Two-dimensional periodic Pauli operator. The effective masses at the lower edge of the spectrum. (English) Zbl 0976.81005

Dittrich, Jaroslav (ed.) et al., Mathematical results in quantum mechanics. QMath7 conference, Prag, Czech Republic, June 22-26, 1998. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 108, 13-31 (1999).
Authors’ abstract: We calculate the tensor of effective masses for the two-dimensional periodic Pauli operator. The explicit representation for this tensor is given in terms of the magnetic field. It is proved that the tensor of effective masses is circular symmetric and always proportional to the unit matrix. We also consider the generalized Pauli operator with a variable metric. In the appendix we study the periodic elliptic operators of the second order and discuss the behaviour of the first band function near its minimum point.
For the entire collection see [Zbl 0911.00055].


81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35Q40 PDEs in connection with quantum mechanics
47N50 Applications of operator theory in the physical sciences