Inhomogeneous Quantum Invariance Group of Multi-Dimensional Multi-parameter Deformed Boson Algebra

Altıntaş, Azmi Ali; Arık, M.; Arikan, Ali Serdar; Dil, Emre

doi:10.1088/0256-307x/29/1/010203

Cited by 7 publications

(5 citation statements)

References 16 publications

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“…Here, the function g(ψ, t, x) denotes the right-hand-side of the expression given in Equation (13). The fractional order Laplacian in Equation ( 13) can be computed using the expression given in Equation ( 9) and IFFT routines.…”

Section: Mathematical Formulation Of the Petviashvili's Methods For T...mentioning

confidence: 99%

“…More specifically, we construct one and two soliton solutions of the fNLSE using the aforementioned numerical scheme and discuss their properties and the effects of fractional order derivative α on these solitons' characteristics and dynamics. Both q-deformed algebras [12,13] and potentials [14] have been considered in various areas from quantum computing [15,16] to quantum metrology [17], quantum thermodynamics [18] and so on. Therefore, in addition to zero potential and photorefractive potential, we consider q-deformed Rosen-Morse potentials and discuss their effects on soliton behavior and dynamics at Section 3.…”

Section: Introductionmentioning

confidence: 99%

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Petviashvili Method for the Fractional Schrödinger Equation

et al. 2022

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In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schrödinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the soliton solutions of the fNLSE by implementing a spectral method, in which the fractional-order spectral derivatives are computed using FFT (Fast Fourier Transform) routines, and the time integration is performed by a 4th order Runge–Kutta time-stepping algorithm. We discuss the effects of the order of the fractional derivative, α, on the properties, shapes, and temporal dynamics of the soliton solutions of the fNLSE. We also examine the interaction of those soliton solutions with zero, photorefractive and q-deformed Rosen–Morse potentials. We show that for all of these potentials, the soliton solutions of the fNLSE exhibit a splitting and spreading behavior, yet their dynamics can be altered by the different forms of the potentials and noise considered.

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Section: Mathematical Formulation Of the Petviashvili's Methods For T...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Petviashvili Method for the Fractional Schrödinger Equation

et al. 2022

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“…In atomic and nuclear physics, q-deformation was considered from theoretical and experimental perspectives [40][41][42][43][44][45][46]. It was considered for obtaining generalizations of quantum spin chains with exact valence-bond ground states [47], and self-localized solitons of q-deformed quantum systems have been recently explored [48].…”

Section: Introductionmentioning

confidence: 99%

Work harvesting by q-deformed statistical mutations in an Otto engine

Güvenilir¹,

Özaydın²,

Müstecaplıoğlu³

et al. 2022

Preprint

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We consider a semi-classical heat engine with a q-deformed quantum oscillator working substance and classical thermal baths. We investigate the influence of the quantum statistical deformation parameter q on the work and efficiency of the engine. In usual heat engines, a Hamiltonian parameter is varied during the work injection and extraction stages while the quantum statistical character of the working substance remains fixed. We point out that even if the Hamiltonian parameters are not changing, work can be harvested by quantum statistical changes of the working substance. Work extraction from thermal resources using quantum statistical mutations of the working substance makes a semi-classical engine cycle without any classical analog. As a concrete example of such a semi-classical heat engine with a profound quantum character, we consider the Otto cycle and use the deformation parameter to define the isentropic steps while keeping the Hamiltonian parameters constant. We verify that our conclusion applies to both bosonic and fermionic oscillator deformations.

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“…While Woronowicz's approach utilizes non-commutative multiplication, in Manin's approach a quantum group is constructed by making linear transformation on the quantum plane. Manin's approach can also be used to construct the inhomogeneous invariance quantum groups [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Self-localized Solitons of a q-Deformed Quantum System

Bayindir,

Altintas,

Ozaydin

2020

Preprint

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Beyond a pure mathematical interest, q-deformation is promising for the modeling and interpretation of various physical phenomena. In this paper, we numerically investigate the existence and properties of the self-localized soliton solutions of the nonlinear Schrödinger equation (NLSE) with a q-deformed Rosen-Morse potential. By implementing a Petviashvili method (PM), we obtain the self-localized one and two soliton solutions of the NLSE with a q-deformed Rosen-Morse potential. In order to investigate the temporal behavior and stabilities of these solitons, we implement a Fourier spectral method with a 4 th order Runge-Kutta time integrator. We observe that the self-localized one and two solitons are stable and remain bounded with a pulsating behavior and minor changes in the sidelobes of the soliton waveform. Additionally, we investigate the stability and robustness of these solitons under noisy perturbations. A sinusoidal monochromatic wave field modeled within the frame of the NLSE with a q-deformed Rosen-Morse potential turns into a chaotic wavefield and exhibits rogue oscillations due to modulation instability triggered by noise, however, the selflocalized solitons of the NLSE with a q-deformed Rosen-Morse potential are stable and robust under the effect of noise. We also show that soliton profiles can be reconstructed after a denoising process performed using a Savitzky-Golay filter.

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Inhomogeneous Quantum Invariance Group of Multi-Dimensional Multi-parameter Deformed Boson Algebra

Cited by 7 publications

References 16 publications

Petviashvili Method for the Fractional Schrödinger Equation

Petviashvili Method for the Fractional Schrödinger Equation

Work harvesting by q-deformed statistical mutations in an Otto engine

Self-localized Solitons of a q-Deformed Quantum System

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