Fermi-bose transformation for the time-dependent Lieb-Liniger gas.
Exact solutions of the Schrödinger equation describing a freely expanding Lieb-Liniger gas of delta-interacting bosons in one spatial dimension are constructed. We demonstrate that for any interaction strength the system enters a strongly correlated regime during such expansion. The asymptotic form of the wave function is shown to have the form characteristic for "impenetrable-core" bosons. Exact solutions are obtained by transforming a fully antisymmetric (fermionic) time-dependent wave function that obeys the Schrödinger equation for a free gas. This transformation employs a differential Fermi-Bose mapping operator that depends on the strength of the interaction and the number of particles.
Buljan
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H
Department of Physics, University of Zagreb, PP 332, 10000 Zagreb, Croatia. hbuljan@phy.hr
Pezer
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R
Gasenzer
T
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