The Stability of many-particle systems
THEORIE QUANTIQUE
PHYSIQUE
STABILITE
Abstract : It is shown that a quantal or classical system of N particles of distinct species ?,? = 1, 2, … ? interacting through pair potentials ???(r) are stable, in the sense that the total energy is always bounded below by ?NB, provided ???(r) exceeds some ???(2)(r) whose Fourier transform ????(p)????(p) corresponds to a positive semidefinite ? × ? matrix for all p.
This result is applied to discuss charged systems and stability is proved for Coulomb interactions if the charges are somewhat smeared rather than concentrated at points. For a large class of potentials it is shown that classical instability implies quantum instability in the case of bosons and, in three or more dimensions, also of fermions. Quantum systems with Coulomb interactions (point charges) are discussed and it is shown in particular that their stability cannot depend on the ratios between the masses of the particles.
RUELLE
FISHER
P/65/03
IHES
1965
A4
17 f.
EN
TEXTE
PREPUBLICATION
P_65_03.pdf
1965