Abstract
We consider the Hartree equations for a system of an infinite number of electrons in a periodic potential consisting of a periodic array of wells. The filling fraction is assumed to be of one electron per well. We prove that if the wells are deep enough to admit a bound state and if they are separated by a distance large enough, then the Hartree equations have a solution in which all single particle wave functions decay exponentially.
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References
Mott, N.: Metal-insulator transitions, London: Taylor & Francis 1974
Albanese, C.: ETH preprint 1988
Albanese, C.: A continuation method for non-linear eigenvalue problems. J. Funct. Anal. (to appear)
Reed, M., Simon, B.: Methods of modern mathematical physics. New York: Academic Press 1979
Glimm, J., Jaffe, A.: Quantum physics. Berlin, Heidelberg, New York: Springer 1981
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Communicated by C. H. Taubes
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Albanese, C. Localised solutions of Hartree equations for narrow-band crystals. Commun.Math. Phys. 120, 97–103 (1988). https://doi.org/10.1007/BF01223207
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DOI: https://doi.org/10.1007/BF01223207