TY - JOUR
TI - A field theoretic approach to roughness corrections of Casimir energies
DO - https://doi.org/doi:10.7282/T30Z74X5
PY - 2014
AB - A systematic field theoretic description of the surface roughness corrections to the Casimir effect is developed. I use the multiple-scattering formalism. The Casimir energy is expressed in terms of the free Green's function and single-body scattering matrix. Finite temperature corrections to the Casimir force are obtained by Matsubara's formalism. The leading thermal corrections at high and low temperatures are presented and discussed. A statistical description of surface roughness is given and I construct the generating functional for roughness correlations. The latter allows me to incorporate roughness in a Quantum Field Theoretic (QFT) framework. I first consider a massless scalar field in the presence of parallel plates where one of which has a rough surface. In this case, semi-transparent boundary conditions are imposed by delta-function potentials. In the strong coupling limit the delta-function potential imposes Dirichlet boundary conditions. The Feynman rules of this equivalent 2+1-dimensional model are derived and its counterterms constructed. The two-loop contribution to the free energy of this model gives the leading roughness correction to the Casimir energy. The resummation of high-momentum loops shows that roughness effectively leads to a change in the mean separation of the order sigma^2/l_c and reduces reflection. The scalar model subsequently is generalized to the electromagnetic case. I derive the dielectric roughness corrections to the electromagnetic Casimir energy in a perturbative framework of the effective low-energy field theory for dielectric materials of Schwinger. It describes the interaction of electromagnetic fields with materials whose plasma frequency sets the low-energy scale. I show that the perturbative expansion of the single-interface scattering matrix in the amplitude of the profile is sensitive to short-wavelength components of the roughness correlation function. Generalized counterterms are introduced to subtract and correct these unphysical high-momentum contributions to the loop expansion. To leading perturbative order, the counterterms reproduce the phenomenological plasmon model. The renormalized low-energy theory is insensitive to the high-momentum behavior of the roughness correlation function and remains finite in the uncorrelated limit. I compare these predictions with the unrenormalized model and with experiment.
KW - Casimir effect
KW - Physics, Applied
KW - Electromagnetic waves
LA - eng
ER -