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Chapter 1 Statistical Mechanics of Quantum Dots Chapter 2 Artificial
Chapter 1 Statistical Mechanics of Quantum Dots Chapter 2 Artificial

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Intro to particle physics 1. Particles, Fields

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... assigns to each ordered pair of real numbers (x, y) in a subset D of the plane a unique real number denoted by f (x, y). The set D is the domain of f and its range is the set of values that f takes on, that is, {f (x, y) : (x, y) ∈ D}. We often write z = f (x, y) to make explicit the values taken on ...
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An introduction to Quantum Optics

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... angular momentum J, and as JZ=LZ+SZ, and as, when calculating the distances and therefore the forces one has to take into account that g for the orbital motion is gL=1 while for the spin is gS=2, we will have the following forces acting on the atoms: F(LZ=+1, SZ=+1/2), F(LZ=+0, SZ=+1/2), F(LZ=-1, SZ ...
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For these questions, use the simulation “Quantum tunelling” and
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... General Periodic Trends – descending a group atomic radii increase, and with s & p blocks they decrease from left to right across period. Period 6 is different, due to lanthanide contraction. The 4f orbitals are being occupied by the lanthanides, and these have poor shielding properties. The repulsi ...
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... The student will investigate and understand how to diagram and construct basic electrical circuits and explain the function of various circuit components The student will investigate and understand that extremely large and extremely small quantities are not necessarily described by the same laws as ...
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Kondo physics in single-molecule transistors

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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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