Single-particle density matrix for a time-dependent strongly interacting one-dimensional Bose gas

Physical Review A (Impact Factor: 2.99). 07/2009; 80(5). DOI: 10.1103/PhysRevA.80.053616
Source: arXiv

ABSTRACT We derive a $1/c$-expansion for the single-particle density matrix of a strongly interacting time-dependent one-dimensional Bose gas, described by the Lieb-Liniger model ($c$ denotes the strength of the interaction). The formalism is derived by expanding Gaudin's Fermi-Bose mapping operator up to $1/c$-terms. We derive an efficient numerical algorithm for calculating the density matrix for time-dependent states in the strong coupling limit, which evolve from a family of initial conditions in the absence of an external potential. We have applied the formalism to study contraction dynamics of a localized wave packet upon which a parabolic phase is imprinted initially.


Available from: T. Gasenzer, Apr 28, 2015
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    ABSTRACT: We investigate the relaxation dynamics of the Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its non-interacting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble, and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.
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    ABSTRACT: We use Gaudin's Fermi-Bose mapping operator to calculate exact solutions for the Lieb-Liniger model in a linear (constant force) potential (the constructed exact stationary solutions are referred to as the Lieb-Liniger-Airy wave functions). The ground state properties of the gas in the wedge-like trapping potential are calculated in the strongly interacting regime by using Girardeau's Fermi-Bose mapping and the pseudopotential approach in the $1/c$-approximation ($c$ denotes the strength of the interaction). We point out that quantum dynamics of Lieb-Liniger wave packets in the linear potential can be calculated by employing an $N$-dimensional Fourier transform as in the case of free expansion.
    Physical Review A 05/2010; DOI:10.1103/PhysRevA.82.023606 · 2.99 Impact Factor
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    ABSTRACT: Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet comprised of N particles, can be found by solving an $N$-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta. Comment: revised version, improved notation, Fig. 5 added
    New Journal of Physics 11/2009; DOI:10.1088/1367-2630/12/5/055010 · 3.67 Impact Factor