1,096 research outputs found
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
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