Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System

被引：0
作者：
Peter A. Markowich
Gerhard Rein
Gershon Wolansky
机构：
[1] Universität Wien,Institut für Mathematik
[2] Technion,undefined
来源：
Journal of Statistical Physics | 2002年 / 106卷
关键词：
Hartree problem; Schrödinger–Poisson system; stationary solutions; nonlinear stability;
D O I：
暂无
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学科分类号：
摘要：
We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.
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页码：1221 / 1239
页数：18
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