超越Kibble-Zurek机制的有限尺寸全息超导环的缠绕
Winding up a finite size holographic superconducting ring beyond Kibble-Zurek mechanism
摘要：
研究了有限尺寸全息超导环中猝灭正常态到超导态相变的序参量和缠绕数$W$的动力学。存在一个临界周长$\tilde{C}$，低于该临界周长将不形成缠绕数，则$\tilde{C}$可以被视为Kibble-Zurek机构（KZM）相关长度$ξ$，其与其淬火速率的四次方根$τ_Q$成比例，该淬火速率也是淬火后形成的独立碎片的平均尺寸。当周长$C \geq 10 ξ$时，观察到绝对缠绕数的平均值与淬火速率$\langle|W|\rangle \propto τ_Q^{-1/8}$之间的关键KZM缩放。在较小的尺寸下，通用缩放将被修改，有两个区域。中等尺寸的$5ξ<C<10ξ$结果$\langle|W|\rangle \propto τ_Q^{-1/5}$与有限尺寸的实验观察结果一致。而在$ξ<C\leq 5ξ$时，绝对圈数的平均值等于圈数的方差，失超率与绝对圈数的平均值之间不存在良好的指数关系。缠绕数量统计可以从具有$\tilde{N}=C/ (f ξ)$试验的三项分布导出，$f\simeq 5$是有效相关的相邻件的平均数量。
英文摘要：
We studied the dynamics of the order parameter and the winding numbers $W$ formation of a quenched normal-to-superconductor state phase transition in a finite size holographic superconducting ring. There is a critical circumference $\tilde{C}$ below it no winding number will be formed, then $\tilde{C}$ can be treated as the Kibble-Zurek mechanism (KZM) correlation length $ξ$ which is proportional to the fourth root of its quench rate $τ_Q$, which is also the average size of independent pieces formed after a quench. When the circumference $C \geq 10 ξ$, the key KZM scaling between the average value of absolute winding number and the quench rate $\langle|W|\rangle \propto τ_Q^{-1/8}$ is observed. At smaller sizes, the universal scaling will be modified, there are two regions. The middle size $5ξ<C<10ξ$ result $\langle|W|\rangle \propto τ_Q^{-1/5}$ agrees with a finite size experiment observation. While at $ξ<C\leq 5ξ$ the the average value of absolute winding number equals to the variance of winding number and there is no well exponential relationship between the quench rate and the average value of absolute winding number. The winding number statistics can be derived from a trinomial distribution with $\tilde{N}=C/ (f ξ)$ trials, $f\simeq 5$ is the average number of adjacent pieces that are effectively correlated.
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