The Peierls-Onsager Effective Hamiltonian in a complete gauge covariant setting: Description of the spectrum
Abstract
Using the procedures in Bu and GMS and the magnetic pseudodifferential calculus we have developped in MP1,MPR1,IMP1,IMP2 we construct an effective Hamitonian that describes the spectrum in any compact subset of the real axis for a large class of periodic pseudodifferential Hamiltonians in a bounded smooth magnetic field, in a completely gauge covariant setting, without any restrictions on the vector potential and without any adiabaticity hypothesis.
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