Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions

D. Jukić, R. Pezer, T. Gasenzer, and H. Buljan
Phys. Rev. A 78, 053602 – Published 3 November 2008

Abstract

The asymptotic form of the wave functions describing a freely expanding Lieb-Liniger gas is derived by using a Fermi-Bose transformation for time-dependent states, and the stationary phase approximation. We find that asymptotically the wave functions approach the Tonks-Girardeau (TG) structure as they vanish when any two of the particle coordinates coincide. We point out that the properties of these asymptotic states can significantly differ from the properties of a TG gas in a ground state of an external potential. The dependence of the asymptotic wave function on the initial state is discussed. The analysis encompasses a large class of initial conditions, including the ground states of a Lieb-Liniger gas in physically realistic external potentials. It is also demonstrated that the interaction energy asymptotically decays as a universal power law with time, Eintt3.

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  • Received 16 April 2008

DOI:https://doi.org/10.1103/PhysRevA.78.053602

©2008 American Physical Society

Authors & Affiliations

D. Jukić1, R. Pezer2, T. Gasenzer3,4, and H. Buljan1,*

  • 1Department of Physics, University of Zagreb, PP 332, 10000 Zagreb, Croatia
  • 2Faculty of Metallurgy, University of Zagreb, Aleja narodnih heroja 3, 44103 Sisak, Croatia
  • 3Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
  • 4Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA

  • *hbuljan@phy.hr

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Vol. 78, Iss. 5 — November 2008

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