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From Physics 212, one might get the impression that going... vacuum to electrostatics in a material is equivalent to replacing...
From Physics 212, one might get the impression that going... vacuum to electrostatics in a material is equivalent to replacing...

... an E-field. This impression is reinforced since both E and D are often calculated using Gauss’s Law. But there are important differences between E and D. One difference is that the curl of D is not zero in some non-Class A dielectrics. This means that the line integral of a D-field can depend on the ...
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... where  is the relativistic mass factor. Assuming a circular beam pipe with radius b (which is important only for the computation of the longitudinal force) and  applying Gauss’s law, the electromagnetic fields can be computed  for a bunch with Gaussian radial density (with rms  x   y   ) u ...
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Many-Minds Relativity and Quantum Mechanics

... where F is the gravitational force between two bodies of mass m1 and m2 at distance r and G is the gravitational constant (≈ 9.81 meter per second2 ), you can e.g. predict by mathematical computation the coming position of the planets in our Solar system from their current positions and velocities. ...
instability of excitation waves induced by electrical fields
instability of excitation waves induced by electrical fields

... typical examples of spontaneous pattern formation in macroscopic systems driven far from thermodynamic equilibrium [Bab86, Cro93]. They may show complex dynamics in time or both in time and in space, and they are sustained by the interplay of non-linear, selfaccelerating reaction kinetics (autocatal ...
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... pairs, is maximized when all three flavors have equal number density. This equality is enforced and the electrical neutrality of the CFL phase is undisturbed even in the presence of a nonzero strange quark mass ms (up to some critical value). Although the CFL ground state breaks the color and electr ...
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... COULOMB ELECTRIC FORCE As discussed in Unit 411, every particle can be characterized by a quantity called its charge q, measured in terms of the SI unit “coulomb” (abbreviated “C”). If two particles are at rest relative to some inertial frame, the electric force on one particle due to the other is c ...
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Geometry and Material Effects in Casimir Physics

... Neutral objects exert a force on one another through electromagnetic fields even if they do not possess permanent multipole moments. Materials that couple to the electromagnetic field alter the spectrum of the field’s quantum and thermal fluctuations. The resulting change in energy depends on the re ...
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... both media are isotropic (i.e. not birefringent). In the following discussion, we’ll suppose that light is travelling from a medium of permittivity ε1 to a medium of greater permittivity ε2. Both permeabilities are equal, and close to µ0. The electric and magnetic fields of the incident wave will be ...
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A Maxwellian Perspective on Particle Acceleration

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The development of the quantum-mechanical electron theory of metals

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... Majorana zero-modes, also referred to as Majorana bound states or Majorinos, are states in the middle of the excitation gap of a superconductor (so at zero excitation energy), bound to a magnetic vortex or other defect. The name goes back to a concept introduced by the Italian physicist Ettore Major ...
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... The generalization of twistor diagrams to TGD framework has been very inspiring (and also frightening) mission impossible and allowed to gain deep insights about what TGD diagrams could be mathematically. I of course cannot provide explicit formulas but the general structure for the construction of ...
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Reference - Wayne State Chemistry Department

... Time-dependent Hartree-Fock 共TD-HF兲 and time-dependent configuration interaction 共TD-CI兲 methods with Gaussian basis sets have been compared in modeling the response of hydrogen molecule, butadiene, and hexatriene exposed to very short, intense laser pulses 共760 nm, 3 cycles兲. After the electric fie ...
Quantum Transport through Single and Double Quantum Dots
Quantum Transport through Single and Double Quantum Dots

... low temperature the electronic levels in the source (drain) contact are filled from the bottom of the conduction band up to the electrochemical potential µS (µD ). In the quantum dot we can also define an electrochemical potential. It describes the energy necessary to add an electron to the dot, giv ...
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Introduction to gauge theory

A gauge theory is a type of theory in physics. Modern theories describe physical forces in terms of fields, e.g., the electromagnetic field, the gravitational field, and fields that describe forces between the elementary particles. A general feature of these field theories is that the fundamental fields cannot be directly measured; however, some associated quantities can be measured, such as charges, energies, and velocities. In field theories, different configurations of the unobservable fields can result in identical observable quantities. A transformation from one such field configuration to another is called a gauge transformation; the lack of change in the measurable quantities, despite the field being transformed, is a property called gauge invariance. Since any kind of invariance under a field transformation is considered a symmetry, gauge invariance is sometimes called gauge symmetry. Generally, any theory that has the property of gauge invariance is considered a gauge theory. For example, in electromagnetism the electric and magnetic fields, E and B, are observable, while the potentials V (""voltage"") and A (the vector potential) are not. Under a gauge transformation in which a constant is added to V, no observable change occurs in E or B.With the advent of quantum mechanics in the 1920s, and with successive advances in quantum field theory, the importance of gauge transformations has steadily grown. Gauge theories constrain the laws of physics, because all the changes induced by a gauge transformation have to cancel each other out when written in terms of observable quantities. Over the course of the 20th century, physicists gradually realized that all forces (fundamental interactions) arise from the constraints imposed by local gauge symmetries, in which case the transformations vary from point to point in space and time. Perturbative quantum field theory (usually employed for scattering theory) describes forces in terms of force-mediating particles called gauge bosons. The nature of these particles is determined by the nature of the gauge transformations. The culmination of these efforts is the Standard Model, a quantum field theory that accurately predicts all of the fundamental interactions except gravity.
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