Generalized complexity measures and chaotic maps

Godó, B.; Nagy, Á.

doi:10.1063/1.4705088

Cited by 8 publications

(8 citation statements)

References 13 publications

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“…It is difficult to proof these theorems for non integral values of α and β. For positive real values of α and β, near continuous property can be verified by counter examples of density functions, such as step function and uniform density function [32][33][34][35][36]38 and so on.…”

Section: B Main Theorems For Near Continuous Property Of the Rényi Co...mentioning

confidence: 95%

“…For two identical density functions (ρ, ρ), the Rényi complexity ratio C (α,β) (ρ,ρ) reduces to generalized Rényi complexity of ρ. It is denoted by C (α,β) and defined by [32][33][34][35][36]…”

Section: E Generalized Rényi Complexity and Shape Rényi Complexitymentioning

confidence: 99%

“…Moreover, shape LMC is modified, so-called shape Rényi complexity (SRC) 30,31 , where Shannon entropy is replaced by Rényi entropy. Again the shape Rényi complexity is modified, so-called generalized Rényi complexity (GRC) [32][33][34][35][36][37] , where disequilibrium is replaced by inverse of Rényi entropic power. The SRC is a one parameter family of complexity measure, whereas GRC is a two parameter family complexity.…”

Section: Introductionmentioning

confidence: 99%

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Properties of Rényi complexity ratio of quantum states for central potential

Nath¹

2020

Preprint

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The Rényi complexity ratio is introduced for two density functions in three dimensional and multidimensional spherical quantum system. Some definitions about the localization property of several density functions are presented. Moreover, five theorems for near continuous property of the Rényi complexity ratio are proved. As an example, the solutions of pseudoharmonic oscillator and a family of isospectral potentials have been addressed.The Rényi entropy, Rényi complexity ratio, generalized Rényi complexity and shape Rényi complexity of integral order are found analytically. The properties of the Rényi complexity ratio are verified for some physical and artificial values of the system parameters. It is an extension of the generalized Rényi complexity.

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Section: B Main Theorems For Near Continuous Property Of the Rényi Co...mentioning

confidence: 95%

Section: E Generalized Rényi Complexity and Shape Rényi Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Properties of Rényi complexity ratio of quantum states for central potential

Nath¹

2020

Preprint

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“…The RCR

C_{(ρ, ρ)}^{(α, β)}

is called GRC of order

((),, α, β)

. It is denoted by

C^{(α, β)}

and defined by [32–36]

C^{(α, β)} = C_{(ρ, ρ)}^{(α, β)} = e^{ℛ_{ρ}^{(α)} - ℛ_{ρ}^{(β)}}, α, β > 0 .

…”

Section: Rényi Complexity Ratiomentioning

confidence: 99%

An introduction to analysis of Rényi complexity ratio of quantum states for central potential

Nath

2021

Int J of Quantum Chemistry

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Rényi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of Rényi complexity ratio are proved by Lebesgue measure. Some properties of Rényi complexity ratio are demonstrated and investigated for different quantum systems. Exact analytical forms of Rényi entropy, Rényi complexity ratio, statistical complexities based on Rényi entropy for integral order have been presented for solutions of pseudoharmonic and a family of isospectral potentials. Some properties of Rényi complexity ratio are verified for six diatomic molecules (CO, NO, N2, CH, H2, and ScH) and for other quantum systems.

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“…First, some simple quantum systems (H-atom, harmonic oscillator and square well) were studied with these measures. Recently, it has been demonstrated [3] that these generalized complexity measures are suitable to describe chaotic behavior. The logistic and Tinkerbell maps were analyzed.…”

Section: Introductionmentioning

confidence: 99%