Tkachenko modes and their damping in the vortex lattice regime of rapidly rotating bosons
Abstract
We have found an exact analytical solution of the Bogoliubovde Gennes equations for the Tkachenko modes of the vortex lattice in the lowest Landau level (LLL) in the thermodynamic limit (geometry of an infinite plane) at any momenta and calculated their damping rates. At finite temperatures both Beliaev and Landau damping leads to momentumindependent damping rates in the lowenergy limit, which shows that, at sufficiently low energies, Tkachenko modes become strongly damped. We then found that the meansquare fluctuations of the density grow logarithmically at large distances, which indicates that the state is ordered in the vortex lattice only on a finite (although exponentially large) distance scale and introduces a lowmomentum cutoff. Using this circumstance we showed that at finite temperatures the onebody density matrix undergoes an exponential decay at large distances.
 Publication:

Physical Review A
 Pub Date:
 March 2011
 DOI:
 10.1103/PhysRevA.83.033604
 arXiv:
 arXiv:1101.0269
 Bibcode:
 2011PhRvA..83c3604M
 Keywords:

 03.75.Lm;
 05.30.Jp;
 73.43.Nq;
 Tunneling Josephson effect BoseEinstein condensates in periodic potentials solitons vortices and topological excitations;
 Boson systems;
 Quantum phase transitions;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 9 pages, 2 figures