Note on the One-Dimensional Gas of Impenetrable Point-Particle Bosons

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Abstract
A one‐dimensional gas of impenetrable point‐particle bosons is considered. An exact expression for the one‐particle density matrix is derived in terms of the Fredholm determinant and resolvent of a certain simple kernel. It is proved that for large r, the density matrix is bounded by const × r−4/π2, and that this implies the absence of a generalized Bose‐Einstein condensation, contrary to a recent approximate calculation by Girardeau, who first defined such a condensation.

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