Analysis of human DNA through power-law statistics

Costa, M. O.; Silva, R.; Anselmo, D.H.A.L.; Silva, J. R. P.

doi:10.1103/physreve.99.022112

Cited by 20 publications

(14 citation statements)

References 49 publications

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“…scitation.org/journal/jmp paramagnetic systems, 77 nonlinear diffusion, 78 social systems, 79 complex networks, 80 analysis of human DNA, 81 blackbody radiation, 82 quantum entanglement, 83 etc. In this work, we employ the κ-algebra for generalizing classical and quantum mechanics with the aim of studying the properties of the resulting noncommuting space originated by the deformation.…”

Section: Articlementioning

confidence: 99%

κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

Costa

Gomez

Portesi

2020

Journal of Mathematical Physics

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We present the quantum and classical mechanics formalisms for a particle with a position-dependent mass in the context of a deformed algebraic structure (named κ-algebra), motivated by the Kappa-statistics. From this structure, we obtain deformed versions of the position and momentum operators, which allow us to define a point canonical transformation that maps a particle with a constant mass in a deformed space into a particle with a position-dependent mass in the standard space. We illustrate the formalism with a particle confined in an infinite potential well and the Mathews-Lakshmanan oscillator, exhibiting uncertainty relations depending on the deformation.

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Section: Articlementioning

confidence: 99%

κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

Costa

Gomez

Portesi

2020

Journal of Mathematical Physics

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“…Over the last two decades, the κ-statistical theory has attracted the interest of many researchers, who have studied its foundations [5][6][7][8][9][10], and the underlying thermodynamics [11][12][13][14][15], and at the same time, have considered specific applications of the theory to various fields of science. A nonexhaustive list of applications includes, among others, those in quantum statistics [16][17][18], in quantum theory [19][20][21], in plasma physics [22][23][24][25][26][27][28], in nuclear fission [29,30], in particle physics [31], in astrophysics [32][33][34][35][36], in cosmology [37][38][39][40][41][42][43], in geomechanics [44,45], in genomics [46,47], in complex networks [48,49], in waveform inversion algorithms [50], in image processing…”

Section: Introductionmentioning

confidence: 99%

New power-law tailed distributions emerging in $κ$-statistics

Kaniadakis

2022

Preprint

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Over the last two decades, it has been argued that the Lorentz transformation mechanism, which imposes the generalization of Newton's classical mechanics into Einstein's special relativity, implies a generalization, or deformation, of the ordinary statistical mechanics. The exponential function, which defines the Boltzmann's factor, emerges properly deformed within this formalism. Starting from this, so-called κ-deformed exponential function, we introduce new classes of statistical distributions emerging as the κ-deformed version of already known distribution as the Generalized Gamma, Weibull, Logistic which can be adopted in the analysis of statistical data that exhibit power-law tails.

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“…58 Concerning these formal structures, the κ-deformed statistics, originated from the κ-exponential and κ-logarithm functions, allows to develop an algebraic structure, called κ-algebra, [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74] with similar properties to the those of the q-algebra. In particular, the κ-statistics has been employed in plasma physics, 75 astrophysics, 76 paramagnetic systems, 77 nonlinear diffusion, 78 social systems, 79 complex networks, 80 analysis of human DNA, 81 blackbody radiation, 82 quantum entanglement, 83 etc.…”

Section: Introductionmentioning

confidence: 99%

$κ$-Deformed quantum and classical mechanics for a system with position-dependent effective mass

da Costa,

Gomez,

Portesi

2020

Preprint

View full text Add to dashboard Cite

We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named κ-algebra), motivated by the Kappa-statistics. From this structure we obtain deformed versions of the position and momentum operators, which allow to define a point canonical transformation that maps a particle with constant mass in a deformed space into a particle with position-dependent mass in the standard space.We illustrate the formalism with a particle confined in an infinite potential well and the Mathews-Lakshmanan oscillator, exhibiting uncertainty relations depending on the deformation.

show abstract

Analysis of human DNA through power-law statistics

Cited by 20 publications

References 49 publications

κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

New power-law tailed distributions emerging in $κ$-statistics

$κ$-Deformed quantum and classical mechanics for a system with position-dependent effective mass

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