1301.0912 (Jorge Berger)

Characterization of the spontaneous symmetry breaking due to quenching
of a one-dimensional superconducting loop    [PDF]

Jorge Berger

We study the final distribution of the winding numbers in a 1D superconducting ring that is quenched through its critical temperature in the absence of magnetic flux. The study is conducted using the stochastic time-dependent Ginzburg--Landau model, and the results are compared with the Kibble--Zurek mechanism (KZM). The assumptions of KZM are formulated and checked as three separate postulates. We find a characteristic length and a characteristic time of this system. Besides the case of uniform rings, we examined the case of rings with several weak links. For temperatures close or below $T_c$, the coherence length does not characterize the correlation length. In order to regard the winding number as a conserved quantity, it is necessary to allow for a short lapse of time during which unstable configurations decay. We found criteria for the validity of the 1D treatment. The is no lower bound for final temperatures that permit 1D treatment. The variance of the winding number, $$, depends not only on the quenching time $\tau_Q$, but also on the size of the change of the reduced temperature. For moderate quenching times, we find the scaling $\propto\tau_Q^{-1/4}$, as predicted by KZM in the case of mean field models; if $\tau_Q$ is smaller than the typical time over which unstable configurations decay, the dependence is weaker.

View original: http://arxiv.org/abs/1301.0912