Reconstructing k-essence

Sen, Anjan A.

doi:10.1088/1475-7516/2006/03/010

Cited by 40 publications

(23 citation statements)

References 43 publications

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“…Finally, it is worth pointing out that none of the uncertainty relations (generalized Heisenberg-like, logarithmic, entropic) depends on the nuclear charge Z, in accordance with the general observations about entropic relations for homogeneous potentials [63].…”

Section: Discussionsupporting

confidence: 86%

Entropy and complexity analysis of hydrogenic Rydberg atoms

López-Rosa

Toranzo

Sánchez-Moreno

et al. 2013

Journal of Mathematical Physics

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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 LMC 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.

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Section: Discussionsupporting

confidence: 86%

Entropy and complexity analysis of hydrogenic Rydberg atoms

López-Rosa

Toranzo

Sánchez-Moreno

et al. 2013

Journal of Mathematical Physics

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“…[15][16][17][18]20,21] The relativistic effect have also been considered in the study of the information-theoretic quantities. [22][23][24][25][26][27] The Shannon entropy S½ q of the electron density, qðrÞ, in the coordinate space is defined as [28,29] S½q52 ð qðrÞ ln qðrÞdr; (1) and the corresponding momentum space Shannon entropy S½c is given by…”

Section: Introductionmentioning

confidence: 99%

Position and momentum information‐theoretic measures of the pseudoharmonic potential

Yahya

Oyewumi

Sen

2015

Int J of Quantum Chemistry

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In this study, the information-theoretic measures in both the position and momentum spaces for the pseudoharmonic potential using Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy and Onicescu information energy are investigated analytically and numerically. The results obtained are applied to some diatomic molecules. The Renyi and Tsallis entropies are analytically obtained in position space using Srivastava-Niukkanen linearization formula in terms of the Lauricella hypergeometric function. Also they are obtained in the momentum space in terms of the multivariate Bell polynomials of Combinatorics. We observed that the Fisher information increases with n in both the position and momentum spaces, but decreases with ℓ for all the diatomic molecules considered. The Shannon entropy also increases with increasing n in the position space and decreases with increasing ℓ. The variations of the Renyi and Tsallis entropies with ℓ are also discussed. The exact and numerical values of the Onicescu information energy are also obtained, after which the ratio of information-theoretic impetuses to lengths for Fisher, Shannon and Renyi are obtained.

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“…These results extend and complement various efforts about the information entropies of harmonic systems. [11,28,29,32,[36][37][38]63,69,70,73,76,77,[84][85][86][87][88][89]…”

Section: Shannon Entropy Of High-dimensional Harmonic Systemsmentioning

confidence: 99%

“…[25][26][27] The entropic properties of electronic systems (which crucially depend on the states' eigenfunctions) quantify the various facets of the spatial extension or multidimensional spreading of the electronic charge. Nowadays, there is an increasing interest on the dimensional dependence of the entropic properties for the stationary states of the multidimensional quantum systems [12,13,[28][29][30][31][32][33][34][35][36][37][38] in order to contribute to the emergent informational representation of the quantum systems which extends and complements the standard energetic representation. This is basically because of the increasing relevance of entropic properties in numerous biological, chemical, and physical phenomena [39][40][41][42][43][44] as well as in electronic correlations [45][46][47][48] and chemical reactions.…”

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confidence: 99%

The Shannon entropy of high‐dimensional hydrogenic and harmonic systems

Dehesa

Belega

Toranzo

et al. 2019

Int J of Quantum Chemistry

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There exists an increasing interest on the dimensionality dependence of the entropic properties for the stationary states of the multidimensional quantum systems in order to contribute to its emergent informational representation, which extends and complements the standard energetic representation. Nowadays, this is specially so for high-dimensional systems as they have been recently shown to be very useful in both scientific and technological fields. In this work, the Shannon entropy of the discrete stationary states of the high-dimensional harmonic (ie, oscillator-like) and hydrogenic systems is analytically determined in terms of the dimensionality, the potential strength, and the state's hyperquantum numbers. We have used an informationtheoretic methodology based on the asymptotics of some entropy-like integral functionals of the orthogonal polynomials and hyperspherical harmonics which control the wave functions of the quantum states, when the polynomial parameter is very large; this is basically because such a parameter is a linear function of the system's dimensionality. Finally, it is shown that the Shannon entropy of the D-dimensional harmonic and hydrogenic systems has a logarithmic growth rate of the type D log D when D ! ∞. K E Y W O R D S high-dimensional harmonic systems, high-dimensional hydrogenic systems, high-dimensional quantum systems, logarithmic integrals of orthogonal polynomials-asymptotics, Shannon entropy of high-dimensional quantum systems 1 | INTRODUCTION Multidimensional quantum systems consisting of many particles are a major challenge in Quantum Chemistry and Physics, as their behavior can be determined only with immense computational power. The physical solutions of their associated wave equations, and consequently all the chemical and physical properties of these systems, crucially depend on the space dimensionality D. Scientists are trying to discover elegant notions and techniques to simplify the problem (see, eg, ref. [1]). The 1986 Nobel Prize in Chemistry winner Dudley Robert Herschbach et al have developed [2][3][4][5] a very useful strategy to study the atomic and molecular systems, the D-dimensional scaling method, where the D is the basic variable. The pseudoclassical or highdimensional (D ! ∞) limit is the starting point of this strategy. Indeed, this method requires to solve a finite many-electron problem in the (D ! ∞)-limit, and then perturbation theory in 1D is used to have an approximate result for the standard dimension (D = 3), obtaining at times a quantitative accuracy comparable to the self-consistent Hartree-Fock calculations. Most important here is that the electronic structure for the (D ! ∞)-limit is beguilingly simple and exactly computable for any atom and molecule. For finite D but very large, the electrons are confined to harmonic oscillations about the fixed positions attained in the (D ! ∞)-limit. Indeed, at this high-dimensional limit, the electrons of a many-electron system assume fixed positions relative to

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Reconstructing k-essence

Cited by 40 publications

References 43 publications

Entropy and complexity analysis of hydrogenic Rydberg atoms

Entropy and complexity analysis of hydrogenic Rydberg atoms

Position and momentum information‐theoretic measures of the pseudoharmonic potential

The Shannon entropy of high‐dimensional hydrogenic and harmonic systems

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