Twodimensional Pauli operator in a magnetic field
Abstract
The twodimensional purely magnetic Schrödinger operator for the nonrelativistic particle with a spin of ½ in a magnetic field has some remarkable properties, that were discovered in the late 70s: its strongly degenerate in the ground state and it admits supersymmetry. In the present work we investigate the special case where the magnetic flux of the periodic field through the elementary cell equals zero. This case has not been covered in the previous publications. An interesting connection with the theory of solitons, in particular with Burgerslike systems and their twodimensional analogues, is revealed. Their linearizability properties are simpler than some famous systems, such as KdV and KP. Members of the AharonovBohmtype system with quantized magnetic flux play a special role in the investigation of this case.
 Publication:

Low Temperature Physics
 Pub Date:
 October 2011
 DOI:
 10.1063/1.3670025
 Bibcode:
 2011LTP....37..829G
 Keywords:

 AharonovBohm effect;
 ground states;
 magnetic flux;
 mathematical operators;
 Schrodinger equation;
 solitons;
 spin dynamics;
 03.65.Ge;
 03.65.Ta;
 Solutions of wave equations: bound states;
 Foundations of quantum mechanics;
 measurement theory