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

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, $E_{\mathrm{int}}\propto t^{-3}$.

Section VI added to v2; published version

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Cited by in corpus (10)

• Quantum distillation: dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps
• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
• Geometric quenches in quantum integrable systems
• Momentum distribution of a freely expanding Lieb-Liniger gas
• Ultracold gases far from equilibrium
• 2PI nonequilibrium versus transport equations for an ultracold Bose gas
• Lieb-Liniger gas in a constant force potential
• Density ripples in expanding low-dimensional gases as a probe of correlations