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On the ubiquity of the Levy integral, its relationship with the generalised Euler-Jacobi series, and their asymptotics beyond all orders
T. M. Garoni, N. E. Frankel
We present here an overview of the history, applications and important properties of a function which we refer to as the Levy integral. For certain values of its characteristic par…
Finite one dimensional impenetrable Bose systems: Occupation numbers
P. J. Forrester, N. E. Frankel, T. M. Garoni +1
Bosons in the form of ultra cold alkali atoms can be confined to a one dimensional (1d) domain by the use of harmonic traps. This motivates the study of the ground state occupation…
Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable Bosons
P. J. Forrester, N. E. Frankel, T. M. Garoni +1
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 pr…