P. Nica

Superconductivity by means of the subquantum medium coherence

In the hydrodynamic formulation of the scale relativity theory one shows that a stable vortices distribution of bipolaron type induces superconducting pairs by means of the quantum potential. Then, usual mechanisms (as, for example, the exchange interaction used in the bipolaron theory) are reduced to the coherence on the subquantum medium, the superconducting pairs resulting as a one-dimensional projection of a fractal. The temperature dependences of the superconducting parameters (coherence length, critical speed, pair breaking time, carriers concentration, penetration depth, critical field, critical current) and the concordance with the experimental data and other theories are analyzed.

Cantorian E(∞) space-time and generalized superconductivity

Abstract In fractal space-time theory we built a superconducting model for generalized fields (electromagnetic and linear gravitation): generalized Maxwell and Londons equations, generalized Meissner and shielding effects, oscillation modes in thin cylindrical generalized superconductors (generalized supertrons) and generalized superconductivity as a gauge theory. In such a context the atomic, planetary and double galaxies systems are self-organized as fractal superconducting structures. The Cantorian E (∞) structure of space-time implies a two-dimensional cnoidal distribution of the particles concentration for the solid–liquid interface and allows the evaluation of the kinetic moment of a neutron star.

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).

El Naschie’s cantorian strings and duality in Weyl–Dirac theory

Abstract In the weak-field approximation, some implications of duality in the Weyl–Dirac (WD) theory, using the Gregorash–Papini–Wood approach, are investigated. Any particle is in a permanent interaction with the ‘subquantic level’ (Madelung’s fluid) and, as a result of this interaction, the particle acquires the proper fluctuation curvature and the proper fluctuation energy, respectively. By fixing the fluctuations scale, the quantum fluid orders either by means of bright cnoidal oscillation modes inducing causality, or by means of dark cnoidal oscillation modes inducing acausality, and non-linear effects, respectively. The periodic mode is associated with the undulatory characteristic, and the solitonic one with the corpuscular one. By not fixing the fluctuations scale and keeping the symmetry, the quantum fluid orders like a two-dimensional (2D) lattice of vortices, so that the duality needs coherence. In the compatibility between quantum hydrodynamics in the Madelung’s representation and the wave mechanics, the self-gravitational field of the Weyl–Dirac type physical object is generated. El Naschie’s space–time implies, by means of transfinite heterotic string theory, the masses of nucleons, and, by the gravitational fractional quantum Hall effect, the dispersion of the wave-packet on the particle. The analysis of the fractal dimension of the physical object described by the WD theory shows that the waves, and corpuscle, respectively are 2D projections of a higher dimensional special string in El Naschie’s space–time (El Naschie’s string).

On the Weyl–Dirac duality by means of a Cantorian fractal string

Abstract The fractal dimension analysis of the Weyl–Dirac type object shows that the wave and the corpuscle are two-dimensional projections of a higher-dimensional string in a Cantorian fractal space–time (Cantorian fractal string).