论文标题
时间演变和时间依赖量子图的schrödinger方程
Time evolution and the Schrödinger equation on time dependent quantum graphs
论文作者
论文摘要
本文的目的是讨论具有时间依赖性边缘长度的度量图上的时间依赖性schrödinger方程，以及构成问题的正确方法，以使相应的时间演变是单一的。我们表明，可以通过用具有谐波电位的磁性schrödinger算子代替标准的kirchhoff laplacian来确保Schrödinger方程的良好性能。然后，我们将结果概括为顶点条件的时间依赖家庭。我们还应用理论来显示与缓慢变化的量子图相关的几何相。
The purpose of the present paper is to discuss the time dependent Schrödinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the corresponding time evolution is unitary. We show that the well posedness of the Schrödinger equation can be guaranteed by replacing the standard Kirchhoff Laplacian with a magnetic Schrödinger operator with a harmonic potential. We then generalize the result to time dependent families of vertex conditions. We also apply the theory to show the existence of a geometric phase associated with a slowly changing quantum graph.
