6 research outputs found
Coarse-Grained Finite-Temperature Theory for the Condensate in Optical Lattices
In this work, we derive a coarse-grained finite-temperature theory for a Bose
condensate in a one-dimensional optical lattice, in addition to a confining
harmonic trap potential. We start from a two-particle irreducible (2PI)
effective action on the Schwinger-Keldysh closed-time contour path. In
principle, this action involves all information of equilibrium and
non-equilibrium properties of the condensate and noncondensate atoms. By
assuming an ansatz for the variational function, i.e., the condensate order
parameter in an effective action, we derive a coarse-grained effective action,
which describes the dynamics on the length scale much longer than a lattice
constant. Using the variational principle, coarse-grained equations of motion
for the condensate variables are obtained. These equations include a
dissipative term due to collisions between condensate and noncondensate atoms,
as well as noncondensate mean-field. To illustrate the usefulness of our
formalism, we discuss a Landau instability of the condensate in optical
lattices by using the coarse-grained generalized Gross-Pitaevskii
hydrodynamics. We found that the collisional damping rate due to collisions
between the condensate and noncondensate atoms changes sign when the condensate
velocity exceeds a renormalized sound velocity, leading to a Landau instability
consistent with the Landau criterion. Our results in this work give an insight
into the microscopic origin of the Landau instability.Comment: 38 pages, 2 figures. Submitted to Journal of Low Temperature Physic