Quantum second virial coefficient paradox

Guido Cognola, Roberto Soldati, Sergio Zerbini

W. D. Kraeft, W. Ebeling, D. Kremp

T. A. Osborn, T.Y. Tsang

Bruno J. Baumgartl

Juan Gonzalo Muga

The so-called Second Quantum Second Virial Coefficient Paradox is generalized and analyzed in detail. A modification of the intertwining relation recovers the coherence of the scattering formalism and avoids the paradox. A special limiting procedure maintains the usual formal structure of the theory but fails to describe the scattering consistently.

C Carvalho, Ludwig Streit

The authors calculate the second virial coefficient of the quantum Lorentz gas with point interaction. It can be evaluated in closed form for arbitrary strength of the interaction. Particular attention is given to the critical coupling which gives rise to a zero-energy resonance. Point interactions satisfy a modified Levinson's theorem; as a consequence they show that there is no cancellation between the bound state and the scattering contributions in the high-temperature expansion of the second virial coefficient, contrary to the regular potentials case. They also derive high- and low-energy sum rules for the point interaction. As an application of the sum rules they rederive a high-temperature expansion for the second virial coefficient.