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

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.