论文标题
schr $ \ ddot {o} $ dinger方程的扰动稳定性
The perturbational stability of the Schr$\ddot{o}$dinger equation
论文作者
论文摘要
通过使用Wigner变换，可以证明，可以通过类似于与Vlasov方程相似的动力学理论来描述非线性Schr $ \ ddot {\ textmd {o}} $ dinger方程，该方程用于描述一个用于描述经典无碰撞等离子的vlasov方程。在本文中，我们主要在量子意义上显示Landau抑制作用，即Wigner-Poisson系统存在量子Landau阻尼。同时，我们还证明了在量子稳定性假设下的非线性Schr $ \ ddot {\ textmd {o}} $ dinger方程的存在和稳定性。
By using the Wigner transform, it is shown that the nonlinear Schr$\ddot{\textmd{o}}$dinger equation can be described, in phase space, by a kinetic theory similar to the Vlasov equation which is used for describing a classical collisionless plasma. In this paper we mainly show Landau damping in the quantum sense, namely,quantum Landau damping exists for the Wigner-Poisson system. At the same time, we also prove the existence and the stability of the nonlinear Schr$\ddot{\textmd{o}}$dinger equation under the quantum stability assumption.
