Asymptotics of Entropic Functionals and Rydberg Physics
J.S. Dehesa (Department of Applied Mathematics and Institute of Theoretical and Computational Physics, University of Granada, Spain), S. Lopez-Rosa (Department of Applied Mathematics and Institute of Theoretical and Computational Physics, University of Granada, Spain) and R.J. Yanez (Department of Applied Mathematics and Institute of Theoretical and Computational Physics, University of Granada, Spain)
Entropic functionals of the special functions with different analytical structures (Shannon, Renyi, Tsallis, Fisher,..) have been found to describe various macroscopic properties of multielectronic systems.
Besides, they are the basic variables in various scientific disciplines as well as for finances and engineering. Their explicit expresion are generally not known except asymptotically. We will survey the recent developments in the asymptotic evaluation of the Shannon entropy of the classical orthogonal polynomials and other special functions. Finally, we will apply the corresponding results for the determination of the information-theoretic measures of the highly-excited (Rydberg) quantum-mechanical states of atomic systems.