On the Deformed Oscillator and the Deformed Derivative Associated with the Tsallis q-exponential

Jagannathan, R.; Khan, Sameen Ahmed

doi:10.1007/s10773-020-04534-w

Cited by 11 publications

(3 citation statements)

References 79 publications

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“…24 belongs to a particular case of a type-1 beta family of functions and for q 1 > 1 (by writing 1−q 1 = −(q 1 −1)), Eq. 24 belongs to a particular case of a type-2 beta family of functions [38][39][40][41][42][43] . The half lifetime characteristic in this case is:…”

Section: Fractional-order Modelsmentioning

confidence: 99%

Non-Debye impedance and relaxation models for dissipative electrochemical capacitors

Allagui,

Benaoum,

Elwakil

et al. 2022

Preprint

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Electrochemical capacitors are a class of energy devices in which complex mechanisms of accumulation and dissipation of electric energy take place when connected to a charging or discharging power system. Reliably modeling their frequency-domain and time-domain behaviors is very important for their proper design and integration in engineering applications, knowing that electrochemical capacitors in general exhibit anomalous tendency that cannot be adequately captured with traditional integer-order-based models. In this study we first review some of the widely used fractional-oder models for the description of impedance and relaxation functions of dissipative resistive-capacitive system, namely the Cole-Cole, Davidson-Cole, and Havriliak-Negami models. We then propose and derive new q-deformed models based on modified evolution equations for the charge or voltage when the device is discharged into a parallel resistive load. We verify our results on anomalous spectral impedance response and time-domain relaxation data for voltage and charge obtained from a commercial supercapacitor.

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Section: Fractional-order Modelsmentioning

confidence: 99%

Non-Debye impedance and relaxation models for dissipative electrochemical capacitors

Allagui,

Benaoum,

Elwakil

et al. 2022

Preprint

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“…I am grateful to Professor Ramaswamy Jagannathan (Institute of Mathematical Sciences, Chennai, India) for my training in accelerator physics, in particular, the novel area "Quantum theory of charged-particle beam optics" [82]- [84], which was the topic of my doctoral thesis. So, also in the subject of "Quantum Algebras" [85]. He came up with the brilliant idea to apply the Foldy-Wouthuysen transformation technique to explore Helmholtz optics and Maxwell optics.…”

Section: Acknowledgementsmentioning

confidence: 99%

Trigonometric Ratios Using Algebraic Methods

Khan¹

2021

Self Cite

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“…Further generalizations were studied, e.g., in Refs. [61][62][63][64][65][66]. In particular, it appears [66][67][68] that the coherent phase states are the special case of a large family of nonlinear coherent states introduced in papers [69,70].…”

Section: Introductionmentioning

confidence: 99%

Coherent Phase States in the Coordinate and Wigner Representations

Freitas

Dodonov

2022

Quantum Reports

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In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard (Klauder–Glauber–Sudarshan) coherent states, especially in the case of the high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is roughly twice weaker than for the vacuum squeezed states. The Robertson–Schrödinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of the (non)Gaussianity of CPS are considered.

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On the Deformed Oscillator and the Deformed Derivative Associated with the Tsallis q-exponential

Cited by 11 publications

References 79 publications

Non-Debye impedance and relaxation models for dissipative electrochemical capacitors

Non-Debye impedance and relaxation models for dissipative electrochemical capacitors

Trigonometric Ratios Using Algebraic Methods

Coherent Phase States in the Coordinate and Wigner Representations

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