Adagideli, Inanc and Goldbart, P.
(2002)
Quantal Andreev billiards: Semiclassical approach to mesoscale oscillations in the density of states.
Int. J. Mod. Phys. B 16, p. 1381.
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Other URL: http://www.worldscinet.com/ijmpb/16/1610/S0217979202010300.html
Abstract
Andreev billiards are finite, arbitrarilyshaped, normalstate regions, surrounded by superconductor. At energies below the superconducting gap, singlequasiparticle excitations are confined to the normal region and its vicinity, the essential mechanism for this confinement being Andreev reflection. This Paper develops and implements a theoretical framework for the investigation of the shortwave ...
Abstract
Andreev billiards are finite, arbitrarilyshaped, normalstate regions, surrounded by superconductor. At energies below the superconducting gap, singlequasiparticle excitations are confined to the normal region and its vicinity, the essential mechanism for this confinement being Andreev reflection. This Paper develops and implements a theoretical framework for the investigation of the shortwave quantal properties of these singlequasiparticle excitations. The focus is primarily on the relationship between the quasiparticle energy eigenvalue spectrum and the geometrical shape of the normalstate region, i.e., the question of spectral geometry in the novel setting of excitations confined by a superconducting pairpotential. Among the central results of this investigation are two semiclassical trace formulas for the density of states. The first, a lowerresolution formula, corresponds to the wellknown quasiclassical approximation, conventionally invoked in settings involving superconductivity. The second, a higherresolution formula, allows the density of states to be expressed in terms of: (i) An explicit formula for the level density, valid in the shortwave limit, for billiards of arbitrary shape and dimensionality. This level density depends on the billiard shape only through the set of stationarylength chords of the billiard and the curvature of the boundary at the endpoints of these chords; and (ii) Higherresolution corrections to the level density, expressed as a sum over periodic orbits that creep around the billiard boundary. Owing to the fact that these creeping orbits are much longer than the stationary chords, one can, inter alia, hear the stationary chords of Andreev billiards.
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Item Type:  Article 

Date:  2002 

Institutions:  UNSPECIFIED 

Identification Number:  Value  Type 

condmat/0108102  arXiv ID 


Related URLs:  

Subjects:  500 Science > 530 Physics 

Status:  Published 

Refereed:  Yes, this version has been refereed 

Created at the University of Regensburg:  Yes 

Deposited On:  20 Mar 2007 

Last Modified:  05 Aug 2009 13:33 

Item ID:  1859 
