QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems
QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems
复制标题
QuantumCumulants.jl：开放量子系统中广义平均场方程的 Julia 框架
作者：
D. Plankensteiner;Christoph Hotter;H. Ritsch
通过主方程对开放量子系统进行完全的量子力学处理通常会受到底层希尔伯特空间大小的限制。作为另一种选择，动力学也可以用海森堡图中的算子的耦合微分方程组来表示。这通常会导致运算符乘积的无穷级数方程。一种公认的方法是忽略高阶量子关联，以在期望值的水平上截断这个无限集。这是通过所谓的累积量展开系统地实现的，该累积量展开将算子乘积的期望值分解成给定低阶的乘积，从而导致一组封闭的方程。在这里，我们提出了一个完全自动化这一方法的开源框架：首先，使用预定义的正则对易关系符号化地推导出直到所需顺序的算子的运动方程。接下来，使用累积量展开方法对得到的期望值的方程进行展开，其中包括直到用户指定的选定阶数的矩。最后，可以从符号方程直接得到数值解。在回顾了理论之后，我们给出了这个框架，并在几个例子问题中展示了它的有效性。
A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled differential equations for operators in the Heisenberg picture. This typically leads to an infinite hierarchy of equations for products of operators. A well-established approach to truncate this infinite set at the level of expectation values is to neglect quantum correlations of high order. This is systematically realized with a so-called cumulant expansion, which decomposes expectation values of operator products into products of a given lower order, leading to a closed set of equations. Here we present an open-source framework that fully automizes this approach: first, the equations of motion of operators up to a desired order are derived symbolically using predefined canonical commutation relations. Next, the resulting equations for the expectation values are expanded employing the cumulant expansion approach, where moments up to a chosen order specified by the user are included. Finally, a numerical solution can be directly obtained from the symbolic equations. After reviewing the theory we present the framework and showcase its usefulness in a few example problems.
驱动耗散迪克模型中的超辐射态和激光态
影响因子：
3.3
作者：
Kirton P
通讯作者：
Kirton P