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... makes the variance look very close to that of a classical gas. In order to observe such fluctuations in space, it is important to have a very low temperature since that will reduce the size of ∆p x ∆py ∆pz . It is also favorable to have a high density because that means that for the subvolume in que ...
Atom: Program 3 - Educational Resource Guide
Atom: Program 3 - Educational Resource Guide

... Einstein, Albert - (14 March 1879 - 18 April 1955) German Swiss Nobel Laureate who is often regarded as the father of modern physics. Einstein's Special Theory of Relativity - The theory proposed in 1905 by Einstein, which assumes that the laws of physics are equally valid in all nonaccelerated fram ...
Coherent states
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MSc Phy App
MSc Phy App

... Solution of Equations and Interpolation Bisection, iterative and Newton Raphson method for finding roots of the equations – solution of simultaneous linear equation by Gauss elimination and Gauss Seidal method – finite differences – Newton’s forward difference interpolation formula. Integration and ...
PPT file - Centre national de la recherche scientifique
PPT file - Centre national de la recherche scientifique

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Very brief introduction to Conformal Field Theory

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Physical problem for Nonlinear Equations:General

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... dimensions that can be fabricated with current technology. Smaller units of time and space discretization can be chosen, but with increased computational cost. We chose the time period T to be 500 (femto-seconds), with 8T = 4000 femto seconds reflecting a 0.25-TeraHz switching clock period. This clo ...
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Digital Wires

Superconducting loop quantum gravity and the cosmological constant
Superconducting loop quantum gravity and the cosmological constant

... and creation operators obeying a fermionic algebra {ckσ , c†k′σ′ } = δkk′ δσσ′ , and u and v are spinorial functions. Due to Eq. (15), in the Hamiltonian there appear fermionic nonlocal correlations of the form ...
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Stefano Bellucci (INFN-Laboratori Nazionali di Frascati)

... role in General Relativity, as well as in modern theoretical physics in general. Particularly special are its thermodynamic properties and connection to string theory, allowing one to expect that quantum gravity should be closely related to these objects. A very particular case of black hole solutio ...
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III. Quantum Model of the Atom

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Review Sheet: Study old quizzes and notes as well
Review Sheet: Study old quizzes and notes as well

... 5.5) Provide all expressions using sin and cos between -360o and 360o that is equivalent to sin 35o. 6.) Find all times when the diver will be 35 feet from the ground algebraically. 7.) The table below lists the average monthly temperatures in degrees Fahrenheit for the city of Fairbanks, Alaska. Th ...


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physics 151h: honors mechanics

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Scales are fishy!

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Renormalization group



In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle (cf. Compton wavelength).A change in scale is called a ""scale transformation"". The renormalization group is intimately related to ""scale invariance"" and ""conformal invariance"", symmetries in which a system appears the same at all scales (so-called self-similarity). (However, note that scale transformations are included in conformal transformations, in general: the latter including additional symmetry generators associated with special conformal transformations.)As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable ""couplings"" which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the ""dressed electron"" seen at large distances, and this change, or ""running,"" in the value of the electric charge is determined by the renormalization group equation.
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