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Critical states of strongly interacting many-particle systems on a circle. (English. Russian original) Zbl 1246.82064

Probl. Inf. Transm. 47, No. 2, 190-200 (2011); translation from Probl. Peredachi Inf. 47, No. 2, 117-127 (2011).
Usually the ground states of classical particles are studied in connection with the problem of existence and the structure of the lattice for the condensed matter state. There are also other models (for example the Toda chain and the Frenkel-Kontorova model), where it is assumed that the potential \(V\) has a minimum. The ground states are considered on the whole real line, but in this paper, the goal is different and the authors study different phenomena in a finite volume, related to the appearance of a finer scale, i.e., in fact related to the second term of the asymptotics of the distances between particles. The approach used in this paper is rather straightforward ideologically but demands cumbersome calculations. Normally, it is accepted that macro variables are completely defined by micro variables, but in the case of a system with strong local interactions, this is not always the case. In the systems considered in this paper (with strong Coulomb repulsion between particles), one can observe an influence of force on the equilibrium state only on a scale much smaller than the standard microscale (for a system with \(N\) particles, a natural microscale is \(\frac{1}{N}\)). Information about the macroforce is not available neither on the macroscale nor on the standard microscale but only on a finer scale. If this phenomenon does not depend on the continuity properties of the applied force, then the mere existence of the equilibrium depends essentially on the continuity properties of the external force.

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
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