Fermi-Bose transformation for the time-dependent Lieb-Liniger gas

Abstract

Exact solutions of the Schrodinger equation describing a freely expanding Lieb-Liniger (LL) gas of delta-interacting bosons in one spatial dimension are constructed. The many-body wave function is obtained by transforming a fully antisymmetric (fermionic) time-dependent wave function which obeys the Schrodinger equation for a free gas. This transformation employs a differential Fermi-Bose mapping operator which depends on the strength of the interaction and the number of particles.

4+ pages, 1 figure; added references

References in corpus (5)

• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Fermionization in an expanding 1D gas of hard-core bosons
• Correlation functions of the one-dimensional attractive Bose gas
• Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wavepacket
• Analytic solutions of the 1D finite coupling delta function Bose gas

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• Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions
• Magnetic ordering and quantum statistical effects in strongly repulsive Fermi-Fermi and Bose-Fermi mixtures
• Momentum distribution of a freely expanding Lieb-Liniger gas
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• Ultracold gases far from equilibrium
• 2PI nonequilibrium versus transport equations for an ultracold Bose gas
• Symplectic tomography of ultracold gases in tight-waveguides
• Density ripples in expanding low-dimensional gases as a probe of correlations