Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System |
| |
Authors: | Peter A. Markowich Gerhard Rein Gershon Wolansky |
| |
Affiliation: | (1) Institut für Mathematik, Universität Wien, Strudlhofgasse 4, 1090 Vienna, Austria;(2) Technion, 32000 Haifa, Israel |
| |
Abstract: | 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. |
| |
Keywords: | Hartree problem Schrö dinger– Poisson system stationary solutions nonlinear stability |
本文献已被 SpringerLink 等数据库收录! |