Casimir force betweenδ−δ′mirrors transparent at high frequencies

Abstract

We investigate, in the context of a real massless scalar field in 1+1 dimensions, models of partially reflecting mirrors simulated by Dirac δ − δ ′ point interactions. In the literature, these models do not exhibit full transparency at high frequencies.In order to provide a more realistic feature for these models, we propose a modified δ − δ ′ point interaction that enables full transparency in the limit of high frequencies.Taking this modified δ − δ ′ model into account, we investigate the Casimir force, comparing our results with those found in the literature.

Local Casimir Effect for a Scalar Field in Presence of a Point Impurity

“…Variations of the same model, concerning both a scalar and a spinor field, were later examined by Bordag, Hennig and Robaschik in [13]. In the last two decades, there has been a renewed interest on surface delta potentials: see, e.g., [11,17,20,22,23,33,35,40,44,49].…”

Vacuum Polarization with Zero-Range Potentials on a Hyperplane

“…We shall henceforth assume the parameters ω, α, β, γ, ς to fulfil the latter Equation ( 31), in addition to the conditions previously stated in Equation (29).…”

“…The Casimir effect in presence of surface Dirac delta potentials, interpreted as semi-transparent walls responsible for a partial confinement of the quantum field, was first addressed by Mamaev and Trunov [18] and later examined in various configurations by several authors [19][20][21][22][23][24][25][26]. More recently, considerable attention was devoted to the study of renormalized vacuum expectations of global observables (such as the total energy) in presence of generalized zero-range interactions concentrated on sets of co-dimension 1, corresponding to mixtures of δ − δ potentials [27][28][29][30][31][32]. Before proceeding, let us also mention that various models with point impurities, modelled via distributional potentials concentrated on sets of co-dimension 3, were analyzed in [33][34][35][36][37][38][39][40][41].…”

Vacuum polarization with zero-range potentials on a hyperplane

“…The Casimir effect in presence of surface Dirac delta potentials, interpreted as semi-transparent walls responsible for a partial confinement of the quantum field, was first addressed by Mamaev and Trunov [40] and later examined in various configurations by several authors [8,11,20,32,34,38,42,46]. More recently, considerable attention was devoted to the study of renormalized vacuum expectations of global observables (such as the total energy) in presence of generalized zero-range interactions concentrated on sets of co-dimension 1, corresponding to mixtures of δ − δ ′ potentials [6,15,17,18,45,47]. Before proceeding, let us also mention that various models with point impurities, modelled via distributional potentials concentrated on sets of co-dimension 3, were analysed in [3,2,14,16,30,35,36,53,57].…”