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Hellmann-Feynman theorem and fluctuation-correlation analysis of the Calogero-Sutherland model

Rudolf A. Roemer·Paul Ziesche
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Abstract

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 mu/x_{ij}^2 particle-particle interaction, the Hellmann-Feynman theorem yields mutually compensating divergences of both the kinetic and the interaction energy in the limiting case mu to -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 mu=-1/4, 0, and 2 allow to analyze particle-number fluctuations. They are suppressed by repulsive interaction (mu>0), enhanced by attraction (mu<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.

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Rudolf A. Roemer, Paul Ziesche. 2000-12-13. Hellmann-Feynman theorem and fluctuation-correlation analysis of the Calogero-Sutherland model. https://doi.org/10.1088/0305-4470%2F34%2F7%2F320

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