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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 me
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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, ai
The fermion condensate (FC) is investigated for a (2+1)-dimensional massive fermionic field confined on a truncated cone with an arbitrary planar angle deficit and threaded by a magnetic flux. Different combinations of the boundary conditions are imp