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. 
Demosthenes Ellinas (Department of Sciences, Section of mathematics,   Technical University of Crete)