Analog of Hamilton-Jacobi theory for the time-evolution operator
Analog of Hamilton-Jacobi theory for the time-evolution operator
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DOI：
10.1103/physreva.100.012132
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发表时间：
2019-02
影响因子：
2.9
通讯作者：
M. Vogl;P. Laurell;A. Barr;G. Fiete
中科院分区：
文献类型：
--
作者：
M. Vogl;P. Laurell;A. Barr;G. Fiete
本文对量子多粒子系统的时间演化算符发展了一个类似的Hamilton-Jacobi理论。该理论提供了一个有用的方法来开发近似的时间演化算子，也提供了一个统一的框架和起点，许多著名的近似的时间演化算子。在频闪时间周期驱动系统的重要特殊情况下，我们发现相对简单的方程的耦合常数的Floquet哈密顿量，一个简单的截断耦合导致一类强大的近似。使用我们的理论，我们构建了一个流程图，说明了各种常见的近似之间的连接，这也突出了一些缺失的连接和相关的近似方案。这些缺失的连接原来意味着一个分析访问近似，是一个旋转框架近似的“逆”，因此有一个范围内的有效性互补it.We数值测试的各种方法上的一维伊辛模型，以确认的有效性范围，人们会期望从使用的近似。该理论提供了一个地图之间的关系越来越多的近似的时间演化算子。我们描述这些关系的表中显示的限制和优点，许多常见的近似，以及本文介绍的新的近似。
In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also provides a unified framework and starting point for many well-known approximations to the time-evolution operator. In the important special case of periodically driven systems at stroboscopic times, we find relatively simple equations for the coupling constants of the Floquet Hamiltonian, where a straightforward truncation of the couplings leads to a powerful class of approximations. Using our theory, we construct a flow chart that illustrates the connection between various common approximations, which also highlights some missing connections and associated approximation schemes. These missing connections turn out to imply an analytically accessible approximation that is the "inverse" of a rotating frame approximation and thus has a range of validity complementary to it. We numerically test the various methods on the one-dimensional Ising model to confirm the ranges of validity that one would expect from the approximations used. The theory provides a map of the relations between the growing number of approximations for the time-evolution operator. We describe these relations in a table showing the limitations and advantages of many common approximations, as well as the new approximations introduced in this paper.