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In this paper we study the behavior of the Casimir energy of a multi-cavity across the transition from the metallic to the superconducting phase of the constituting plates. Our analysis is carried out in the framework of the ARCHIMEDES experiment, aiming at measuring the interaction of the electromagnetic vacuum energy with a gravitational field. For this purpose it is foreseen to modulate the Casimir energy of a layered structure composing a multi-cavity coupled system by inducing a transition from the metallic to the superconducting phase. This implies a thorough study of the behavior of the cavity, where normal metallic layers are alternated with superconducting layers, across the transition. Our study finds that, because of the coupling between the cavities, mainly mediated by the transverse magnetic modes of the radiation field, the variation of energy across the transition can be very large.
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We apply a perturbative approach to evaluate the Casimir energy for a massless real scalar field in 3+1 dimensions, subject to Dirichlet boundary conditions on two surfaces. One of the surfaces is assumed to be flat, while the other corresponds to a small deformation, described by a single function $eta$, of a flat mirror. The perturbative expansion is carried out up to the fourth order in the deformation $eta$, and the results are applied to the calculation of the Casimir energy for corrugated mirrors in front of a plane. We also reconsider the proximity force approximation within the context of this expansion.
In this paper we compute the Casimir energy for a coupled fermion-pseudoscalar field system. In the model considered in this paper the pseudoscalar field is textit{static} and textit{prescribed} with two adjustable parameters. These parameters determine the values of the field at infinity ($pm theta_0$) and its scale of variation ($mu$). One can build up a field configuration with arbitrary topological charge by changing $theta_0$, and interpolate between the extreme adiabatic and non-adiabatic regimes by changing $mu$. This system is exactly solvable and therefore we compute the Casimir energy exactly and unambiguously by using an energy density subtraction scheme. We show that in general the Casimir energy goes to zero in the extreme adiabatic limit, and in the extreme non-adiabatic limit when the asymptotic values of the pseudoscalar field properly correspond to a configuration with an arbitrary topological charge. Moreover, in general the Casimir energy is always positive and on the average an increasing function of $theta_0$ and always has local maxima when there is a zero mode, showing that these configurations are energetically unfavorable. We also compute and display the energy densities associated with the spectral deficiencies in both of the continua, and those of the bound states. We show that the energy densities associated with the distortion of the spectrum of the states with $E>0$ and $E<0$ are mirror images of each other. We also compute and display the Casimir energy density. Finally we compute the energy of a system consisting of a soliton and a valance electron and show that the Casimir energy of the system is comparable with the binding energy.
We compute the Casimir energy for a system consisting of a fermion and a pseudoscalar field in the form of a prescribed kink. This model is not exactly solvable and we use the phase shift method to compute the Casimir energy. We use the relaxation method to find the bound states and the Runge-Kutta-Fehlberg method to obtain the scattering wavefunctions of the fermion in the whole interval of $x$. The resulting phase shifts are consistent with the weak and strong forms of the Levinson theorem. Then, we compute and plot the Casimir energy as a function of the parameters of the pseudoscalar field, i.e. the slope of $phi(x)$ at x=0 ($mu$) and the value of $phi(x)$ at infinity ($theta_0$). In the graph of the Casimir energy as a function of $mu$ there is a sharp maximum occurring when the fermion bound state energy crosses the line of E=0. Furthermore, this graph shows that the Casimir energy goes to zero for $murightarrow 0$, and also for $murightarrow infty$ when $theta_0$ is an integer multiple of $pi$. Moreover, the graph of the Casimir energy as a function of $theta_0$ shows that this energy is on the average an increasing function of $theta_0$ and has a cusp whenever there is a zero fermionic mode. We finally compute the total energy of a system consisting of a valence fermion in the ground state. Most importantly, we show that this energy (the sum of the Casimir energy and the energy of the fermion) is minimum when the background field has winding number one, independent of the details of the background profile. Throughout the paper we compare our results with those of a simple exactly solvable model, where a piece-wise linear profile approximates the kink. We find that the kink is an almost reflectionless barrier for the fermions, within the context of our model.
We perform a theoretical analysis of a setup intended to measure the repulsive (outward) Casimir forces predicted to exist inside of perfectly conducting rectangular cavities. We consider the roles of the conductivity of the real metals, of the temperature and surface roughness. The use of this repulsive force to reduce friction and wear in micro and nanoelectromechanical systems (MEMS and NEMS) is also considered.
The ALADIN experiment aims at observing how the critical magnetic field of a superconducting Aluminum film is modified, when it constitutes one of the reflecting surfaces of a Casimir cavity. If successful, such an observation would reveal the influence of vacuum energy on the superconducting phase transition. In this paper a rigorous analysis of experimental data is reported, the results are discussed and compared with theoretical predictions based on Lifshitz theory of dispersion forces, and the BCS formula for the optical conductivity of superconductors. The main novelty with respect to a previous data analysis by some of the authors, is the use of a cross-correlation method which is more rigorous and leads to better estimates.
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