## 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 non-linear 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.

Original language | English (US) |
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Pages (from-to) | 1221-1239 |

Number of pages | 19 |

Journal | Journal of Statistical Physics |

Volume | 106 |

Issue number | 5-6 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |

## Keywords

- Hartree problem
- Nonlinear stability
- Schrödinger-Poisson system
- Stationary solutions

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics