论文标题
从随机旋转链到量子kardar-parisi-zhang动力学
From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
论文作者
论文摘要
我们介绍了量子对称简单排除过程的不对称扩展，该过程是带有随机振幅的晶格跳跃的随机模型。在这种情况下，我们分析表明，费米子的时间集成电流定义了一个高度场，该高度场表现出量子非线性随机Kardar-Parisi-Zhang动力学。与经典的简单排除过程类似，我们进一步引入了高度场的离散Cole-Hopf（或Gärtner）变换，该高度场满足了随机热方程的量子版本。最后，我们调查了著名的kardar-parisi-zhang缩放率和几乎指示量子噪声的状态下的连续体中高度场理论的极限。
We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process which is a stochastic model of fermions on a lattice hopping with random amplitudes. In this setting, we analytically show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear stochastic Kardar-Parisi-Zhang dynamics. Similarly to classical simple exclusion processes, we further introduce the discrete Cole-Hopf (or Gärtner) transform of the height field which satisfies a quantum version of the Stochastic Heat Equation. Finally, we investigate the limit of the height field theory in the continuum under the celebrated Kardar-Parisi-Zhang scaling and the regime of almost-commuting quantum noise.
