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Rydberg multidimensional states: Rényi and Shannon entropies in momentum space
- Source :
- Journal of Physics A: Mathematical and Theoretical. 54:035305
- Publication Year :
- 2020
- Publisher :
- IOP Publishing, 2020.
-
Abstract
- In this work the momentum spreading of a multidimensional hydrogenic system in highly excited (Rydberg) states is quantified by means of the Rényi and Shannon entropies of its momentum probability density. These quantities, which rest at the core of numerous fields from atomic and molecular physics to quantum technologies, are determined by means of a methodology based on the strong degree-asymptotics of a modified L q -norm of the Gegenbauer polynomials which control the wavefunctions of these states in momentum space. The leading term of these entropic quantities is found from first principles, i.e. by means of the Coulomb potential parameters (space dimensionality, the nuclear charge) and the states’s hyperquantum numbers, in a rigorous simple manner. It is shown that they fulfill a logarithmic growth scaling law with the principal hyperquantum number n which characterizes the Rydberg state.
- Subjects :
- Computer Science::Machine Learning
Statistics and Probability
Physics
General Physics and Astronomy
Statistical and Nonlinear Physics
Position and momentum space
Computer Science::Digital Libraries
symbols.namesake
Modeling and Simulation
Quantum mechanics
Computer Science::Mathematical Software
Rydberg formula
symbols
Mathematical Physics
Subjects
Details
- ISSN :
- 17518121 and 17518113
- Volume :
- 54
- Database :
- OpenAIRE
- Journal :
- Journal of Physics A: Mathematical and Theoretical
- Accession number :
- edsair.doi...........5736aa21d23adf8721632e1143a6f178