量子临界点非线性淬火中的缺陷产生
Defect production in non-linear quench across a quantum critical point
摘要：
我们表明，缺陷密度$n$，对于一个缓慢的非线性幂律淬火率$τ^{-1}$和指数$α>0$，它需要通过一个临界点，其特征在于相关长度和动力学临界指数$ν$和$z$的系统，标度为$n \sim τ^{-ανd/ (αzν+1)}$ [ $n \sim (αg^{(α-1)/α}/τ)^{νd/(zν+1)}$ ]，如果淬火采取系统在时间$t=0$ [$t=t_0 \ne 0$ ]跨越临界点，其中，$g$是非通用常数，$d$是系统维度。这些标度律构成的第一个理论结果，在非线性淬火量子临界点的缺陷生产和再现其著名的对应线性淬火（$α=1$）作为一个特殊情况。我们补充我们的结果与数值研究知名的模型，并建议实验来测试我们的理论。
英文摘要：
We show that the defect density $n$, for a slow non-linear power-law quench with a rate $τ^{-1}$ and an exponent $α>0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $ν$ and $z$, scales as $n \sim τ^{-ανd/ (αzν+1)}$ [$n \sim (αg^{(α-1)/α}/τ)^{νd/(zν+1)}$], if the quench takes the system across the critical point at time $t=0$ [$t=t_0 \ne 0$], where $g$ is a non-universal constant and $d$ is the system dimension. These scaling laws constitute the first theoretical results for defect production in non-linear quenches across quantum critical points and reproduce their well-known counterpart for linear quench ($α=1$) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.
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