Dynamics of observables in a q-deformed harmonic oscillator

Pradeep, Aditi; Anupama, S.; Sudheesh, C.

doi:10.1140/epjd/e2019-100436-y

Cited by 10 publications

(4 citation statements)

References 32 publications

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“…It has been demonstrated that the time series of the anticipated values of dynamic variables, such as observables related to position and momentum, display periodic, quasi-periodic, or chaotic behavior contingent upon the deformation parameter q [13]. Similarly, in this scenario, we have distinctly observed the indications of periodic, quasi-periodic, or chaotic behavior in the entanglement dynamics of the system.…”

Section: Field Initially In the Deformed Coherent Statesupporting

confidence: 56%

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Wave packet dynamics of entangled q-deformed states

Rohith,

Anupama,

Sudheesh

2024

Phys. Scr.

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This paper explores the wave packet dynamics of a math-type q-deformed field interacting with atoms in a Kerr-type nonlinear medium. The primary focus is on the generation and dynamics of entanglement using the q-deformed field, with the quantification of entanglement accomplished through the von Neumann entropy. Two distinct initial q-deformed states, the q-deformed Fock state, and the q-deformed coherent state, are investigated. The entanglement dynamics reveal characteristics of periodic, quasi-periodic, and chaotic behaviour. Non-deformed initial states display wave packet near revivals and fractional revivals in entanglement dynamics while introducing q-deformation eliminates these features. The q-deformation significantly influences wave packet revivals and fractional revivals, with even a slight introduction causing their disappearance. For large values of q, the entanglement dynamics exhibit a chaotic nature. In the case of a beam splitter-type interaction applied to the initial deformed Fock state, an optimal deformation parameter q is identified, leading to maximum entanglement exceeding the non-deformed scenario.

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Section: Field Initially In the Deformed Coherent Statesupporting

confidence: 56%

“…A comprehensive discourse on the qdeformed generalized Weyl algebra can be found in [12]. A recent study on the dynamics of the math-type qdeformed harmonic oscillator revealed the signatures of chaos in the system [13]. The realization of the thermostatistics of q-deformed algebra can be built on the formalism of q-calculus [14].…”

Section: Introductionmentioning

confidence: 99%

Wave packet dynamics of entangled q-deformed states

Rohith,

Anupama,

Sudheesh

2024

Phys. Scr.

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“…We will focus on q deformations of SU(2)-like algebras. For a better understanding of q deformations and their various applications, we direct the readers' attention to the references [85][86][87][88][89][90][91][92][93][94][95].…”

Section: Q-deformed Su(2) Algebra and Lanczos Coefficientsmentioning

confidence: 99%

Probing quantum scars and weak ergodicity breaking through quantum complexity

2022

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Scar states are special many-body eigenstates that weakly violate the eigenstate thermalization hypothesis (ETH). Using the explicit formalism of the Lanczos algorithm, usually known as the forward scattering approximation in this context, we compute the Krylov state (spread) complexity of typical states generated by the time evolution of the PXP Hamiltonian, hosting such states. We show that the complexity for the Néel state revives in an approximate sense, while complexity for the generic ETH-obeying state always increases. This can be attributed to the approximate SU(2) structure of the corresponding generators of the Hamiltonian. We quantify such "closeness" by the q-deformed SU(2) algebra and provide an analytic expression of Lanczos coefficients for the Néel state within the approximate Krylov subspace. We intuitively explain the results in terms of a tight-binding model. We further consider a deformation of the PXP Hamiltonian and compute the corresponding Lanczos coefficients and the complexity. We find that complexity for the Néel state shows nearly perfect revival while the same does not hold for a generic ETH-obeying state.

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“…Various dynamic equations of NLSE type with q-deformed potentials have been proposed to model q-deformed processes in nuclear and atomic physics (see i.e. [55][56][57] and the references therein), and very recently Nutku et al studied the complexity of q-deformed quantum harmonic oscillator [58].…”

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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Dynamics of observables in a q-deformed harmonic oscillator

Cited by 10 publications

References 32 publications

Wave packet dynamics of entangled q-deformed states

Wave packet dynamics of entangled q-deformed states

Probing quantum scars and weak ergodicity breaking through quantum complexity

Self-localized Solitons of a q-Deformed Quantum System

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