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MP: Theoretische und Mathematische Grundlagen der Physik
MP 17: POSTER
MP 17.1: Poster
Donnerstag, 21. März 2002, 14:00–18:00, Galerie 2
Hellmann-Feynman theorem and correlation-fluctuation analysis for the Calogero-Sutherland model — •Rudolf A. Römer1 and Paul Ziesche2 — 1Institut für Physik, Technische Universität, 09107 Chemnitz — 2Max-Planck-Institut für die Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden
Exploiting the results of the exact solution for the ground state of the one-dimensional spinless quantum gas of Fermions and impenetrable Bosons with the µ/xij2 particle-particle interaction, the Hellmann-Feynman theorem yields mutually compensating divergences of both the kinetic and the interaction energy in the limiting case µ →− 1/4. These divergences result from the peculiar behavior of both the momentum distribution (for large momenta) and the pair density (for small inter-particle separation). The available analytical pair densities for µ=−1/4, 0, and 2 allow to analyze particle-number fluctuations. They are suppressed by repulsive interaction (µ>0), enhanced by attraction (µ<0), and may therefore measure the kind and strength of correlation. Other recently proposed purely quantum-kinematical measures of the correlation strength arise from the small-separation behavior of the pair density or — for Fermions — from the non-idempotency of the momentum distribution and its large-momenta behavior. They are compared with each other and with reference-free, short-range correlation-measuring ratios of the kinetic and potential energies.