arXiv subjects
Publications and source records attributed to Irina Pirozhenko.
We study the spectrum of the 1D Dirac Hamiltonian encompassing the bound and scattering states of a fermion distorted by a static background built from $δ$-function potentials. We distinguish between "mass-spike" and "electrostatic" $δ$-potentials. Differences in the spectra arising depending on the type of $δ$-potential studied are thoroughly explored.
We consider polarizable sheets modeled by a lattice of delta function potentials. The Casimir interaction of two such lattices is calculated at nonzero temperature. The heat kernel expansion for periodic singular background is discussed in relation with the high temperature asymptote of the free energy.
The results on the heat kernel expansion for the electromagnetic field in the background of dielectric media are briefly reviewed. The common approaches to the calculation of the heat kernel coefficients are discussed from the viewpoint of their applicability to the electromagnetic field interacting with dielectric body of arbitrary form. Using the toy-model of scalar photons we develop multiple reflection expansion method which seems the most promising one when the field obeys dielectric-like matching conditions on an arbitrary interface and show that the heat kernel coefficients are expressible through geometric invariants of the latter.