Tkachenko modes and their damping in the vortex lattice regime of rapidly rotating bosons
Abstract
We have found an exact analytical solution of the Bogoliubov-de 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 momentum-independent damping rates in the low-energy limit, which shows that, at sufficiently low energies, Tkachenko modes become strongly damped. We then found that the mean-square 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 low-momentum cutoff. Using this circumstance we showed that at finite temperatures the one-body 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 Bose-Einstein condensates in periodic potentials solitons vortices and topological excitations;
- Boson systems;
- Quantum phase transitions;
- Condensed Matter - Quantum Gases;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 9 pages, 2 figures