One-Dimensional Impenetrable Bosons in Thermal Equilibrium

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Abstract
The simple relationship between the wavefunctions of a system of impenetrable one‐dimensional bosons and impenetrable one‐dimensional fermions is exploited to derive an expansion of the boson reduced density matrices in terms of the fermion reduced density matrices and vice versa. This expansion is independent of the statistical ensemble used, and of the interparticle potential (subject to the impenetrability condition). The special case of zero impenetrability radius with no other forces is treated in detail, using the grand canonical ensemble. This leads to a natural generalization of a formula previously found for zero temperature only, for the one‐particle reduced density matrix.

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