On the structure of the lower edge of the spectrum of the periodic magnetic Schrödinger operator with small magnetic potential

Shterenberg, R.

doi:10.1090/S1061-0022-06-00933-2

On the structure of the lower edge of the spectrum of the periodic magnetic Schrödinger operator with small magnetic potential
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by R. G. Shterenberg
Translated by: the author

St. Petersburg Math. J. 17 (2006), 865-873

DOI: https://doi.org/10.1090/S1061-0022-06-00933-2

Published electronically: July 27, 2006

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Abstract:

For the periodic magnetic Schrödinger operator, the structure of the lower edge of the spectrum is investigated. It is known that in the nonmagnetic case the energy depends quadratically on the quasimomentum in the neighborhood of the lower edge of the spectrum. Herewith, the operator admits a convenient “multiplicative” factorization, which makes it possible to investigate the threshold effects efficiently. It is shown that for sufficiently small magnetic potential the magnetic Schrödinger operator also admits a similar factorization.

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