论文标题
组合湍流扩散中的量子动力学和放松
Quantum dynamics and relaxation in comb turbulent diffusion
论文作者
论文摘要
考虑梳子几何形状中湍流扩散的量子对应物的连续时间量子行走。骨干不均匀的对流$δ（y）x \ partial_x $沿$ x $轴的相互作用，该轴仅在$ y = 0 $下发生，而在$ y $ y $ y axis内部的正常扩散$ \ partial_y^2 $沿着$ y $ y $ axis的铅引起了动荡的扩散。由于梳理几何形状和扩张算子的特性而引起的运输系数的几何约束导致考虑了两种可能的量子力学情况。连续时间量子步行的这两个变体由表格$ \ hat {\ cal h} = \ hat {a}+i \ hat {b} $描述。操作员$ \ hat {a} $是负责统一转换的原因，而操作员$ i \ hat {b} $负责量子/经典放松。在第一个量子场景中，初始波数据包可以与经典流有关。这种量子游泳在上游是由于扩张算子造成的，该伸缩液负责沿主链沿量子（不是统一的）动力学，而经典放松则在手指中进行。在第二种情况下，扩张算子负责假想的光电位的形式量子松弛，而量子单位动力学则在手指中发生。对波和格林的功能进行了严格的分析分析。
Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. The interplay between the backbone inhomogeneous advection $δ(y)x\partial_x$ along the $x$ axis, which takes place only at the $y=0$, and normal diffusion inside fingers $\partial_y^2$ along the $y$ axis leads to turbulent diffusion. This geometrical constraint of transport coefficients due to comb geometry and properties of a dilatation operator lead to consideration of two possible scenarios of quantum mechanics. These two variants of continuous time quantum walks are described by non-Hermitian operators of the form $\hat{\cal H}=\hat{A}+i\hat{B}$. Operator $\hat{A}$ is responsible for the unitary transformation, while operator $i\hat{B}$ is responsible for quantum/classical relaxation. At the first quantum scenario, the initial wave packet can move against the classical streaming. This quantum swimming upstream is due to the dilatation operator, which is responsible for the quantum (not unitary) dynamics along the backbone, while the classical relaxation takes place in fingers. In the second scenario, the dilatation operator is responsible for the quantum relaxation in the form of an imaginary optical potential, while the quantum unitary dynamics takes place in fingers. Rigorous analytical analysis is performed for both wave and Green's functions.
