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A CENTRAL LIMIT THEOREM FOR MAGNETIC TRANSITION OPERATORS ON A CRYSTAL LATTICE

Published online by Cambridge University Press:  24 March 2003

MOTOKO KOTANI
MOTOKO KOTANI
Affiliation:
Mathematical Institute, Graduate School of Sciences, Tohoku University, Aoba, Sendai 980-8578, Japan; [email protected]
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Abstract

A central limit theorem for a generalized Harper operator on a crystal lattice is obtained. As the limit, the continuous semigroup of a uniform magnetic Schrödinger operator is captured on a vector space equipped with a special Euclidean structure. The standard realization of the crystal lattice is a key to the Euclidean structure and a linear vector potential on the Euclidean space from combinatorial data of the generalized Harper operator.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 464 - 482
Copyright
The London Mathematical Society, 2002

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