1 research outputs found
Bosonizing one-dimensional cold atomic gases
We present results for the long-distance asymptotics of correlation functions
of mesoscopic one-dimensional systems with periodic and open (Dirichlet)
boundary conditions, as well as at finite temperature in the thermodynamic
limit. The results are obtained using Haldane's harmonic-fluid approach (also
known as ``bosonization''), and are valid for both bosons and fermions, in
weakly and strongly interacting regimes. The harmonic-fluid approach and the
method to compute the correlation functions using conformal transformations are
explained in great detail. As an application relevant to one-dimensional
systems of cold atomic gases, we consider the model of bosons interacting with
a zero-range potential. The Luttinger-liquid parameters are obtained from the
exact solution by solving the Bethe-ansatz equations in finite-size systems.
The range of applicability of the approach is discussed, and the prefactor of
the one-body density matrix of bosons is fixed by finding an appropriate
parametrization of the weak-coupling result. The formula thus obtained is shown
to be accurate, when compared with recent diffusion Montecarlo calculations,
within less than 10%. The experimental implications of these results for Bragg
scattering experiments at low and high momenta are also discussed.Comment: 39 pages + 14 EPS figures; typos corrected, references update