Blanchard Ph, Hongler M-O
Fakultät für Physik and BiBoS, Universität Bielefeld, D-33619 Bielefeld, Germany.
Phys Rev Lett. 2004 Mar 26;92(12):120601. doi: 10.1103/PhysRevLett.92.120601.
In the continuous space and time limit, we show that the probability density to find the quantum random walk (QRW) driven by the Hadamard "coin" solves a hyperbolic evolution equation similar to the one obtained for a random two-velocity evolution with spatially inhomogeneous transition rates between the velocity states. In spite of the presence of a nonlinear drift term, it is remarkable that the QRW position can easily be described in simple analytical terms. This allows us to derive the quadratic time dependence of the variance typical for the QRW.
在连续的时空极限下，我们表明，由哈达玛“硬币”驱动的量子随机游走（QRW）的概率密度满足一个双曲型演化方程，该方程类似于在速度态之间具有空间非均匀跃迁率的随机双速度演化所得到的方程。尽管存在非线性漂移项，但值得注意的是，QRW的位置可以很容易地用简单的解析形式来描述。这使我们能够推导出QRW典型的方差随时间的二次方依赖关系。
