Equations Meissner effect

The authors of Ref. [12] reconsidered the problem of magnetic field in quark matter taking into account the rotated electromagnetism . They came to the conclusion that magnetic field can exist in superconducting quark matter in any case, although it does not form a quantized vortex lattice, because it obeys sourceless Maxwell equations and there is no Meissner effect. In our opinion this latter result is incorrect, since the equations for gauge fields were not taken into account and the boundary conditions were not posed correctly. 

Similarly, Eq. (911) becomes the equation of the Meissner effect in superconductivity ... 

The report of the Meissner effect stimulated the London brothers to develop the London equations, which explained this effect, and which also predicted how far a static external magnetic field can penetrate into a superconductor. The next theoretical advance came in 1950 with the theory of Ginzburg and Landau, which described superconductivity in terms of an order parameter and provided a derivation for the London equations. Both of these theories are macroscopic or phenomenological in nature. In the same year, 1950, the... 

Equation 26.28 implies that either the term in the brackets is a constant or 0. For a superconductor above the transition temperature, B can penetrate the material even though js = 0 because s = 0. As the material is cooled below Tc, js 7 0 and s 7 therefore, B = 0, which is required by the Meissner effect. We therefore assume the term is zero because it is consistent with the observed behavior of superconductors and the persistent supercurrents are given by... 

Whitney and Pagano [6-32] extended Yang, Norris, and Stavsky s work [6-33] to the treatment of coupling between bending and extension. Whitney uses a higher order stress theory to obtain improved predictions of a, and and displacements at low width-to-thickness ratios [6-34], Meissner used his variational theorem to derive a consistent set of equations for inclusion of transverse shearing deformation effects in symmetrically laminated plates [6-35]. Finally, Ambartsumyan extended his treatment of transverse shearing deformation effects from plates to shells [6-36]. 

A further point which should be mentioned concerns the treatment of incomplete model spaces. Meissner and his collaborators [61], have shown that the cancellation of terms corresponding to disconnected diagrams in the equations for amplitudes is, in general, not a sufficient condition for extensivity. In any Hilbert-space MRCC method, extensivity may be destroyed by diagonalization of the effective Hamiltonian matrix. For the complete model spaces employed in the studies reviewed here, the diagonalization has a full Cl-like character and, therefore, extensivity is ensured. Although Meissner and collaborators [61,62] devised an approach which should also be extensive for the case of an incomplete model space, practical implementation appears somewhat complicated. 

In 1935, Fritz and Heinz London (London and London, 1935) provided a first phenomenological approach to the theory of superconductivity. Using the concept of a superelectron with twice the electron s mass and charge, the London equations described very well the properties of a superconductor that is, its infinite electric conductivity as well as the decay of the magnetic field in a thin surface layer of a superconductor (the Meissner-Ochsenfeld effect) (see Appendix E). 

In the classical model of superconductivity, the London equations (London and London 1935) are equivalent to Ohm s law j = o-E for a normal electric conductor. The first of the London equations [Eq. (E.l)] represents a conductor with R = 0, while the second [Eq. (E.2)] is equivalent to the Meissner-Ochsenfeld effect (Figure E.l), and describes the decay of a magnetic field within a thin surface layer characterized by the penetration depth,... 

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