无序系统动力学的随机积分表示
Stochastic Integral Representation for the Dynamics of Disordered Systems
摘要：
研究了无序相互作用量子系统的动力学行为，利用伊藤随机演算得到了无序平均量子量的精确表示。随机积分表示提供了许多优点，包括服从解析近似，适用于相互作用的系统，并与现有的张量网络方法的兼容性。积分可以展开以产生一系列近似，其中第一个近似已经包括所有扩散校正，并且进一步地，显然是完全正的。波动的加入导致一系列收敛的系统校正。作为例子，给出了Anderson模型的态密度、谱形状因子和非时间阶数的表达式。
英文摘要：
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many advantages, including amenability to analytic approximation, applicability to interacting systems, and compatibility with existing tensor network methods. The integral may be expanded to produce a series of approximations, the first of which already includes all diffusive corrections and, further, is manifestly completely positive. The addition of fluctuations leads to a convergent series of systematic corrections. As examples, expressions for the density of states, spectral form factor, and out-of-time-order correlators for the Anderson model are obtained.
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