Moving Pearl Vortices in Thin-Film Superconductors

The magnetic field hz of a moving Pearl vortex in a superconducting thin-film in (x,y) plane is studied with the help of the time-dependent London equation. It is found that for a vortex at the origin moving in +x direction, hz(x,y) is suppressed in front of the vortex, x>0, and enhanced behind (x<0). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.

New Quantum Diodes with Superconducting Properties at Non-Freezing Temperatures, and Their Computing Applications

Two opposed p&ndash;n diodes are connected with another junction that causes cancellation of the electric field in the depletion layer of each diode by the field of the other diode. This derived quantum diode is called the A system. Another dual diode, constructed by the same process but with the p- and n-types positioned as duality, called the B system. When a bias voltage is applied between the A and B systems, Lorentz conservation imparts a momentum (i.e., a wave number) to the carriers in the absence of any internal voltage. Thus, a superconducting bias current density appears without the need for cooling. The reappearances of electron&ndash;hole pairs on the junction surfaces are assumed to be described by entire wavefunctions normalized by the band gap. Based on the bias superconducting current, NOT and NAND gates were constructed from the quantum diode systems. Numerical calculations revealed that the constant phases of the entire wavefunctions of the p-and n-types converged. Accordingly, it was clarified that Bose&ndash;Einstein condensation and the Meissner effect (described by the London equation) occurred in the quantum diode systems. Moreover, the systems exhibited rectification characteristics and a switching speed of the order of 10-14 s. Combining this switching property with the large bias superconducting current (of the order of several V), we developed NOT and NAND gates with direct quantum correlations among many qubits, which are unaffected by random and thermal noises. These gates have memorization and initialization properties and are compatible with existing and accumulating programing algorithms. Moreover, when harvesting a divergent current output from these systems, the bias superconducting current and memorization property preserve the formed quantum correlations.

Mean-field Theory of the Meissner Effect in Bulk Revisited

We show that the implementation of the 1/c&sup2; transverse current-current interaction between electrons into the standard self-consistent electron BCS model in bulk under thermal equilibrium ensures in the stable superconductive phase the full compensation of a constant external magnetic field by the internal magnetic field created by the electrons i.e. one has an ideal diamagnet. However, no proof of the phenomenological London equation emerges within the bulk approach.

New Quantum Diodes with Superconducting Properties at Non-Freezing Temperatures, and Their Computing Applications

Two opposed p&ndash;n diodes are connected with another junction that causes cancellation of the electric field in the depletion layer of each diode by the field of the other diode. This derived quantum diode is called the A system. Another dual diode, constructed by the same process but with the p- and n-types positioned as duality, called the B system. When a bias voltage is applied between the A and B systems, Lorentz conservation imparts a momentum (i.e., a wave number) to the carriers in the absence of any internal voltage. Thus, a superconducting bias current density appears without the need for cooling. The reappearances of electron&ndash;hole pairs on the junction surfaces are assumed to be described by entire wavefunctions normalized by the band gap. Based on the bias superconducting current, NOT and NAND gates were constructed from the quantum diode systems. Numerical calculations revealed that the constant phases of the entire wavefunctions of the p-and n-types converged. Accordingly, it was clarified that Bose&ndash;Einstein condensation and the Meissner effect (described by the London equation) occurred in the quantum diode systems. Moreover, the systems exhibited rectification characteristics and a switching speed of the order of 10-14 s. Combining this switching property with the large bias superconducting current (of the order of several V), we developed NOT and NAND gates with direct quantum correlations among many qubits, which are unaffected by random and thermal noises. These gates have memorization and initialization properties and are compatible with existing and accumulating programing algorithms. Moreover, when harvesting a divergent current output from these systems, the bias superconducting current and memorization property preserve the formed quantum correlations.

Fractional Meissner–Ochsenfeld effect in superconductors

Fractional calculus (FC) is a valuable tool in the modeling of many phenomena, and it has become a topic of great interest in science and engineering. This mathematical tool has proved its efficiency in modeling the intermediate anomalous behaviors observed in different physical phenomena. The Meissner–Ochsenfeld effect describes the levitation of superconductors in a nonuniform magnetic field if they are cooled below critical temperature. This paper presents analytical solutions of the fractional London equation that describes the Meissner–Ochsenfeld effect considering the Liouville–Caputo, Caputo–Fabrizio–Caputo, Atangana–Baleanu–Caputo, fractional conformable derivative in Liouville–Caputo sense and Atangana–Koca–Caputo fractional-order derivatives. Numerical simulations were obtained for different values of the fractional-order.

Potential Energy Surfaces

This chapter discusses potential energy surfaces, that is, the electronic energy as a function of the internuclear coordinates as obtained from the electronic Schrödinger equation. It focuses on the general topology of such energy surfaces for unimolecular and bimolecular reactions. To that end, concepts like saddle point, barrier height, minimum-energy path, and early and late barriers are discussed. It concludes with a discussion of approximate analytical solutions to the electronic Schrödinger equation, in particular, the interaction of three hydrogen atoms expressed in terms of Coulomb and exchange integrals, as described by the so-called London equation. From this equation it is concluded that the total electronic energy is not equal to the sum of H–H pair energies. Finally, a semi-empirical extension of the London equation—the LEPS method—allows for a simple but somewhat crude construction of potential energy surfaces.