Regensburg 2002 – wissenschaftliches Programm
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TT: Tiefe Temperaturen
TT 7: Postersitzung I: Anwendungen der Supraleitung (1-6), Dünne Schichten, Josephsonkontakte, SQUIDs (7-17), Neue und unkonv. Supraleiter(18-23), Amorphe- und Tunnelsyst. (24-28), Quantenflüssigkeiten (29-30), Syst. korr. Elektr.: Theorie I (31-45)
TT 7.36: Poster
Montag, 11. März 2002, 14:30–18:00, A
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.
[1] R. A. Römer, P. Ziesche, J. Phys. A 34, 1485–1506 (2001).