The Dynamic Structure Factor of the 1D Bose Gas near the Tonks-Girardeau Limit

Abstract

While the 1D Bose gas appears to exhibit superfluid response under certain conditions, it fails the Landau criterion according to the elementary excitation spectrum calculated by Lieb. The apparent riddle is solved by calculating the dynamic structure factor of the Lieb-Liniger 1D Bose gas. A pseudopotential Hamiltonian in the fermionic representation is used to derive a Hartree-Fock operator, which turns out to be well-behaved and local. The Random-Phase approximation for the dynamic structure factor based on this derivation is calculated analytically and is expected to be valid at least up to first order in $1/\gamma$, where $\gamma$ is the dimensionless interaction strength of the model. The dynamic structure factor in this approximation clearly indicates a crossover behavior from the non-superfluid Tonks to the superfluid weakly-interacting regime, which should be observable by Bragg scattering in current experiments.

4 pages, 2 figures misprints in formulas corrected

References in corpus (2)

• A density-functional approach to fermionization in the 1D Bose gas
• Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

Cited by in corpus (16)

• Dynamical density-density correlations in the one-dimensional Bose gas
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• Density form factors of the 1D Bose gas for finite entropy states
• Dynamic structure factor and drag force in a one-dimensional strongly-interacting Bose gas at finite temperature
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Decay of superfluid currents in the interacting one-dimensional Bose gas
• Exact results of dynamical structure factor of Lieb-Liniger model
• Duality between weak and strong interactions in quantum gases
• Ground-state properties of dilute spinless fermions in fractional dimensions
• Approximate expression for the dynamic structure factor in the Lieb-Liniger model
• Bulk viscosity of dual Bose and Fermi gases in one dimension
• The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas
• One-body dynamical correlation function of Lieb-Liniger model at finite temperature
• Regularization of a strong-weak duality between pointlike interactions in one dimension
• Wavelet representation of hardcore bosons
• Momentum Evolution Numerics of an Impurity in a Quantum Quench