Low Temperature Physics: 37, 829 (2011); https://doi.org/10.1063/1.3670025 (5 pages)
Fizika Nizkikh Temperatur: Volume 37, Number 9-10 (September 2011), p. 1040-1045 ( to contents , go back )
Two-dimensional Pauli operator in magnetic field
P.G. Grinevich1, A.E. Mironov2, and S.P. Novikov1,3
1Институт теоретической физики им. Л.Д. Ландау РАН просп. Акад. Семенова, 1а, г. Черноголовка, Московская область, 142432, Россия
2Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences,4 Acad. Koptyug avenue, 630090 Novosibirsk Russia
3University of Maryland at College Park, College Park, MD, 20742, USA
Received March 1, 2011
The 2D purely magnetic Pauli operator for the nonrelativistic particle with spin 1/2 in magnetic field has some remarkable properties discovered in the late 70's: its ground level is highly degenerate; it admits supersymmetry. In the present work we investigate the special case where magnetic flux through the elementary cell is equal to zero. This case was not covered by the previous works. An interesting connection is revealed here with the theory of solitons, in particular with Burgers-like systems and their 2D analogs. They can be linearized by the elementary transformations and are much simpler than KdV or KP. The Aharonov-Bohm type terms with quantized magnetic flux play special important role in our investigation.
PACS: 02.30.Tb Operator theory;
Key words: two-dimensional system, pure magnetic Pauli operator, ground state, supersymmetry, Burgers hierarchy.