Two-dimensional Pauli operator in magnetic field

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.