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Microlocalization, Percolation, and Anderson Localization for the Magnetic Schrödinger Operator with a Random Potential

✍ Scribed by Wei-Min Wang

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
480 KB
Volume
146
Category
Article
ISSN
0022-1236

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✦ Synopsis

We study the spectral properties of the magnetic Schro dinger operator with a random potential. Using results from microlocal analysis and percolation, we show that away from the Landau levels, the spectrum is almost surely pure point with (at least) exponentially decaying eigenfunctions. Moreover, it is shown that the rate of decay is proportional to -B.

1997 Academic Press

where x=(x 1 , x 2 ), :=[: i ] i # Z 2 form a random field, i.e. a family of random variables indexed by Z 2 on a probability space (0, P). Note that article no. FU963032

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