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

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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.