter, are obtained without adding by hand a mass term to the Faddeev-Popov Lagrangian. Coincidence limits of second covariant derivatives of the associated Hadamard function are also evaluated, as a first step towards the energy-momentum tensor in the non-minimal case.
Aladin2 is an experiment devoted to the first measurement of variations of Casimir energy in a rigid cavity. The main scientific motivation relies on the possibility of the first demonstration of a phase transition influenced by vacuum fluctuations. The guiding principle of the measurement, based on the behaviour of the critical field for an in-cavity superconducting film, will be only briefly recalled. In this paper, after an introduction to the long term motivations, the experimental apparatus and the results of the first measurement of sensitivity will be presented in detail, particularly in comparison with the expected signal. Last, the most important steps towards the final measurement will be discussed.
We consider a five-layer Casimir cavity, including a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the microwave region) of the reflection coefficient of the film produces a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very small, its magnitude can be comparable to the condensation energy of the superconducting film, and thus causes a significant increase in the value of the critical magnetic field, required to destroy the superconductivity of the film. The proposed scheme might also help clarifying the current controversy about the magnitude of the contribution to Casimir free energy from the TE zero mode, as we find that alternative treatments of this mode strongly affect the shift of critical field.
We consider a Casimir cavity, one plate of which is a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the far infrared) of the reflection coefficient of the film engenders a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very small, its magnitude can be comparable to the condensation energy of the superconducting film, and this gives rise to a number of testable effects, including a significant increase in the value of the critical magnetic field, required to destroy the superconductivity of the film. The theoretical ground is therefore prepared for the first experiment ever aimed at measuring variations of the Casimir energy itself.
Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral representation of photon Green functions, we link them to the evaluation of integrals involving Gamma functions. Eventually, the full asymptotic expansion of the Feynman photon Green function at small values of the world function, as well as its explicit dependence on the gauge parameter, are obtained without adding by hand a mass term to the Faddeev--Popov Lagrangian. Coincidence limits of second covariant derivatives of the associated Hadamard function are also evaluated, as a first step towards the energy-momentum tensor in the non-minimal case.
A detailed investigation is presented of the energy-momentum tensor approach to the evaluation of the force acting on a rigid Casimir cavity in a weak gravitational field. Such a force turns out to have opposite direction with respect to the gravitational acceleration. The order of magnitude for a multi-layer cavity configuration is derived and experimental feasibility is discussed, taking into account current technological resources.
We discuss the possibility of verifying the equivalence principle for the zero-point energy of quantum electrodynamics, by evaluating the force, produced by vacuum fluctuations, acting on a rigid Casimir cavity in a weak gravitational field. The resulting force has opposite direction with respect to the gravitational acceleration; the order of magnitude for a multi-layer cavity configuration is derived and experimental feasibility is discussed, taking into account current technological resources.
Vacuum fluctuations produce a force acting on a rigid Casimir cavity in a weak gravitational field. Such a force is here evaluated and is found to have opposite direction with respect to the gravitational acceleration; the order of magnitude for a multi-layer cavity configuration is analyzed and experimental detection is discussed, bearing in mind the current technological resources.
Electrodynamics for self-interacting scalar fields in spatially flat Friedmann-Robertson-Walker space-times is studied. The corresponding one-loop field equation for the expectation value of the complex scalar field in the conformal vacuum is derived. For exponentially expanding universes, the equations for the Bogoliubov coefficients describing the coupling of the scalar field to gravity are solved numerically. They yield a non-local correction to the Coleman-Weinberg effective potential which does not modify the pattern of minima found in static de Sitter space. Such a correction contains a dissipative term which, accounting for the decay of the classical configuration in scalar field quanta, may be relevant for the reheating stage. The physical meaning of the non-local term in the semiclassical field equation is investigated by evaluating this contribution for various background field configurations.
Zeta-function regularization is applied to evaluate the one-loop effective potential for SO(10) grand-unified theories in de Sitter cosmologies. When the Higgs scalar field belongs to the 210-dimensional irreducible representation of SO(10), attention is focused on the mass matrix relevant for the SU(3)xSU(2)xU(1) symmetry-breaking direction, to agree with low-energy phenomenology of the particle-physics standard model. The analysis is restricted to those values of the tree-level-potential parameters for which the absolute minima of the classical potential have been evaluated. As shown in the recent literature, such minima turn out to be SO(6)xSO(4)- or SU(3)xSU(2)xSU(2)xU(1)-invariant. Electroweak phenomenology is more naturally derived, however, from the former minima. Hence the values of the parameters leading to the alternative set of minima have been discarded. Within this framework, flat-space limit and general form of the one-loop effective potential are studied in detail by using analytic and numerical methods. It turns out that, as far as the absolute-minimum direction is concerned, the flat-space limit of the one-loop calculation about a de Sitter background does not change the results previously obtained in the literature, where the tree-level potential in flat space-time was studied. Moreover, when curvature effects are no longer negligible in the one-loop potential, it is found that the early universe remains bound to reach only the SO(6)xSO(4) absolute minimum.
Dirac's theory of constrained Hamiltonian systems is applied to the minimal conformally invariant SU(5) grand-unified model studied at 1-loop level in a de Sitter universe. For this model, which represents a simple and interesting example of GUT theory and at the same time is a step towards theories with larger gauge group like SO(10), second-class constraints in the Euclidean-time regime exist. In particular, they enable one to prove that, to be consistent with the experimentally established electroweak standard model and with inflationary cosmology, the residual gauge-symmetry group of the early universe, during the whole de Sitter era, is bound to be SU(3) x SU(2) x U(1). Moreover, the numerical solution of the field equations subject to second-class constraints is obtained. This confirms the existence of a sufficiently long de Sitter phase of the early universe, in agreement with the initial assumptions.