Arnold, Anton; Markowich, Peter A.; Mauser, Norbert The one-dimensional periodic Bloch-Poisson equation. (English) Zbl 0828.34073 Math. Models Methods Appl. Sci. 1, No. 1, 83-112 (1991). Summary: We analyze the Bloch-Poisson model describing quantum steady states of electrons in thermodynamical equilibrium. The problem is set in a one- dimensional periodic geometry. The existence of a unique smooth solution for every positive temperature is proved, a convergent iterative procedure useful for the numerical simulation is obtained, and the classical limit is analyzed. Cited in 4 Documents MSC: 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 34A45 Theoretical approximation of solutions to ordinary differential equations 65C20 Probabilistic models, generic numerical methods in probability and statistics 81V35 Nuclear physics Keywords:Schrödinger equation; Bloch-Poisson model; quantum steady states of electrons; convergent iterative procedure; numerical simulation PDF BibTeX XML Cite \textit{A. Arnold} et al., Math. Models Methods Appl. Sci. 1, No. 1, 83--112 (1991; Zbl 0828.34073) Full Text: DOI OpenURL