Fermi-Bose mapping for one-dimensional Bose gases

V. I. Yukalov; M. D. Girardeau

doi:10.1002/lapl.200510011

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Fermi-Bose mapping for one-dimensional Bose gases

V. I. Yukalov·M. D. Girardeau

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Abstract

One-dimensional Bose gases are considered, interacting either through the hard-core potentials or through the contact delta potentials. Interest in these gases gained momentum because of the recent experimental realization of quasi-one-dimensional Bose gases in traps with tightly confined radial motion, achieving the Tonks-Girardeau (TG) regime of strongly interacting atoms. For such gases the Fermi-Bose mapping of wavefunctions is applicable. The aim of the present communication is to give a brief survey of the problem and to demonstrate the generality of this mapping by emphasizing that: (i) It is valid for nonequilibrium wavefunctions, described by the time-dependent Schrödinger equation, not merely for stationary wavefunctions. (ii) It gives the whole spectrum of all excited states, not merely the ground state. (iii) It applies to the Lieb-Liniger gas with the contact interaction, not merely to the TG gas of impenetrable bosons.

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V. I. Yukalov, M. D. Girardeau. 2005-07-18. Fermi-Bose mapping for one-dimensional Bose gases. https://doi.org/10.1002/lapl.200510011

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