Physics – Condensed Matter – Superconductivity
Scientific paper
2005-05-18
Physics
Condensed Matter
Superconductivity
9 pages, 5 figures, To be submitted to JLTP
Scientific paper
10.1007/s10909-006-9204-x
Kinetics of merging and breaking down vortex loops is the important part of the whole vortex tangle dynamics. Another part is the motion of individual lines, which obeys the Biot-Savart law in presence of friction force and of applied external velocity fields if any. In the present work we evaluate the coefficients of the reconnection rates $A(l_{1},l_{2},l)$ and $B(l,l_{1},l_{2})$. Quantity $A$ is a number (per unit of time and per unit of volume) of events, when two loops with lengths $l_{1}$and $l_{2}$ collide and form the single loop of length $ l=l_{1}+l_{2}$. Quantity $% B(l,l_{1},l_{2}) $ describes the rate of events, when the single loop of the length $l$ breaks down into two the daughter loops of lengths $ l_{1}$ and $l_{2}$. These quantities ave evaluated as the averaged numbers of zeroes of vector $\mathbf{S}%_{s}(\xi_{2},\xi_{1},t)$ connecting two points on the loops of $\xi_{2}$ and $ \xi_{1}$ at moment of time $t$. Statistics of the individual loops is taken from the Gaussian model of vortex tangle. PACS-number 67.40
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