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Painlevé Transcendent Evaluations of Finite System Density Matrices for 1d Impenetrable Bosons

2003
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Communications in Mathematical Physics
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The recent experimental realisation of a one-dimensional Bose gas of ultra cold alkali atoms has renewed attention on the theoretical properties of the impenetrable Bose gas. Of primary concern is the ground state occupation of effective single particle states in the finite system, and thus the tendency for Bose-Einstein condensation. This requires the computation of the density matrix. For the impenetrable Bose gas on a circle we evaluate the density matrix in terms of a particular Painlevé VI

doi:10.1007/s00220-003-0851-3
fatcat:gf2njgtdnvgxhh5fcwgo4dxzvm