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On diamagnetism and de Haas-van Alphen effect. (English) Zbl 0715.35070
The authors consider some problems for the Schrödinger equation with a periodic potential and a weak magnetic field being of interest for the theory of diamagnetism.
They find the density of the states for the operator being essentially selfadjoint thus giving (by means of an abstract operator calculus and of the calculus of pseudo-differential operators) a rigorous justification of the known physical results, e.g. the Haas-van Alphen effect based on the Onsager’s rule if one uses the Peierls ansatz which is here rigorously proved in the case of overlapping bands. The authors give also a precise description of the density of states, especially in the case of the non crossing Floquet eigenvalues near the Fermi level.
Reviewer: S.M.Zverev

MSC:
35Q40 PDEs in connection with quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
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