Fermion Particle Production in Dynamical Casimir Effect in a Three Dimensional Box

In this paper we investigate the problem of fermion creation inside a three dimensional box. We present an appropriate wave function which satisfies the Dirac equation in this geometry with MIT bag model boundary condition. We consider walls of the box to have dynamic and introduce the time evolution of the quantized field by expanding it over the 'instantaneous basis'. We explain how we can obtain the average number of particles created. In this regard we find the Bogliubove coefficients. We consider an oscillation and determine the coupling conditions between different modes that can be satisfied depending on the cavity's spectrum. Assuming the parametric resonance case we obtain an expression for the mean number of created fermions in each mode of an oscillation and their dynamical Casimir energy.Comment: 5 pages, no figur

Casimir Energy For a Massive Dirac Field in One Spatial Dimension: A Direct Approach

In this paper we calculate the Casimir energy for a massive fermionic field confined between two points in one spatial dimension, with the MIT Bag Model boundary condition. We compute the Casimir energy directly by summing over the allowed modes. The method that we use is based on the Boyer's method, and there will be no need to resort to any analytic continuation techniques. We explicitly show the graph of the Casimir energy as a function of the distance between the points and the mass of the fermionic field. We also present a rigorous derivation of the MIT Bag Model boundary condition.Comment: 8 Pages, 4 Figure

The effects of an electrolyte solution on screening the Casimir interaction between two symmetric double-layered media

Using the scattering approach besides the Matsubara formalism, this paper aims at investigating screening and intensifying the thermal Casimir force in an electrolyte solution surrounded by two layers of local media within two semispaces. The electric field in an electrolyte solution is decomposed into its transverse and longitudinal components. We construct the reflection matrix describing the combination of the transverse and the longitudinal modes contribution to the incident wave to make the reflection wave for zero and nonzero Matsubara frequencies, individually. It is shown that the longitudinal modes contribution to the Casimir interaction in the Hamaker coefficient is significant only at zero frequency, and it shows that the presence of layers on the substrates intensifies the transverse modes contribution to the Hamaker coefficient in both the conductor and insulator media. It is illustrated that screening in the Hamaker coefficient shows similar behavior for different layers of the conductor and the insulator. Our calculations reveal that increasing the electrolyte’s concentration increases the Hamaker coefficient. Furthermore, the longitudinal modes contribution to the Hamaker coefficient—present due to the ions—is weaker if the electrolyte is surrounded by a conductor rather than being surrounded by a dielectric media. Interestingly, the zero-frequency portion of this coefficient asymptotically reaches its longitudinal contribution at zero frequency for different layers and different concentrations. Our investigation illustrates that in the presence of an electrolyte solution within two dielectric layers surrounded by two other dielectric semispaces, the intensification of the Casimir force per unit area becomes weaker in comparison to the case in which the solution is absent in such a system