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Stability of many-particle systems — Fisher and Ruelle

1966 AD · Transmission: Global
PhysicsMathematicsTheoryBritishFrench

Michael E. Fisher, then professor of physics at King's College London shortly before his move to Cornell, and David Ruelle, of the Institut des Hautes Études Scientifiques in France, publish in February 1966 "The Stability of Many-Particle Systems", showing that a quantum or classical system of N particles interacting via pairwise potentials is stable — in the sense that the total energy is always bounded from below — provided the potential satisfies a condition on its Fourier transform (positive semi-definiteness). The result applies to "charged" systems and demonstrates stability for Coulomb interactions when charges are slightly smeared rather than concentrated at points; for a broad class of potentials, they also show that classical instability implies quantum instability in the case of bosons, and in three or more dimensions also of fermions. The work rigorously formalizes, via verifiable stability criteria, a problem that until then had only been addressed with not fully rigorous physical arguments — such as Onsager's in 1939 — but leaves unresolved the physically more demanding case of unsmoothed point-like Coulomb charges, which Dyson and Lenard would prove a year later, explicitly citing this work as a direct precedent.

InstitutionKing's College London (Fisher) / Institut des Hautes Études Scientifiques, Bures-sur-Yvette (Ruelle)
Historical regionUnited Kingdom (London) and France
Primary sourceFisher, M.E. & Ruelle, D. — "The Stability of Many-Particle Systems" (Journal of Mathematical Physics, 7(2), 260-270, 1966). DOI: 10.1063/1.1704928
Secondary sourceDyson, F.J. & Lenard, A. — "Stability of Matter I" (Journal of Mathematical Physics, 8, 423-434, 1967), which directly cites and extends this result to the case of point-like Coulomb charges
Original languageEnglish
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