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Aubry–André Model
The Aubry–André model is a statistical toy model to study thermodynamic properties in condensed matter. The model is usually employed to study quasicrystals and the transition metal-insulator in disordered systems predicted by Anderson localization. It was first developed by Serge Aubry and Gilles André in 1980. Tight–binding description Aubry–André model defines a periodic potential over a one-dimensional lattice with hopping between nearest neighbors sites with no interactions. In tight-binding, the on-site energies of Aubry-André potential have a periodicity that is incommensurate with the periodicity of the lattice. The potential can be written as :V=\sum_ \epsilon_n , n\rangle\langle n, , where the sum goes over all sites n, , n\rangle is a Wannier state on lattice site n and the on-site energies are given by :\epsilon_n=\lambda\cos(2\pi \beta n +\varphi). where \lambda is the disorder strength, \varphi is a phase and \beta is the periodicity of the potential. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toy Model
In the modeling of physics, a toy model is a deliberately simplistic model with many details removed so that it can be used to explain a mechanism concisely. It is also useful in a description of the fuller model. * In "toy" mathematical models, this is usually done by reducing or extending the number of dimensions or reducing the number of fields/variables or restricting them to a particular symmetric form. * In Macroeconomics modelling, are a class of models, some may be only loosely based on theory, others more explicitly so. But they have the same purpose. They allow for a quick first pass at some question, and present the essence of the answer from a more complicated model or from a class of models. For the researcher, they may come before writing a more elaborate model, or after, once the elaborate model has been worked out. Blanchard list of examples includes IS–LM model, the Mundell–Fleming model, the RBC model, and the New Keynesian model. * In "toy" physical descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theories to develop mathematical models. The diversity of systems and phenomena available for study makes condensed matter p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasicrystal
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold. Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of natural quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the field of crystallography. In crystallography the quasicrystals were predicted in 1981 by a five-fold symmetry study of Alan Lindsay Mackay,—that also brought in 1982, with the crystallographic Fourier transform of a Penrose tiling,Alan L. Mackay, "Crystallography ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anderson Localization
In condensed matter physics, Anderson localization (also known as strong localization) is the absence of diffusion of waves in a ''disordered'' medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first to suggest that electron localization is possible in a lattice potential, provided that the degree of randomness (disorder) in the lattice is sufficiently large, as can be realized for example in a semiconductor with impurities or defects. Anderson localization is a general wave phenomenon that applies to the transport of electromagnetic waves, acoustic waves, quantum waves, spin waves, etc. This phenomenon is to be distinguished from weak localization, which is the precursor effect of Anderson localization (see below), and from Mott localization, named after Sir Nevill Mott, where the transition from metallic to insulating behaviour is ''not'' due to disorder, but to a strong mutual Coulomb repulsion of electrons. Introduction In the or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serge Aubry (physicist)
Serge Dieudonne Aubry (January 2, 1942 – October 30, 2011) was a Canadian professional ice hockey goaltender who played 142 games in the World Hockey Association and an NHL coach. Early life Aubry was born in Montreal, Quebec. He played junior hockey with the Sherbrooke Castors and Windsor Maple Leafs. Career Aubry played with the Quebec Nordiques and Cincinnati Stingers. During a five-season career, Aubry posted a record of 65-53-5, with five shutouts. His best season came during his rookie year in 1972–73, when he compiled a 25–22–3 record, with two shutouts. His goals-against average that season was the best of his career at 3.59. Aubry later served as the NHL Nordiques' goalie coach during the 1988–89 season and as a scout for the Los Angeles Kings. Personal life On October 30, 2011, Aubry died in a Lévis, Quebec, hospital from diabetes Diabetes, also known as diabetes mellitus, is a group of metabolic disorders characterized by a high blood sugar lev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gilles André
The Gilles are the oldest and principal participants in the Carnival of Binche in Belgium. They go out on Shrove Tuesday from 4 am until late hours and dance to traditional songs. Other cities, such as La Louvière and Nivelles, have a tradition of Gilles at carnival, but the Carnival of Binche is by far the most famous. In 2003, the Carnival of Binche was proclaimed one of the Masterpieces of the Oral and Intangible Heritage of Humanity by UNESCO.Logan p.223 Costume Around 1000 Gilles, all male, some as young as three years old, wear the traditional costume of the Gille on Shrove Tuesday. The outfit features a linen suit with red, yellow, and black heraldic designs (the colours of the Belgian flag), trimmed with large white-lace cuffs and collars. The suit is stuffed with straw, giving the Gille a hunched back. Gilles also wear wooden clogs and have bells attached to their belts. In the morning, they wear a wax mask of a particular design. After reaching the town hall, they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tight-binding
In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. The method is closely related to the LCAO method (linear combination of atomic orbitals method) used in chemistry. Tight-binding models are applied to a wide variety of solids. The model gives good qualitative results in many cases and can be combined with other models that give better results where the tight-binding model fails. Though the tight-binding model is a one-electron model, the model also provides a basis for more advanced calculations like the calculation of surface states and application to various kinds of many-body problem and quasiparticle calculations. Introduction The name "tight binding" of this electronic band structure model suggests that this quantum mechanical model describes the properties of tightl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wannier Function
The Wannier functions are a complete set of orthogonal functions used in solid-state physics. They were introduced by Gregory Wannier in 1937. Wannier functions are the localized molecular orbitals of crystalline systems. The Wannier functions for different lattice sites in a crystal are orthogonal, allowing a convenient basis for the expansion of electron states in certain regimes. Wannier functions have found widespread use, for example, in the analysis of binding forces acting on electrons; the existence of exponentially localized Wannier functions in insulators was proved in 2006. Specifically, these functions are also used in the analysis of excitons and condensed Rydberg matter. Definition Although, like localized molecular orbitals, Wannier functions can be chosen in many different ways, the original, simplest, and most common definition in solid-state physics is as follows. Choose a single band in a perfect crystal, and denote its Bloch states by :\psi_(\mathbf) = e^u_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian (quantum Mechanics)
Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian with two-electron nature ** Molecular Hamiltonian, the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule * Hamiltonian (control theory), a function used to solve a problem of optimal control for a dynamical system * Hamiltonian path, a path in a graph that visits each vertex exactly once * Hamiltonian group, a non-abelian group the subgroups of which are all normal * Hamiltonian economic program, the economic policies advocated by Alexander Hamilton, the first United States Secretary of the Treasury See also * Alexander Hamilton (1755 or 1757–1804), American statesman and one of the Founding Fathers of the US * Hamilton (other) Hamilton may refer to: People * Hamilton (name), a common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( or \phi) denotes the golden ratio. The constant \varphi satisfies the quadratic equation \varphi^2 = \varphi + 1 and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of \varphi—may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
