19 research outputs found

    Quantum Diffusions and Appell Systems

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    Within the algebraic framework of Hopf algebras, random walks and associated diffusion equations (master equations) are constructed and studied for two basic operator algebras of Quantum Mechanics i.e the Heisenberg-Weyl algebra (hw) and its q-deformed version hw_q. This is done by means of functionals determined by the associated coherent state density operators. The ensuing master equations admit solutions given by hw and hw_q-valued Appell systems.Comment: Latex 12 pages, no figures. Submitted to Journal of Computational and Applied Mathematics. Special Issue of Proccedings of Fifth Inter. Symp. on Orthogonal Polynomaials, Special Functions and their Application
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