论文标题
尺度的分离：复合量子系统的动力近似
Separation of scales: Dynamical approximations for composite quantum systems
论文作者
论文摘要
我们考虑可以将可以分配到弱相互作用的子系统中的复合量子动力学系统，类似于系统托架类型的情况。使用分解的波函数ansatz，我们数学表征了动态比例的分离。特别是，我们研究了一种耦合r {é} gime，该轴是部分平坦的，即，与一组变量相对于一组变量，例如，浴缸的变化。此外，我们研究了其中一组变量的情况是半经典缩放并得出量子古典公式的情况。在这两种情况下，我们都提出了两种降低维度的方案：一个基于泰勒膨胀（搭配），另一个基于部分平均（平均场）。我们分析了波函数的误差和可观察物的作用，从而获得了两种方法的可比估计。本研究是在张力波函数表示的背景下进行规模分离的一般分析的第一步。
We consider composite quantum-dynamical systems that can be partitioned into weakly interacting subsystems, similar to system-bath type situations. Using a factorized wave function ansatz, we mathematically characterize dynamical scale separation.Specifically, we investigate a coupling r{é}gime that is partially flat, i.e., slowly varying with respect to one set of variables, for example, those of the bath. Further, we study the situation where one of the sets of variables is semiclassically scaled and derive a quantum-classical formulation. In both situations, we propose two schemes of dimension reduction: one based on Taylor expansion (collocation) and the other one based on partial averaging (mean-field). We analyze the error for the wave function and for the action of observables, obtaining comparable estimates for both approaches. The present study is the first step towards a general analysis of scale separation in the context of tensorized wavefunction representations.
