Information measures of a deformed harmonic oscillator in a static electric field

Nascimento, J.P.G.; Ferreira, Fischer; Aguiar, V.; Guedes, I.; Filho, R. N. Costa

doi:10.1016/j.physa.2018.02.036

Cited by 10 publications

(6 citation statements)

References 32 publications

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“…As well, it would be interesting to extend the generalized Heisenberg expressions here found to quantum information [119]. Finally, the extension of the stationary study here shown and reviewed remain to be done for the time-dependent multidimensional harmonic oscillators as well as to Dirac oscillators and some anharmonic oscillators [120,121,122,123,124].…”

Section: Discussionmentioning

confidence: 78%

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Dispersion and entropy-like measures of multidimensional harmonic systems. Application to Rydberg states and high-dimensional oscillators

Dehesa

Toranzo

2020

Preprint

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The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like quantities (Fisher information, Shannon and Rényi entropies, disequilibrium) of its quantum probability distribution together with their associated uncertainty relations. They are explicitly given, at times in a closed compact form, by means of the potential parameters (oscillator strength, dimensionality, D) and the hyperquantum numbers (nr, µ1, µ2, . . . , µD−1) which characterize the state. Emphasis is placed on the highly-excited Rydberg (high radial hyperquantum number nr, fixed D) and the high-dimensional (high D, fixed hyperquantum numbers) states. We have used a methodology where the theoretical determination of the integral functionals of the Laguerre and Gegenbauer polynomials, which describe the spreading quantities, leans heavily on the algebraic properties and asymptotical behavior of some weighted Lq-norms of these orthogonal functions.

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Section: Discussionmentioning

confidence: 78%

“…To prove the remaining expression given by Equation (121) we start from the Shannon-like integral functional of the orthonormal Gegenbauer polynomials…”

Section: The Shannon Entropy Of High-dimensional Oscillatorsmentioning

confidence: 99%

Dispersion and entropy-like measures of multidimensional harmonic systems. Application to Rydberg states and high-dimensional oscillators

Dehesa

Toranzo

2020

Preprint

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“…Although the Heisenberg uncertainty relations play an important role in quantum mechanics, new forms of uncertainty relations that may lead to limits beyond those given by the Heisenberg uncertainty relation have been taken into account. For instance, we mention the entropic uncertainty relations obtained from the Shannon entropy [30][31][32][33] and the generalized and extendend uncertainty principle [34,35].…”

Section: Theorymentioning

confidence: 99%

London superconductivity approach in a time-dependent background

Aguiar¹,

Nascimento²,

Guedes³

et al. 2021

Physica C: Superconductivity and its Applications

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“…Shannon entropy is a well-known theory for uncertainty measure in the probabilistic framework, which has attracted much attention in real applications [ 32 , 33 , 34 ]. However, due to the reason that a mass function is the generalized probability assigned on the power set of the frame of discernment (FOD), Shannon entropy cannot be used directly among mass functions in the framework of Dempster–Shafer evidence theory.…”

Section: Introductionmentioning

confidence: 99%

Measuring Uncertainty in the Negation Evidence for Multi-Source Information Fusion

Tang

Chen

Zhou

2022

Entropy

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Dempster–Shafer evidence theory is widely used in modeling and reasoning uncertain information in real applications. Recently, a new perspective of modeling uncertain information with the negation of evidence was proposed and has attracted a lot of attention. Both the basic probability assignment (BPA) and the negation of BPA in the evidence theory framework can model and reason uncertain information. However, how to address the uncertainty in the negation information modeled as the negation of BPA is still an open issue. Inspired by the uncertainty measures in Dempster–Shafer evidence theory, a method of measuring the uncertainty in the negation evidence is proposed. The belief entropy named Deng entropy, which has attracted a lot of attention among researchers, is adopted and improved for measuring the uncertainty of negation evidence. The proposed measure is defined based on the negation function of BPA and can quantify the uncertainty of the negation evidence. In addition, an improved method of multi-source information fusion considering uncertainty quantification in the negation evidence with the new measure is proposed. Experimental results on a numerical example and a fault diagnosis problem verify the rationality and effectiveness of the proposed method in measuring and fusing uncertain information.

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Information measures of a deformed harmonic oscillator in a static electric field

Cited by 10 publications

References 32 publications

Dispersion and entropy-like measures of multidimensional harmonic systems. Application to Rydberg states and high-dimensional oscillators

Dispersion and entropy-like measures of multidimensional harmonic systems. Application to Rydberg states and high-dimensional oscillators

London superconductivity approach in a time-dependent background

Measuring Uncertainty in the Negation Evidence for Multi-Source Information Fusion

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