IJPAM: Volume 53, No. 2 (2009)

ON A STATISTICAL INTERRELATION BETWEEN SPECTRAL
GAP AND TRANSITION TO SUPERCONDUCTIVITY

Eugen Grycko$^1$, Werner Kirsch$^2$, Jens Rentmeister$^3$
$^{1,2}$Department of Mathematics and Computer Science
University of Hagen
125, Lützowstrasse, Hagen, D-58084, GERMANY
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$OmegaSpace.de
90, Thingslindestrasse, Kierspe, D-58566, GERMANY
e-mail: [email protected]


Abstract.Recently random Schrödinger operators based on a discrete position space have drawn some attention. We illustrate the applicability of these models to a physically plausible statistical explanation of the phenomenon of superconductivity. In particular, a physically interpretable random Schrödinger operator for the description of a pair of electrons interacting with a lattice of ions is introduced. The functional dependence of the expected spectral gap of the operator on the lattice constant is studied based on a long term computer experiment. It turns out that the obtained function carries valuable statistical information about the temperature of transition to superconductivity for 24 chemical elements.


$\textstyle \parbox{9cm}{Dedicated to Professor Holger Petersson from Hagen on the occasion of his 70-th birthday.}$

Received: April 27, 2009

AMS Subject Classification: 46N50

Key Words and Phrases: Coulomb interaction, Lennard-Jones potential, Cooper pairs, regression

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 2