On fractal structure of the spectrum for periodic point perturbations of the Schrödinger operator with a uniform magnetic field

1999 ◽  
pp. 259-265 ◽  
Author(s):  
V. A. Geyler ◽  
K. V. Pankrashkin
Keyword(s):  
Magnetic Field ◽  
Periodic Point ◽  
Schrödinger Operator ◽  
Uniform Magnetic Field ◽  
Fractal Structure ◽  
Schrodinger Operator

THE BETHE–SOMMERFELD CONJECTURE FOR THE 3-DIMENSIONAL PERIODIC LANDAU OPERATOR

2004 ◽  
Vol 16 (10) ◽  
pp. 1259-1290 ◽  
Author(s):  
DANIEL M. ELTON
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Schrödinger Operator ◽  
Electric Potential ◽  
Uniform Magnetic Field ◽  
Schrodinger Operator ◽  
Regularity Assumption ◽  
3 Dimensional

The 3-dimensional Schrödinger operator H corresponding to a uniform magnetic field and a periodic electric potential V is considered. Under the condition of magnetic flux rationality, and with a mild regularity assumption on V, it is shown that the number of gaps in the spectrum of H is finite.

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