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This chapter describes the properties of any system where superconducting regions are coupled together by links which transmit phase coherence as the superconducting wire. Microscopic theories for the current flowing through a weak link coupling together two superconductors are divided into two types, based on either perturbation theory or the Green's function method. The Green's function method is applied only to equilibrium situations, and it has the advantage over the perturbation theory method in that the latter is valid only when the weak link is a tunneling barrier. An alternative formula for the current through a weak link, in which the propagation of electrons through the link is described in terms of the electron Green's function instead of the tunneling Hamiltonian, has been derived by Josephson. The excess current is seen to be strongly dependent on the electromagnetic properties of the barrier.

It is argued that at a sufficiently deep level the conventional quantitative approach to the study of nature faces difficult problems, and that biological processes should be seen as more fundamental, in a way that can be elaborated on the basis of Peircean semiotics and Yardley’s Circular Theory. In such a world-view, Wheeler’s observer-participation and emergent law arise naturally, rather than having to be imposed artificially. This points the way to a deeper understanding of nature, where meaning has a fundamental role to play that is invisible to quantitative science.

It is hypothesised, following Conrad et al. (1988) (http://www.tcm.phy.cam.ac.uk/~bdj10/papers/urbino.html) that quantum physics is not the ultimate theory of nature, but merely a theoretical account of the phenomena manifested in nature under particular conditions. These phenomena parallel cognitive phenomena in biosystems in a number of ways and are assumed to arise from related mechanisms. Quantum and biological accounts are complementary in the sense of Bohr and quantum accounts may be incomplete. In particular, following ideas of Stapp, 'the observer' is a system that, while lying outside the descriptive capacities of quantum mechanics, creates observable phenomena such as wave function collapse through its probing activities. Better understanding of such processes may pave the way to new science., Comment: 6 pages. Invited contribution to the forthcoming issue of BioSystems in memory of Michael Conrad. Now includes links to references on the Web

In what light should a scientist regard the assertions of a religion, or of religions in general? One extreme position is the atheistic one of regarding the assertions of religion as falsehoods. Such a position can be sustained only by regarding the experiences which individuals consider as validating their religious beliefs as being explicable in other ways and, in the absence of an adequate research programme to support it, must be considered more as falling within the field of opinion that as within that of science. The alternative to this atheistic position is that there exists an aspect of reality-that one may for convenience call transcendental-which embraces the subject matter of religion (or as some may prefer to term it, the spiritual aspect of life) and which is not at present encompassed by science. The question then arises whether some future science may be able to cope with this aspect of reality, or whether it will remain forever beyond the scope of science. The author attempts to explain the ways in which current scientific orthodoxies are being challenged and to convey some idea of the alternatives presently emerging. A number of important themes here include the questions of the validity of reductionism and the universality of quantum mechanics, as well as that of the relevance of mystical experience.

The magnetic field dependence of the surface reactance of superconducting tin has been measured at a frequency of 174 MHz. In the perpendicular field configuration (RF and static fields perpendicular to each other) the behaviour observed is approximately that expected from the Ginzburg-Landau theory in the static limit. In the parallel field configuration complicated behaviour is observed, even the sign of the reactance change being different at different temperatures. Near Tc there is a region where the reactance change has approximately linear dependence on the magnitude of the applied field, instead of the quadratic dependence expected in fields that not not too large.

The usual derivation of Maxwell's equations for magnetic materials rests on the assumption that the sources of magnetic field within the material can be split up into a magnetization density M and a current density j. In metals the same electrons (the conduction electrons) contribute both to M and to j, and one is forced to consider the question of what one means by M and what one means by j. In this paper we answer the question for systems in equilibrium, using a thermodynamic approach. The separation of sources of magnetic field into M and j is to a large extent arbitrary, but can be done in such a way that M is uniquely related to the local magnetic field and j is zero for a normal metal in equilibrium, while in the mixed state of a superconductor it satisfies the force-balance equation $\frac{(\mathbf{j}\ifmmode\times\else\texttimes\fi{}\mathbf{B})}{c}+\mathbf{P}=0$, P being the pinning force. The stress tensor for a magnetic system is derived from first principles (not assuming the field equations), and used to obtain the force-balance equation by an alternative method. Finally, two-dimensional systems such as superconducting thin films and surface sheaths are examined by similar methods.

Superconducting systems partitioned by barriers which are thin enough to allow supercurrents to pass through them are discussed. The implications for such systems of superconducting long-range order are considered, and a phenomenological theory developed and applied to a number of topics: penetration of a magnetic field into a barrier, interference of supercurrents in the presence of a magnetic field, the cut-off frequency associated with the propagation of electromagnetic waves along a barrier, a.c. supercurrents, and structure in the d.c. current-voltage characteristics of a barrier resulting from an applied microwave field or the a.c. supercurrent. The phenomenological theory is justified by the use of microscopic theory, and a new approach, based on the Gor'kov method, is described. The results of this approach, which is of more general validity than the tunnelling Hamiltonian method, are shown to be expressible in terms of Feynman diagrams. Attention is drawn to the analogy between supercurr...

The events leading to the discovery of tunnelling supercurrents are discussed. The devopment of the theory for d.c. and for a.c. supercurrents is discussed. 24 references.

Two functions of state ξ and η are derived, such that any equation of state for the critical region consistent with the scaling hypothesis can be expressed in the form η = (ξ). The representation has the useful property that the function has no unphysical singularities (such as the branch points associated with the critical isotherm or elsewhere in the usual representations of scaling-law equations of state).

Relations are derived between the superfluid density, the order parameter, and the specific heat singularity for superfluid helium near the lambda point.