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London Equation
The London equations, developed by brothers Fritz and Heinz London in 1935, are constitutive relations for a superconductor relating its superconducting current to electromagnetic fields in and around it. Whereas Ohm's law is the simplest constitutive relation for an ordinary conductor, the London equations are the simplest meaningful description of superconducting phenomena, and form the genesis of almost any modern introductory text on the subject. A major triumph of the equations is their ability to explain the Meissner effect, wherein a material exponentially expels all internal magnetic fields as it crosses the superconducting threshold. Description There are two London equations when expressed in terms of measurable fields: :\frac = \frac\mathbf, \qquad \mathbf\times\mathbf_ =-\frac\mathbf. Here _ is the (superconducting) current density, E and B are respectively the electric and magnetic fields within the superconductor, e\, is the charge of an electron or proton, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Fixing
In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a certain transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom. Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bcs Theory
In physics, the Bardeen–Cooper–Schrieffer (BCS) theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes superconductivity as a microscopic effect caused by a condensation of Cooper pairs. The theory is also used in nuclear physics to describe the pairing interaction between nucleons in an atomic nucleus. It was proposed by Bardeen, Cooper, and Schrieffer in 1957; they received the Nobel Prize in Physics for this theory in 1972. History Rapid progress in the understanding of superconductivity gained momentum in the mid-1950s. It began with the 1948 paper, "On the Problem of the Molecular Theory of Superconductivity", where Fritz London proposed that the phenomenological London equations may be consequences of the coherence of a quantum state. In 1953, Brian Pippard, motivated by penetration experiments, proposed that this would mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Force Law
Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum Laurentum was an ancient Rome, ancient Roman city of Latium situated between Ostia Antica, Ostia and Lavinium, on the west coast of the Italian Peninsula southwest of Rome. Roman writers regarded it as the original capital of Italy, before Lavin ...". It is the German form of Laurence. Notable people with the name include: Given name * Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyboardist * Lorentz Dietrichson (1834–1917), Norwegian poet and historian of art and literature * Lorentz Eichstadt (1596–1660), German mathematician and astronomer * Lorentz Harboe Ree (1888–1962), Norwegian architect * Lorentz Lange (1783–1860), Norwegian judge and politician * Lorentz Reige (born 1990), Swedish dancer * Lorentz Reitan (born 1946), Norwegian musicologist Mononym * Lorentz (rapper), real name Lorentz Alexander, Swedish singer and rapper Surname * Dominique Lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nanometers
330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm), or nanometer (American and British English spelling differences#-re, -er, American spelling), is a units of measurement, unit of length in the International System of Units (SI), equal to one billionth ( short scale) or one thousand million (long scale) of a meter (0.000000001 m) and to 1000 picometres. One nanometre can be expressed in scientific notation as 1 × 10−9 m and as m. History The nanometre was formerly known as the "''millimicrometre''" – or, more commonly, the "''millimicron''" for short – since it is of a micrometer. It was often denoted by the symbol ''mμ'' or, more rarely, as ''μμ'' (however, ''μμ'' should refer to a ''millionth'' of a micron). Etymology The name combines the SI prefix ''nano-'' (from the Ancient Greek , ', "dwarf") with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
London Penetration Depth
In superconductors, the London penetration depth (usually denoted as \lambda or \lambda_L) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to e^ times that of the magnetic field at the surface of the superconductor. Typical values of λL range from 50 to 500 nm. It was first derived by Geertruida de Haas-Lorentz in 1925, and later by Fritz and Heinz London in their London equations (1935).Fossheim, Kristian, and Asle Sudbø. ''Superconductivity: physics and applications''. John Wiley & Sons, 2005. The London penetration depth results from considering the London equation and Ampère's circuital law. If one considers a superconducting half-space, i.e. superconducting for x>0, and weak external magnetic field B0 applied along ''z'' direction in the empty space ''x''<0, then inside the superconductor the magnetic field is given by |
Laplacian
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the nabla operator), or \Delta. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems, such as cylindrical and spherical coordinates, the Laplacian also has a useful form. Informally, the Laplacian of a function at a point measures by how much the average value of over small spheres or balls centered at deviates from . The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics: the Laplacian of the gravitational potential due to a given mass density distribution is a constant multiple of that de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmholtz Equation
In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation: \nabla^2 f = -k^2 f, where is the Laplace operator, is the eigenvalue, and is the (eigen)function. When the equation is applied to waves, is known as the wave number. The Helmholtz equation has a variety of applications in physics and other sciences, including the wave equation, the diffusion equation, and the Schrödinger equation for a free particle. In optics, the Helmholtz equation is the wave equation for the electric field. The equation is named after Hermann von Helmholtz, who studied it in 1860. from the Encyclopedia of Mathematics. Motivation and uses The Helmholtz equation often arises in the study of physical problems involving par ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Vector
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point. A normal vector is a vector perpendicular to a given object at a particular point. A normal vector of length one is called a unit normal vector or normal direction. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by results in the opposite vector, which may be used for indicating sides (e.g., interior or exterior). In three-dimensional space, a surface normal, or simply normal, to a surface at point is a vector perpendicular to the tangent plane of the surface at . The vector field of normal directions to a surface is known as '' Gauss map''. The word "normal" is also used as an adjective: a line ''normal'' to a plane, the ''normal'' component of a for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Vector Potential
In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field, B: \nabla \times \mathbf = \mathbf. Together with the electric potential ''φ'', the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials ''φ'' and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields. Magnetic vector potential was independently introduced by Franz Ernst Neumann and Wilhelm Eduard Weber in 1845 and in 1846, respectively to discuss Ampère's circuital law. William Thomson also introduced the modern version of the vector potential in 1847, along with the formula relating it to the magnetic field. Unit conventions This article uses the SI system. In the SI system, the units of A are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
