938 research outputs found
Absolutely continuous spectrum for the isotropic Maxwell operator with coefficients that are periodic in some directions and decay in others
The purpose of this paper is to prove that the spectrum of an isotropic
Maxwell operator with electric permittivity and magnetic permeability that are
periodic along certain directions and tending to a constant super-exponentially
fast in the remaining directions is purely absolutely continuous. The basic
technical tools is a new ``operatorial'' identity relating the Maxwell operator
to a vector-valued Schrodinger operator. The analysis of the spectrum of that
operator is then handled using ideas developed by the same authors in a
previous paper
Spectral asymptotics of Pauli operators and orthogonal polynomials in complex domains
We consider the spectrum of a two-dimensional Pauli operator with a compactly
supported electric potential and a variable magnetic field with a positive mean
value. The rate of accumulation of eigenvalues to zero is described in terms of
the logarithmic capacity of the support of the electric potential. A connection
between these eigenvalues and orthogonal polynomials in complex domains is
established.Comment: 16 page
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