Generalized Kac problem for Bose gas in polygonal region |
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Authors: | S Poghosyan |
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Institution: | 1.Institute of Mathematics,National Academy of Sciences of Armenia,Yerevan,Armenia |
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Abstract: | The paper considers interacting Bose gas in a polygonal domain and studies the asymptotics of the log-partition function in
its Feynman-Kac representation as the domain is delated to infinity. It is proved that for repulsive interaction with power
decay at infinity the asymptotics of the log-partition function determines the area of the domain, the length of its boundary
and the constant term defined by the angles of the polygon. This is a natural generalization of the Kac’s famous problem on
computing the asymptotics of the partition function Tre
βδ, where δ is the Dirichlet Laplacian for a polygonal domain. |
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Keywords: | |
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