Time quantization and<i>q</i>-deformations

Albanese, Claudio; Lawi, Stephan

doi:10.1088/0305-4470/37/8/009

Cited by 9 publications

(11 citation statements)

References 14 publications

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“…8 The same should then concern the strong field alternative to Eq. (16), but the identification of further experimental manifestations of present DLC's is desirable. It should be noted that a further signature of the dynamic localization is provided by the negative conductance observed in which can also be rewritten as …”

Section: Discussionmentioning

confidence: 99%

“…We have to remark that other realizations of the extremal condition could eventually be considered but such alternatives do not rely appropriately on Eq. (16). Differentiating once more again the MSD, one finds…”

Section: Minimizing the Mean Square Displacementmentioning

confidence: 95%

“…(79) is able to reproduce Eq. (16) as an approximation if an extra p = 1-selection would be done, 23 but this point requires further clarifications. Approximate though somewhat intricate versions of the "exact" dynamic localization have also been proposed, but this concerns again a rather restricted class of modulations.…”

Section: Rectangular Wave Fields and Other Applicationsmentioning

confidence: 99%

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Time Discretization Approach to Dynamic Localization Conditions

Papp

2006

Int. J. Mod. Phys. B

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An alternative wavefunction to the description of the dynamic localization of a charged particle moving on a one-dimensional lattice under the influence of a periodic time dependent electric field is written down. For this purpose the method of characteristics such as applied by Dunlap and Kenkre [Phys. Rev. B 34, 3625 (1986)] has been modified by using a different integration variable. Handling this wavefunction one is faced with the selection of admissible time values. This results in a conditionally exactly solvable problem, now by accounting specifically for the implementation of a time discretization working in conjunction with a related dynamic localization condition. In addition, one resorts to the strong field limit, which amounts to replace, to leading order, the large order zeros of the Bessel function J 0 (z), used before in connection with the cosinusoidal modulation, by integral multiples of π. Here z stands for the ratio between the field amplitude and the frequency. The modulation function of the electric field vanishes on the nodal points of the time grid, which stands for an effective field-free behavior. This opens the way to propose quickly tractable dynamic localization conditions for arbitrary periodic modulations. We have also found that the present time discretization approach produces the minimization of the mean square displacement characterizing the usual exact wavefunction. Other realizations and comparisons have also been presented.

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Section: Discussionmentioning

confidence: 99%

Section: Minimizing the Mean Square Displacementmentioning

confidence: 95%

Section: Rectangular Wave Fields and Other Applicationsmentioning

confidence: 99%

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Time Discretization Approach to Dynamic Localization Conditions

Papp

2006

Int. J. Mod. Phys. B

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“…At this point, the theory of time discontinuity is worth mentioning along with a chronon unit [32,33]. To conclude, light travels jumping at constant velocity.…”

Section: Discoursementioning

confidence: 99%

The Universe is Like a Hollowed Sphere. The Wave Concept of Time

Głuszak

Kluza

2015

: Interdiscip. Descr. Complex Syst.

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There is space for new ideas of the essence and the entity of time. The article refers to our time concept as a special wave type and presents results of our investigations on this subject. Thus, time defined as waves and an energy carrier could give explanation to multiple unclear phenomena. It could explicate gravity, organization in the planetary systems and light speed limit. A hypothesis that matter exists due to time wave motion would emerge from the elementary particle mass generation by the waves. Time becomes the main driving force in the Universe. The discussed thoughts need further analyses and verification but their confirmation may mean civilization changes.

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“…This connection centers on the notion of Bochner subordination of stochastic processes [5], [6], [18], [32], whereby a given Markov process X(t), t > 0, is observed in new stochastic 'operational time' S(t), rather than in standard clock time t, resulting in the process X(S(t)). This concept has found fruitful application in several branches of science, engineering, and finance [1], [15], [19], [20], [35]. In that context, generalized Linnik characteristic functions describe the family of processes obtained when isotropic Lévy stable motions are observed in the randomized operational time Γ(t), where for each t > 0, Γ(t) obeys a Gamma distribution on u ≥ 0.…”

mentioning

confidence: 99%

Bochner subordination, logarithmic diffusion equations, and blind deconvolution of hubble space telescope imagery and other scientific data

Carasso¹

2009

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Abstract. Generalized Linnik processes and associated logarithmic diffusion equations can be constructed by appropriate Bochner randomization of the time variable in Brownian motion and the related heat conduction equation. Remarkably, over a large but finite frequency range, generalized Linnik characteristic functions can exhibit almost Gaussian behavior near the origin, while behaving like low exponent isotropic Lévy stable laws away from the origin. Such behavior matches Fourier domain behavior in a large class of real blurred images of considerable scientific interest, including Hubble space telescope imagery and scanning electron micrographs. This paper develops a powerful blind deconvolution procedure based on postulating system optical transfer functions (otf) in the form of generalized Linnik characteristic functions. The system otf and 'true' sharp image are then reconstructed by solving a related logarithmic diffusion equation backwards in time, using the blurred image as data at time t = 1. The present methodology significantly improves upon previous work based on system otfs in the form of Lévy stable characteristic functions. Such improvement is validated by the substantially smaller image Lipschitz exponents that ensue, confirming increased fine structure recovery. These results resolve the unexplained appearance of exceptionally low Lévy stable exponents in previous work on the same class of images. The paper is illustrated with striking enhancements of gray scale and colored images.

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Time quantization andq-deformations

Cited by 9 publications

References 14 publications

Time Discretization Approach to Dynamic Localization Conditions

Time Discretization Approach to Dynamic Localization Conditions

The Universe is Like a Hollowed Sphere. The Wave Concept of Time

Bochner subordination, logarithmic diffusion equations, and blind deconvolution of hubble space telescope imagery and other scientific data

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