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Results in Physics

Shannon entropy and complexity measures for Bohr Hamiltonian with triaxial nuclei

P. O. Amadi, A. N. Ikot, U. S. Okorie, Lewis F. Obagboye, Gaotsiwe Joel Rampho, R. Horchani, M. C. Onyeaju, Haifa I. Alrebdi, Abdel‐Haleem Abdel‐Aty

Published Jun 18, 2022• 3 citations
Publisher

Abstract

The Shannon entropy, disequilibrium, and complexity measures for n=0,1 in position and momentum space are investigated within the framework of Bohr Hamiltonian for triaxial nuclei with Davidson potential. The effect of the angular momentum quantum number L and that parameter of the minimum potential βo on the quantum information theoretic measures are studied in detail. The results for the disequilibrium, Shannon entropy, and complexity measures in position and momentum spaces are reported. Finally, the BBM for the Shannon entropy and the minimum inequality relation for the Lopez-Mancini-Calbet CLMCxCLMCp⩾1 are validated.

DOI
10.1016/j.rinp.2022.105744

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The Shannon entropy, disequilibrium, and complexity measures for n=0,1 in position and momentum space are investigated within the framework of Bohr Hamiltonian for triaxial nuclei with Davidson potential. The effect of the angular momentum quantum number L and that parameter of the minimum potential βo on the quantum information theoretic measures are studied in detail. The results for the disequilibrium, Shannon entropy, and complexity measures in position and momentum spaces are reported. Finally, the BBM for the Shannon entropy and the minimum inequality relation for the Lopez-Mancini-Calbet CLMCxCLMCp⩾1 are validated.
We have studied the variation of the position space statistical complexity measure defined by López-Ruiz, Mancini, and Calbet such as the product of exponential of the Shannon information entropy and the disequilibrium by using the 1D-normalized probability densities derived from solutions of the Schrödinger equation corresponding to the q-deformed harmonic oscillator and q-deformed Morse potentials. An analysis of the numerical results in terms of Shannon information entropy, disequilibrium and complexity measure are presented. In q-deformed harmonic oscillator, q-dependence of the complexity shows a minimum point for all excited energy levels. In the case of q-deformed Morse Potential, complexity decreases with increasing qqq for the investigated diatomic molecules.
The internal disorder of hydrogenic Rydberg atoms as contained in their position and momentum probability densities is examined by means of the following information-theoretic spreading quantities: the radial and logarithmic expectation values, the Shannon entropy, and the Fisher information. As well, the complexity measures of Crámer-Rao, Fisher-Shannon, and López Ruiz-Mancini-Calvet 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 Heisenberg-like, 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.
The position-momentum Shannon and R\'enyi uncertainty products of general quantum systems are shown to be bounded not only from below (through the known uncertainty relations), but also from above in terms of the Heisenberg-Kennard product $\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}\ensuremath{\langle}{p}^{2}\ensuremath{\rangle}$. Moreover, the Cram\'er-Rao, Fisher-Shannon, and L\'opez-Ruiz, Mancini, and Calbet shape measures of complexity (whose lower bounds have been recently found) are also bounded from above. The improvement of these bounds for systems subject to spherically symmetric potentials is also explicitly given. Finally, applications to hydrogenic and oscillator-like systems are done.
The approximate solutions of the Schrödinger equation with the central generalized Hulthén and Yukawa potential are investigated within the framework of the functional method. The obtained wave function and the energy levels are used to study the Shannon entropy, Renyi entropy, Fisher information, Shannon Fisher complexity, Shannon power and Fisher-Shannon product in both position and momentum spaces for the ground and first excited states. The theoretic information theories such as Shannon entropies Sr,Sp, Fisher information Ip,Ip and Renyi entropies Rβ as well as the information entropy probability densities ρ(r),ϕ(p) are illustrated graphically. The Bialynicki-Birula – Mycielski (BBM) inequality for the Shannon entropies and the Cramer-Rao inequality for the Fisher information are satisfied for the potential model.
In this work, we study the Shannon information entropies [Formula: see text] and [Formula: see text] of an infinite spherical well. The Shannon entropy [Formula: see text] is calculated numerically in terms of the analytical result of the wave function in momentum space. Some typical features of the position and momentum probability densities [Formula: see text] and [Formula: see text] as well as the information entropy densities [Formula: see text] and [Formula: see text] are demonstrated. We find that the position entropy [Formula: see text] increases with the radius a of the spherical well for given quantum numbers l, m and n. It is interesting to note that the position entropy [Formula: see text] decreases with the quantum numbers l and n for a fixed radius a and quantum number m. The position entropy [Formula: see text] is almost independent of the quantum numbers l, m and n. The momentum entropy [Formula: see text] first increases and then decreases with respect to the radius a. We also note that the [Formula: see text] increases with the radius a and finally arrives at a constant. In addition, the Bialynicki–Birula–Mycielski (BBM) inequality is verified and also hold for this confined system.