Fermi-Bose mapping for one-dimensional Bose gases

✍ Scribed by V.I. Yukalov; M.D. Girardeau

• Book ID: 102443940
• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 130 KB
• Volume: 2
• Category: Article
• ISSN: 1612-2011
• DOI: 10.1002/lapl.200510011

✦ Synopsis

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.