Wave functions of the super-Tonks-Girardeau gas and the trapped one-dimensional hard-sphere Bose gas
- College of Optical Sciences, University of Arizona, Tucson, Arizona 85721 (United States)
- Departament de Fisica i Enginyeria Nuclear, Campus Nord B4, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain)
Recent theoretical and experimental results demonstrate a close connection between the super-Tonks-Girardeau (STG) gas and a one-dimensional (1D) hard-sphere Bose (HSB) gas with hard-sphere diameter nearly equal to the 1D scattering length a{sub 1D} of the STG gas, a highly excited gaslike state with nodes only at interparticle separations |x{sub jl}|=x{sub node{approx_equal}}a{sub 1D}. It is shown herein that when the coupling constant g{sub B} in the Lieb-Liniger interaction g{sub B{delta}}(x{sub jl}) is negative and |x{sub 12}|{>=}x{sub node}, the STG and HSB wave functions for N=2 particles are not merely similar, but identical; the only difference between the STG and HSB wave functions is that the STG wave function allows a small penetration into the region |x{sub 12}|<x{sub node}, whereas for a HSB gas with hard-sphere diameter a{sub hs}=x{sub node}, the HSB wave function vanishes when |x{sub 12}|<a{sub hs}. Arguments are given suggesting that the same theorem holds also for N>2. The STG and HSB wave functions for N=2 are given exactly in terms of a parabolic cylinder function, and for N{>=}2, x{sub node} is given accurately by a simple parabola. The metastability of the STG phase generated by a sudden change of the coupling constant from large positive to large negative values is explained in terms of the very small overlap between the ground state of the Tonks-Girardeau gas and collapsed cluster states.
- OSTI ID:
- 21407881
- Journal Information:
- Physical Review. A, Vol. 81, Issue 6; Other Information: DOI: 10.1103/PhysRevA.81.061601; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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