Fine structure of a one-dimensional discrete point system |
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Authors: | V A Malyshev |
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Affiliation: | 1. Laboratory of Large Random Systems, Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow, Russia
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Abstract: | We consider a system of N points x 1 < ... < x N on a segment of the real line. An ideal system (crystal) is a system where all distances between neighbors are the same. Deviation from idealness is characterized by a system of finite differences ? i 1 = x x+1 ? x i , ? i k+1 = ? i+1 k ? ? i k , for all possible i and k. We find asymptotic estimates as N ?? ??, k????, for a system of points minimizing the potential energy of a Coulomb system in an external field. |
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