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This paper is devoted to the spectral analysis of a non elliptic operator , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator has been derived, we determine its continuous spectrum. Then, we show that is unbounded from below and that it has a sequence of negative eigenvalues tending to . Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions...
This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines.
Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A
is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of
its positive eigenvalues is given. Thanks to this characterization, some...
The method of choice for describing attractive quantum systems is Hartree−Fock−Bogoliubov (HFB) theory. This is a nonlinear model which allows for the description of pairing effects, the main explanation for the superconductivity of certain materials at very low temperature. This paper is the first study of Hartree−Fock−Bogoliubov theory from the point of view of numerical analysis. We start by discussing its proper discretization and then analyze the convergence of the simple fixed point (Roothaan)...
In this paper, we construct a combined upwinding and mixed finite
element method for the numerical solution of a two-dimensional mean
field model of superconducting vortices. An advantage of our method
is that it works
for any unstructured regular triangulation. A simple convergence
analysis is given without resorting to the discrete maximum principle.
Numerical examples are also presented.
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