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Discrete Schrödinger-Poisson systems preserving energy and mass

✍ Scribed by C. Ringhofer; J. Soler

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
343 KB
Volume
13
Category
Article
ISSN
0893-9659

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✦ Synopsis

A discrete predictor-corrector SchrSdinger-Poisson system is proposed which has the property of mass and energy conservation exactly on the discrete level. The discretization is based on the Cranck-Nicholson scheme, which preserves these invariants of the Schr6dinger-Poisson syst;em, but involves the solution of nonlinear equations at each time step. A modified linearized scheme is proposed where conservation is achieved by introducing a phase modulation in the corrector step.

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On quasi-linear Schrödinger–Poisson syst
On quasi-linear Schrödinger–Poisson systems
✍ R. Illner; H. Lange; B. Toomire; Paul Zweifel 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB

We study a high-field version of the periodic Schro¨dinger-Poisson system, for which the Poisson equation includes nonlinear terms corresponding to a field-dependent dielectric constant. Using a Galerkin scheme, we prove global existence and uniqueness, and present the matrix equations for the numer