Spectral properties of reduced Bloch Hamiltonians |
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Authors: | JE Avron A Grossmann R Rodriguez |
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Institution: | 1. Department of Physics, Princeton University, Princeton, New Jersey, USA;2. Wigner F. Fellow, Technische Universität, Berlin, Germany |
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Abstract: | Bloch Hamiltonians are defined, and the existence of bands is proven for a large class of periodic operators. The results are strong enough to include most of the reasonable physical models of a single electron in crystals. A notable exception is the Dirac Bloch Hamiltonian for a Coulombic crystal with high charge. Properties of the Bloch waves are briefly described and it is shown that “simple” Bloch Hamiltonians do not have Bloch waves with a finite number of Fourier coefficients. The asymptotic distribution of the bands is determined, and it is shown that for a large class of Hamiltonians, it is determined by the kinetic energy alone. |
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