Ferminoic Casimir effect between spheres

Abstract

We consider the Casimir interaction between two spheres corresponding to massless Dirac fields with MIT-bag boundary conditions. Using operator approach, we derive the TGTG-formula for the Casimir interaction energy between the two spheres. A byproduct is the explicit formula for the translation matrix that relates the fermionic spherical waves in different coordinate systems. In the large separation limit, it is found that the order of the Casimir interaction energy is $L^{-5}$, where $L$ is the separation between the centers of the spheres. This order is intermediate between that of two Dirichlet spheres (of order $L^{-3}$) and two Neumann spheres (of order $L^{-7}$). In the small separation limit, we derive analytically the asymptotic expansion of the Casimir interaction energy up to the next-to-leading order term. The leading term agrees with the proximity force approximation. The result for the next-to-leading order term is compared to the corresponding results for scalar fields and electromagnetic fields.

14 pages

References in corpus (22)

• Casimir forces between arbitrary compact objects
• The Casimir effect within scattering theory
• Casimir forces in a T operator approach
• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Casimir Forces between Compact Objects: I. The Scalar Case
• Exact Casimir interaction between eccentric cylinders
• Fluctuation induced quantum interactions between compact objects and a plane mirror
• Multiple Scattering Methods in Casimir Calculations
• Casimir force for a sphere in front of a plane beyond Proximity Force Approximation
• Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation
• Fermionic current densities induced by magnetic flux in a conical space with a circular boundary
• Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
• Casimir forces between arbitrary compact objects: Scalar and electromagnetic field
• Exact Casimir Interaction Between Semitransparent Spheres and Cylinders
• Fermionic Casimir effect in toroidally compactified de Sitter spacetime
• Fermionic condensate in a conical space with a circular boundary and magnetic flux
• Fermionic current from topology and boundaries with applications to higher-dimensional models and nanophysics
• Spinor Casimir effect for concentric spherical shells in the global monopole spacetime
• Fermionic vacuum densities in higher-dimensional de Sitter spacetime
• Finite Temperature Casimir Effect for Massless Majorana Fermions in a Magnetic Field
• Casimir energy between media-separated cylinders: the scalar case
• Mode summation approach to Casimir effect between two objects