Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-11-10
Journal of Physics B: Atomic, Molecular and Optical Physics,Vol.37, 2699 (2004).
Physics
Condensed Matter
Statistical Mechanics
revised paper 11 pages with 2 figures, all in Pdf format
Scientific paper
10.1088/0953-4075/37/13/007
Using path integral formalism, we show that the Abrikosov-Tkachenko vortex lattice may equivalently be understood as an array of Josephson junctions. The Tkachenko modes are found to be basically equivalent to the low energy excitations (Goldstone modes) of an ordered state. The calculated frequencies are in very good agreement with recent experimental data. Calculations of the fluctuations of the relative displacements of the vortices show that vortex melting is a result of quantum fluctuations around the ordered state due to the low energy excitations (Tkachenko modes)and occurs when the ratio of the kinectic energy to the potential energy of the vortex lattice is 0.001.
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