The dynamic structure factor of the 1D Bose gas near the Tonks-Girardeau
limit
Alexander Cherny
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Moscow region, Russia
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/γ, where γ 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.
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