Boundary condition for Ginzburg-Landau theory of superconducting layers

Electrostatic charging changes the critical temperature of superconducting thin layers. To understand the basic mechanism, it is possible to use the Ginzburg-Landau theory with the boundary condition derived by de Gennes from the BCS theory. Here we show that a similar boundary condition can be obtained from the principle of minimum free energy. We compare the two boundary conditions and use the Budd-Vannimenus theorem as a test of approximations.Comment: 6 pages, 4 figure

The Determination of Technology and Commodity Policy in the U.S. Dairy Industry

United States dairy policy includes both predatory and productive components. The milk price support program is designed to transfer income to dairy farmers while research and extension expenditures are designed to increase social welfare. The purpose of this chapter is to provide an empirical example of the theory developed in the previous chapter. It has long been recognized the government research and extension policies have been significant contributors to technological advance in agriculture (Evenson and Kislev 1976, Evenson, Waggoner, and Ruttan 1979). The advent of technological change on agriculture and its policy implications was first noted by Schultz (1945, 1953). Some, like Cochrane (1958) in characterizing his famous technological treadmill thesis, argued for price supports in order to compensate farmers for the adverse effects of research on farmers\u27 welfare. Indeed, commentators like Thurow (1981) and Schlesinger (1984) argue that public good provision in agriculture is one of the few major economic success stories of government intervention in the history of the United States. Nevertheless, one of the most stylized facts in government policy intervention in agriculture is the pervasive level and overwhelming evidence of underinvestment in public research (Ruttan 1982). Concomitant to this notion, economists have alleged that governments \u27overinvest\u27 in commodity policies because of the associated deadweight losses generated

Electrostatic potential in a superconductor

The electrostatic potential in a superconductor is studied. To this end Bardeen's extension of the Ginzburg-Landau theory to low temperatures is used to derive three Ginzburg-Landau equations - the Maxwell equation for the vector potential, the Schroedinger equation for the wave function and the Poisson equation for the electrostatic potential. The electrostatic and the thermodynamic potential compensate each other to a great extent resulting into an effective potential acting on the superconducting condensate. For the Abrikosov vortex lattice in Niobium, numerical solutions are presented and the different contributions to the electrostatic potential and the related charge distribution are discussed.Comment: 19 pages, 11 figure

Optical BCS conductivity at imaginary frequencies and dispersion energies of superconductors

We present an efficient expression for the analytic continuation to arbitrary complex frequencies of the complex optical and AC conductivity of a homogeneous superconductor with arbitrary mean free path. Knowledge of this quantity is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type-I superconducting bodies. When considered for imaginary frequencies, our formula evaluates faster than previous schemes involving Kramers--Kronig transforms. A number of applications illustrates its efficiency: a simplified low-frequency expansion of the conductivity, the electromagnetic bulk self-energy due to longitudinal plasma oscillations, and the Casimir free energy of a superconducting cavity.Comment: 20 pages, 7 figures, calculation of Casimir energy adde

Failed theories of superconductivity

Almost half a century passed between the discovery of superconductivity by Kamerlingh Onnes and the theoretical explanation of the phenomenon by Bardeen, Cooper and Schrieffer. During the intervening years the brightest minds in theoretical physics tried and failed to develop a microscopic understanding of the effect. A summary of some of those unsuccessful attempts to understand superconductivity not only demonstrates the extraordinary achievement made by formulating the BCS theory, but also illustrates that mistakes are a natural and healthy part of the scientific discourse, and that inapplicable, even incorrect theories can turn out to be interesting and inspiring.Comment: 14 pages, 3 figures (typos fixed), to appear in: Bardeen Cooper and Schrieffer: 50 YEARS, edited by Leon N Cooper and Dmitri Feldma

Interaction between ionic lattices and superconducting condensates

The interaction of the ionic lattice with the superconducting condensate is treated in terms of the electrostatic force in superconductors. It is shown that this force is similar but not identical to the force suggested by the volume difference of the normal and superconducting states. The BCS theory shows larger deviations than the two-fluid model.Comment: 6 pages no figure

Comparison among Various Expressions of Complex Admittance for Quantum System in Contact with Heat Reservoir

Relation among various expressions of the complex admittance for quantum systems in contact with heat reservoir is studied. Exact expressions of the complex admittance are derived in various types of formulations of equations of motion under contact with heat reservoir. Namely, the complex admittance is studied in the relaxation method and the external-field method. In the former method, the admittance is calculated using the Kubo formula for quantum systems in contact with heat reservoir in no external driving fields, while in the latter method the admittance is directly calculated from equations of motion with external driving terms. In each method, two types of equation of motions are considered, i.e., the time-convolution (TC) equation and time-convolutionless (TCL) equation. That is, the full of the four cases are studied. It is turned out that the expression of the complex admittance obtained by using the relaxation method with the TC equation exactly coincides with that obtained by using the external-field method with the TC equation, while other two methods give different forms. It is also explicitly demonstrated that all the expressions of the complex admittance coincide with each other in the lowest Born approximation for the systemreservoir interaction. The formulae necessary for the higher order expansions in powers of the system-reservoir interaction are derived, and also the expressions of the admittance in the n-th order approximation are given. To characterize the TC and TCL methods, we study the expressions of the admittances of two exactly solvable models. Each exact form of admittance is compared with the results of the two methods in the lowest Born approximation. It is found that depending on the model, either of TC and TCL would be the better method.Comment: 34pages, no figur