Hydrodynamic formulation of scale relativity theory and unified superconductivity by means of a fractal string

Agop, M.; Ioannou, P.; Buzea, Cristina; Nica, P.

doi:10.1016/s0921-4534(02)02805-8

Cited by 7 publications

(6 citation statements)

References 28 publications

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“…We shall investigate other interesting issues (Ghirardi and Marinatto, 2004;Avancini and Krein, 1995;Harju et al, 2002;Braun and Vechernin, 2004;Kuze and Sirois, 2003;Yabu et al, 2004;Schrieffer, 2004;Agop et al, 2003;Ichinose and Matsui, 2003;Fradkin et al, 1998) in the future.…”

Section: Resultsmentioning

confidence: 99%

“…The progress in semiconductor technology has opened a rich field of studies focused on the fundamental electron-electron interactions and quantum effects in artificial atoms and molecules (composite particles Ghirardi and Marinatto, 2004;Avancini and Krein, 1995;Harju et al, 2002;Braun and Vechernin, 2004;Kuze and Sirois, 2003;Yabu et al, 2004;Schrieffer, 2004;Agop et al, 2003;Ichinose and Matsui, 2003;Fradkin et al, 1998). The most striking feature of two-dimensional semiconductor quantum dots (QD) and quantum dot molecules (QDM) is that the correlation and magnetic field effects are greatly enhanced compared with their normal counterparts.…”

Section: Introductionmentioning

confidence: 99%

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Plane Waves Propagating in Gases Composed of Composite Particles

Chu¹

2005

Int J Theor Phys

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The quantum discrete kinetic equations are solved to study the propagation of plane waves in a system of composite particles with hard-sphere interactions and the filling factor (ν) being 1/2. We compare the dispersion relations thus obtained by the relevant Pauli-blocking parameter B which describes the different-statistics particles for the quantum analog of the discrete Boltzmann system when B is positive (Bose gases), zero (Boltzmann gases), and negative (Fermi Gases). We found, as the effective magnetic field being zero (ν = 1/2 using the composite fermion formulation), the electric field effect will induce anomalous dispersion relations.KEY WORDS: Pauli-blocking effect; external field.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Plane Waves Propagating in Gases Composed of Composite Particles

Chu¹

2005

Int J Theor Phys

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“…with Λ and D having the significance of a small elementary distance and of the 'cinematic viscosity' (or amplitude of the fractal fluctuations), respectively, and U(x) is the velocity of the 'Newtonian fluid', which is nothing but the imaginary part of the complex velocity [13]. In what follows, we solve this equation accurately by means of the WKBJ approximation method with connection formulas.…”

Section: Fractal Space-time and The Motion Equation Of Free Particlesmentioning

confidence: 99%

Quantum Effects Through a Fractal Theory of Motion

Agop¹,

Buzea²,

Bācāiţā³

et al. 2013

Advances in Quantum Mechanics

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“…In other words, we get from the calculus, that the velocity field V\s indeed transported by the motion of the 'Newtonian fluid' particles with the velocity U(x) (the imaginary part of the complex velocity [7]). it can be transmitted, attenuated or reflected at this scale length.…”

Section: Velocity Potential γ (χ) and The Quantum Barriermentioning

confidence: 99%

Motion of Free Particles in Fractal Space-time

Buzea¹,

Bejinariu²,

Boris³

et al. 2009

International Journal of Nonlinear Sciences and Numerical Simulation

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When considering time and space scales such that the description of the trajectories of these bodies is in the shape of non-differentiable curves, one gets fractal curves of fractal dimension 2. Continuity and non-differentiability yield a fractal space and a symmetry breaking of the differential time element which gives a doubling of the velocity fields. An application of these principles on the motion equation of free particles leads to the occurrence of a supplementary TISE (time independent, Schr dinger-type equation). When using a WKBJ method to solve this equation, one gets some interesting results. In other words, scale transformation laws produce, on the motion equation of free particles under some peculiar assumptions, effects which are analogous to those of a "macroscopic quantum mechanics".

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Hydrodynamic formulation of scale relativity theory and unified superconductivity by means of a fractal string

Cited by 7 publications

References 28 publications

Plane Waves Propagating in Gases Composed of Composite Particles

Plane Waves Propagating in Gases Composed of Composite Particles

Quantum Effects Through a Fractal Theory of Motion

Motion of Free Particles in Fractal Space-time

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