22,908 research outputs found
Birman-Schwinger and the number of Andreev states in BCS superconductors
The number of bound states due to inhomogeneities in a BCS superconductor is
usually established either by variational means or via exact solutions of
particularly simple, symmetric perturbations. Here we propose estimating the
number of sub-gap states using the Birman-Schwinger principle. We show how to
obtain upper bounds on the number of sub-gap states for small normal regions
and derive a suitable Cwikel-Lieb-Rozenblum inequality. We also estimate the
number of such states for large normal regions using high dimensional
generalizations of the Szego theorem. The method works equally well for local
inhomogeneities of the order parameter and for external potentials.Comment: Final version to appear in Phys Rev
Faraday effect revisited: sum rules and convergence issues
This is the third paper of a series revisiting the Faraday effect. The
question of the absolute convergence of the sums over the band indices entering
the Verdet constant is considered. In general, sum rules and traces per unit
volume play an important role in solid state physics, and they give rise to
certain convergence problems widely ignored by physicists. We give a complete
answer in the case of smooth potentials and formulate an open problem related
to less regular perturbations.Comment: Dedicated to the memory of our late friend Pierre Duclos. Accepted
for publication in Journal of Physics A: Mathematical and Theoretical
Dipoles in Graphene Have Infinitely Many Bound States
We show that in graphene charge distributions with non-vanishing dipole
moment have infinitely many bound states. The corresponding eigenvalues
accumulate at the edges of the gap faster than any power
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