论文标题
在连续测量的经典单一随机步行器中的KPZ物理和相变
KPZ physics and phase transition in a classical single random walker under continuous measurement
论文作者
论文摘要
我们介绍并研究了一个新的模型，该模型由一个经典的随机助行器组成，经过离散晶格的速度$γ$进行连续监视。尽管这种连续的测量不能影响物理可观察物，但它对随机步行者的概率分布有非平凡的影响。在小$γ$时，我们可以分析地表明，后者的时间进化可以映射到随机热方程（SHA）。在此限制下，对数概率的宽度因此遵循了家庭 - vicsek缩放定律，$ n^αf（t/n^{α/β}）$，具有与Kardar-Parisi-Zhang（KPZ）通用类相对应的粗糙度和增长指数，即$α^{\ rm {1d}} _ {\ rm {kpz}} = 1/2 $和$β^{\ rm {1d}} _ {\ rm {\ rm {kpz}} = 1/3 $。当$γ$在此制度之外增加时，我们在1D中找到了从KPZ类中的交叉跨度到以指数为特征的新通用类，其特征是$α^{1 \ rm {d}} _ {\ text {m}}} \ of texch _ {m}} \ 1 $和$β^^{1 $ and $β^{1 \ rm {d}在3D中，$γ$超出了关键值$γ^c _ {\ rm {m}} $，导致我们从平稳阶段识别为Edwards-Wilkinson（ew）类的阶段过渡到具有$α^{3 \ rm {d}} _ {\ text}的新通用类，均为$α^{3 \ rm {d} _ {
We introduce and study a new model consisting of a single classical random walker undergoing continuous monitoring at rate $γ$ on a discrete lattice. Although such a continuous measurement cannot affect physical observables, it has a non-trivial effect on the probability distribution of the random walker. At small $γ$, we show analytically that the time-evolution of the latter can be mapped to the Stochastic Heat Equation (SHE). In this limit, the width of the log probability thus follows a Family-Vicsek scaling law, $N^αf(t/N^{α/β})$, with roughness and growth exponents corresponding to the Kardar-Parisi-Zhang (KPZ) universality class, i.e $α^{\rm{1D}}_{\rm{KPZ}}=1/2$ and $β^{\rm{1D}}_{\rm{KPZ}}=1/3$ respectively. When $γ$ is increased outside this regime, we find numerically in 1D a crossover from the KPZ class to a new universality class characterized by exponents $α^{1\rm{D}}_{\text{M}}\approx 1$ and $β^{1\rm{D}}_{\text{M}}\approx 1.4$. In 3D, varying $γ$ beyond a critical value $γ^c_{\rm{M}}$ leads to a phase transition from a smooth phase that we identify as the Edwards-Wilkinson (EW) class to a new universality class with $α^{3\rm{D}}_{\text{M}}\approx1$.
