Entropy and complexity analysis of hydrogenic Rydberg atoms
Abstract
The internal disorder of hydrogenic Rydberg atoms as contained in their position and momentum probability densities is examined by means of the following informationtheoretic spreading quantities: the radial and logarithmic expectation values, the Shannon entropy, and the Fisher information. As well, the complexity measures of CramerRao, FisherShannon, and Lopez RuizManciniCalvet types are investigated in both reciprocal spaces. The leading term of these quantities is rigorously calculated by use of the asymptotic properties of the concomitant entropic functionals of the Laguerre and Gegenbauer orthogonal polynomials which control the wavefunctions of the Rydberg states in both position and momentum spaces. The associated generalized Heisenberglike, logarithmic and entropic uncertainty relations are also given. Finally, application to linear (l= 0), circular (l=n 1), and quasicircular (l=n 2) states is explicitly done.
 Authors:
 Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071Granada (Spain)
 (Spain)
 Publication Date:
 OSTI Identifier:
 22163004
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 5; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ASYMPTOTIC SOLUTIONS; ATOMS; DENSITY; ENTROPY; EXPECTATION VALUE; HYDROGEN; POLYNOMIALS; PROBABILITY; RYDBERG STATES; WAVE FUNCTIONS
Citation Formats
LopezRosa, S., Departamento de Fisica Aplicada II, Universidad de Sevilla, 41012Sevilla, Toranzo, I. V., Dehesa, J. S., Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, 18071Granada, SanchezMoreno, P., and Departamento de Matematica Aplicada, Universidad de Granada, 18071Granada. Entropy and complexity analysis of hydrogenic Rydberg atoms. United States: N. p., 2013.
Web. doi:10.1063/1.4807095.
LopezRosa, S., Departamento de Fisica Aplicada II, Universidad de Sevilla, 41012Sevilla, Toranzo, I. V., Dehesa, J. S., Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, 18071Granada, SanchezMoreno, P., & Departamento de Matematica Aplicada, Universidad de Granada, 18071Granada. Entropy and complexity analysis of hydrogenic Rydberg atoms. United States. doi:10.1063/1.4807095.
LopezRosa, S., Departamento de Fisica Aplicada II, Universidad de Sevilla, 41012Sevilla, Toranzo, I. V., Dehesa, J. S., Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, 18071Granada, SanchezMoreno, P., and Departamento de Matematica Aplicada, Universidad de Granada, 18071Granada. Wed .
"Entropy and complexity analysis of hydrogenic Rydberg atoms". United States.
doi:10.1063/1.4807095.
@article{osti_22163004,
title = {Entropy and complexity analysis of hydrogenic Rydberg atoms},
author = {LopezRosa, S. and Departamento de Fisica Aplicada II, Universidad de Sevilla, 41012Sevilla and Toranzo, I. V. and Dehesa, J. S. and Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, 18071Granada and SanchezMoreno, P. and Departamento de Matematica Aplicada, Universidad de Granada, 18071Granada},
abstractNote = {The internal disorder of hydrogenic Rydberg atoms as contained in their position and momentum probability densities is examined by means of the following informationtheoretic spreading quantities: the radial and logarithmic expectation values, the Shannon entropy, and the Fisher information. As well, the complexity measures of CramerRao, FisherShannon, and Lopez RuizManciniCalvet types are investigated in both reciprocal spaces. The leading term of these quantities is rigorously calculated by use of the asymptotic properties of the concomitant entropic functionals of the Laguerre and Gegenbauer orthogonal polynomials which control the wavefunctions of the Rydberg states in both position and momentum spaces. The associated generalized Heisenberglike, logarithmic and entropic uncertainty relations are also given. Finally, application to linear (l= 0), circular (l=n 1), and quasicircular (l=n 2) states is explicitly done.},
doi = {10.1063/1.4807095},
journal = {Journal of Mathematical Physics},
number = 5,
volume = 54,
place = {United States},
year = {Wed May 15 00:00:00 EDT 2013},
month = {Wed May 15 00:00:00 EDT 2013}
}

Oscillations are shown to exist in the inversion symmetry of the electronic wave function of a hydrogenic atom coherently excited to a Rydberg state by a short pulse of laser radiation in a uniform electric field. The dependence of these oscillations on field strength is shown to scale as {ital n}{sup 2} where {ital n} is the principal quantum number. The possibility of using these oscillations to measure electric signals on picosecond timescales (terahertz frequencies) is suggested. {copyright} {ital 1996 American Institute of Physics.}

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