H-stability and “weak” collapse

Ph. Choquard and R. Rentsch

Physica A: Statistical Mechanics and its Applications, 1986, vol. 138, issue 1, 125-136

Abstract: The stability of classical systems of particles interacting pairwise with potentials which are functions or distributions of positive type and mean value zero is examined. It is found (i) that such systems experience a “weak” collapse in the sense that their ground state density tends to infinity sublinearly with the number of particles; (ii) that stable potentials do not insure against weak collapse and (iii) that unstable potentials do not necessarily cause ordinary collapse. Physical examples of such potentials are given. Superstability is invoked to prevent such a pathological behaviour.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:138:y:1986:i:1:p:125-136

DOI: 10.1016/0378-4371(86)90176-7

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