Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures

Correlation functions related to the dynamic density response of the one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An exact Bose-Fermi mapping is used to work in a fermionic representation with a pseudopotential Hamiltonian. The Hartree-Fock and generalized random phase approximations are derived and the dynamic polarizability is calculated. The results are valid to first order in 1/\gamma where \gamma is Lieb-Liniger coupling parameter. Approximations for the dynamic and static structure factor at finite temperature are presented. The results preclude superfluidity at any finite temperature in the large-\gamma regime due to the Landau criterion. Due to the exact Bose-Fermi duality, the results apply for spinless fermions with weak p-wave interactions as well as for strongly interacting bosons.