Abstract
By direct examination of the path (Wiener)-integral representation of the diffusion Green’s function in the presence of an opaque sphere, we are able to obtain upper and lower bounds for that Green’s function. These bounds are asymptotically correct for short-time, even in the shadow region. Essentially, we have succeeded in showing that diffusion probabilities for short-time intervals are concentrated mainly on the optical path. By integrating the Green’s function, we obtain upper- and lower-bound estimates for the exchange part of the second virial coefficient of a hard-sphere gas.
This paper was supported by the U. S. Air Force Office of Scientific Research under Grant No. 508–66 at Yeshiva University, New York.
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Lieb, E.H. (1967). Calculation of Exchange Second Virial Coefficient of a Hard-Sphere Gas by Path Integrals. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Statistical Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10018-9_5
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DOI: https://doi.org/10.1007/978-3-662-10018-9_5
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