Calin Buzea

Some physical implications of the gravitoelectromagnetic field in fractal space-time theory

It is shown that in terms of the fractal space–time theory the gravitoelectric potential is responsible for the quantisation of the planetary and binary galaxy motions. On a cosmic scale a homogeneous gravitomagnetic field allows not only an ordering of the Universe, but a ‘global’ redshift quantisation of galaxies as well.

The uncertainty relation for an assembly of Planck-type oscillators. A possible GR-quantum mechanics connection

Abstract It is shown that an assembly of Planck-type oscillators may be described by a continuous group with three parameters. In such a case, the uncertainty relation may be obtained by the application of a theorem on the invariant functions, when a simultaneous action of two isomorphic groups is involved. The groups parameters are interpreted by means of a variational principle, as field amplitudes of a stationary metric, while the groups invariant function is interpreted as the square root of a wave function satisfying a Schrodinger-type equation.

Cantorian ε(∞) space-time, a hydrodynamical model and unified superconductivity

Abstract We prove that the fractal space-time interpretation of Nelson’s stochastic quantum mechanics may be put into a one-to-one correspondence to the hydrodynamic model of quantum mechanics. Some implications of this correspondence are analyzed: Navier–Stokes type equations, uncertainty relation and type II superconductivity by means of a higher-dimensional fractal string. The two-dimensional (2D) projections of the higher fractal string corresponds to the anyons and 1D projections to the Cooper pair. The Cantorian-fractal structures occur, either by assimilating the Cooper pair with a two coupled oscillators (a simple mechanical model for e (∞) theory), or by El Naschie’s filling factor ν ≡ φ 3 =0.23606 (Cantorian-fractal quantum Hall effect).

Wave-particle duality and superconductivity in Weyl-Dirac theories

In the Gregorash–Papini–Wood approach to the Weyl–Dirac theory, some superconducting properties of the wave equation are analysed. In a special topology, for a constant modulus of the wavefunction, the phase gradient verifies an effect analogous to the gravitational Meissner effect (there is no momentum transfer between the wave and the particle, and the wave–particle duality is achieved by self-tunnelling). Through the gravitational Meissner effect the oscillation modes of a particle are cnoidal, and in a superconducting cylinder a quantum fluid moving along its axis is self-focusing. The matching between quantum hydrodynamics and wave mechanics is similar to the quantization of the gravitational fluxoid, and their unmatching is analogous to the gravitational analogue of the Aharonov–Bohm effect. The absence of the gravitational Meissner effect implies a permanent transfer of momentum between the wave and the particle such as the interior of the particle structured like a lattice. By defining a free energy we show that the wave–particle duality is equivalent to a normal–superconducting phase transition. In this context by generalizing the one-dimensional solution of the WD equation to the two-dimensional case, one can induce a superconducting state by in-phase oscillations of a vortex lattice.

Focusing and Guiding Charged Particles by a Superconducting Tube: An Analytical Nonlinear Approach for the Complete Flux Expulsion Model

We give an analytical solution for the nonlinear equation of motion of an electron beam in the radial direction of a superconducting tube, for the case of electrons moving close to the tube axis, in the complete flux expulsion model. Hence, we deduce a general expression for the focusing length that is dependent on the parameters of the superconducting tube and electron stream. Our focusing length is inversely proportional to x0, the width of the electron beam, and is in good agreement with experimental data.

Focusing and Guiding Charged Particles using Two-layer Superconducting Tubes: A Theoretical Approach.

A theoretical model of self-focusing of an impulse electron beam in a two-layered superconducting tube is designed. The self-focusing force is calculated and, by defining the pair breaking time of the superconducting pair, it is shown that this is conditioned among others by the ratio of the beam pulse period to the pair breaking time. The model is validated by evaluating both the breaking time and the focusing length.

The Time of Diffusion and Infinite Conductivity of High‐Tc Superconductors

In the composite fermion approach, extending in complex space the elliptic cn function (which is the perturbative solution of the Ginzburg-Landau equation in the strong coupling limit), we estimate the diffusion time of the superconductor charge carriers and we find that it diverges for particular values of the coherence length. We believe this mechanism may account for the infinite conductivity of high-temperature superconductors.

Focusing and Guiding Charged Particles Using a Superconducting Tube: An Analytical Nonlinear Approach

We present an analytical solution for the nonlinear equation of motion of an electron beam in the radial direction of a superconducting tube, for the case of electrons moving close to the tube axis. Accordingly, we deduce a general expression for the focusing length dependence on the parameters of the superconducting tube and the electron stream. Our calculated focusing length is in good agreement with the experimental data.

The isotope effect coefficient dependence on nonstoichiometry for single CuO layer superconductors

Considering that the variation of the critical temperature can be explained if the impurity potential acts only by the non-spin-flip part, in the presence of either a pure d-wave or anisotropic s-wave gap symmetry, and inserting the pair-breaking time dependence on temperature, we obtain a quantitative expression for the isotope effect coefficient α as a function of measured critical temperature Tc maximal critical temperature T and degree of anisotropy of the energy gap. Our result predicts the achievement of a large range of values in α for different ratios T/Tc. Introducing the dependence of the critical temperature and pair-breaking time on dopant content for a single CuO layer superconductors, we can describe the variation of the isotope effect coefficient with nonstoichiometry for these materials. The result for the case of anisotropic s-wave gap symmetry is in good agreement with the experimental data.

Improved Confinement of Neon Plasma Inside a High-Critical Temperature Superconducting Tube: A Theoretical Approach

A mathematical model, aiming at the improved confinement of neon plasma inside a high-Tc superconducting tube, is given. It is shown that the presence of the superconducting tube modifies the decay time of the plasma by means of the characteristic length of diffusion for generating a double-layer structure.