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

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

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

The concept of correlated density and its application

The correlated density appears in many physical systems ranging from dense interacting gases up to Fermi liquids which develop a coherent state at low temperatures, the superconductivity. One consequence of the correlated density is the Bernoulli potential in superconductors which compensates forces from dielectric currents. This Bernoulli potential allows to access material parameters. Though within the surface potential these contributions are largely canceled, the bulk measurements with NMR can access this potential. Recent experiments are explained and new ones suggested. The underlying quantum statistical theory in nonequilibrium is the nonlocal kinetic theory developed earlier.Comment: 14 pages, CMT30 proceeding

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

Are entrepreneurs' forecasts of economic indicators biased?

Insight into the investment behaviour of firms is central in understanding economic dynamics. A critical question, however, is whether firms provide sufficiently reliable data to enable them to make plausible forecasts at the meso (regional or sectoral) level. This paper analyses Dutch investment forecasts at different levels of aggregation. The central research question is whether entrepreneurs, individually or as a group, make systematic errors in their investment forecasts. A statistical test reveals that investment forecasts are not biased at the aggregated (regional and sectoral) level. At the micro level, however, there is a significant bias. Hence, using aggregated (regional and sectoral) data to test the lack of bias (unbiasedness) of forecasts may lead to the wrong conclusions. Moreover, aggregated investment forecasts may then be an inappropriate source for policy recommendations, despite their seemingly high reliability. This finding may in principle be valid for many European countries, since data collection on investment is organized in similar ways throughout Europe

Deterministic and controllable photonic scattering media via direct laser writing

Photonic scattering materials, such as biological tissue and white paper, are made of randomly positioned nanoscale inhomogeneities in refractive index that lead to multiple scattering of light. Typically these materials, both naturally-occurring or man-made, are formed through self assembly of the scattering inhomogeneities, which imposes challenges in tailoring the disorder and hence the optical properties. Here, We report on the nanofabrication of photonic scattering media using direct laser writing with deterministic design. These deterministic scattering media consist of submicron thick polymer nanorods that are randomly oriented within a cubic volume. We study the total transmission of light as a function of the number density of rods and of the sample thickness to extract the scattering and transport mean free paths using radiative transfer theory. Such photonic scattering media with deterministic and controllable properties are model systems for fundamental light scattering in particular with strong anisotropy and offer new applications in solid-state lighting and photovoltaics.Comment: 18 pages, 9 figure