19 research outputs found
Quantum Diffusions and Appell Systems
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