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The second virial coefficient for quantum-mechanical sticky spheres. (English) Zbl 0866.60094

Fannes, Mark (ed.) et al., On three levels. Micro-, meso-, and macro-approaches in physics. Proceedings of a NATO Advanced Research Workshop, Leuven, Belgium, July 19–23, 1993. New York, NY: Plenum Press. NATO ASI Ser., Ser. B, Phys. 324, 381-384 (1994).
For a 3-dimensional system of hard spheres of diameter \(D\) and mass \(m\), let \(B_D\) denote the quantum second virial coefficient. Let \(B_{D,a}\) denote the quantum second virial coefficient when there is an added attractive square-well two-body interaction of width \(a\) and depth \({\mathcal E}\). We demonstrate nonrigorously that in the limit \(a\to 0\) at constant \(\alpha: ={\mathcal E} ma^2/(2\hbar^2)\) with \(\alpha< \pi^2/8\), \[ B_{D,a} =B_D-a \left({\tan \sqrt{(2\alpha)} \over \sqrt{(2\alpha)}} -1 \right){d \over dD}B_D+o(a). \] The result is true equally for Boltzmann, Bose and Fermi statistics. A rigorous proof is given by the authors with G. Stell [Rev. Math. Phys. 6, No. 5a, 947-975 (1994; Zbl 0841.60094)].
For the entire collection see [Zbl 0845.00058].

MSC:

60K40 Other physical applications of random processes
82B10 Quantum equilibrium statistical mechanics (general)
81S25 Quantum stochastic calculus

Citations:

Zbl 0841.60094
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