Existence and nonlinear stability of steady states of the Schrödinger-Poisson system

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dc.creatorMarkowich, Peter A.
dc.creatorRein, Gerhard
dc.creatorWolansky, Gershon
dc.date2001-01-18
dc.date.accessioned2026-07-25T22:14:53Z
dc.descriptionWe consider the Schrödinger-Poisson system in the attractive (plasma physics) Coulomb case. Given a steady state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such steady 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 steady state of the Schrödinger-Poisson system and lies in the stability class. The steady states are parametrized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0101020
dc.identifierhttp://arxiv.org/abs/math-ph/0101020
dc.identifierJournal of Statistical Physics, 106 (5-6), 1221-1239 (2002)
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/87275
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject35Q40,35Q55,35B35,82D10
dc.titleExistence and nonlinear stability of steady states of the Schrödinger-Poisson system
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