The one-dimensional periodic Bloch-Poisson equation. (English) Zbl 0828.34073

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.


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
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