耗散型随机非线性薛定谔方程的共形动量

Conformal Momentum of Damped Stochastic Nonlinear Schr?dinger Equation

摘要: 在本文中，介绍了耗散型随机非线性薛定谔方程，它是通过对经典薛定谔方程进行修正得到的，证明了它具有随机共形动量演化规律，并研究了耗散型随机非线性薛定谔方程的一种新的离散数值格式，离散梯度格式，众所周知，构造出可以保持原始系统物理性质的数值格式具有重要意义，因此接下来我们研究了随机共形动量演化规律在离散梯度格式下是否成立，通过证明它是成立的。

Abstract: In this paper, the damped stochastic nonlinear Schrödinger equation is introduced; it is obtained by modifying the classical Schrödinger equation. It is proved that it has a stochastic conformal momentum evolution law, and a new discrete numerical scheme, discrete gradient scheme, is studied. As we all know, it is of great significance to construct a numerical scheme which can maintain the physical properties of the original system. Therefore, we then study whether the random conformal momentum evolution law is valid in the discrete gradient scheme, and prove that it is valid.