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Calogero–Moser–Sutherland Model
Calogero–Moser–Sutherland models (short CMS models) are a type of integrable one-dimensional many-body systems, which can be studied with exact results both from the classical and quantum perspective. Such models describe pointlike particles on a line or a circle with quadratic or inverse quadratic interactions between them. CMS models are named after Francesco Calogero, Jürgen Moser and Bill Sutherland. Calogero, in 1971, first considered the quantum model on a line with both a quadratic and inverse quadratic interaction. He computed the energy spectrum and described soliton scattering without the quadratic term. Sutherland, also in 1971, further considered the quantum model on the circle and modified the inverse quadratic interaction to include the sine. He also computed the energy spectrum and developed an algorithm to obtain the corresponding eigenfunctions. Moser, later in 1975, proved the integrability of both systems using Lax pairs and solved the scattering problem. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrable System
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space. Three features are often referred to as characterizing integrable systems: * the existence of a ''maximal'' set of conserved quantities (the usual defining property of complete integrability) * the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) * the explicit determination of solutions in an explicit functional form (not an intrinsic property, but something often referred to as solvability) Integrable systems may be seen as very different in qualitative character from more ''generic'' dynamical systems, which are more typically chaotic syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relativistic
Relativity may refer to: Physics * Galilean relativity, Galileo's conception of relativity * Numerical relativity, a subfield of computational physics that aims to establish numerical solutions to Einstein's field equations in general relativity * Principle of relativity, used in Einstein's theories and derived from Galileo's principle * Theory of relativity, a general treatment that refers to both special relativity and general relativity ** General relativity, Albert Einstein's theory of gravitation ** Special relativity, a theory formulated by Albert Einstein, Henri Poincaré, and Hendrik Lorentz ** '' Relativity: The Special and the General Theory'', a 1920 book by Albert Einstein Social sciences * Linguistic relativity * Cultural relativity * Moral relativity Arts and entertainment Music * Relativity Music Group, a Universal subsidiary record label for releasing film soundtracks * Relativity Records, an American record label * Relativity (band), a Scots-Irish tradition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Nature
Springer Nature or the Springer Nature Group is a German-British academic publishing company created by the May 2015 merger of Springer Science+Business Media and Holtzbrinck Publishing Group's Nature Publishing Group, Palgrave Macmillan, and Macmillan Education. History The company originates from several journals and publishing houses, notably Springer-Verlag, which was founded in 1842 by Julius Springer in Berlin (the grandfather of Bernhard Springer who founded Springer Publishing in 1950 in New York), Nature Portfolio, Nature Publishing Group which has published ''Nature (journal) , Nature'' since 1869, and Macmillan Education, which goes back to Macmillan Publishers founded in 1843. Springer Nature was formed in 2015 by the merger of Nature Publishing Group, Palgrave Macmillan, and Macmillan Education (held by Holtzbrinck Publishing Group) with Springer Science+Business Media (held by BC Partners). Plans for the merger were first announced on 15 January 2015. The transactio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advances In Mathematics
''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed at publishing articles addressed to a broader "mathematical community", and not only to mathematicians in the author's field. Herbert Busemann writes, in the preface of the first issue, "The need for expository articles addressing either all mathematicians or only those in somewhat related fields has long been felt, but little has been done outside of the USSR. The serial publication ''Advances in Mathematics'' was created in response to this demand." Abstracting and indexing The journal is abstracted and indexed in: * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review A
''Physical Review A'' (also known as PRA) is a monthly peer-reviewed scientific journal published by the American Physical Society covering atomic, molecular, and optical physics and quantum information. the editor was Jan M. Rost ( Max Planck Institute for the Physics of Complex Systems). History In 1893, the '' Physical Review'' was established at Cornell University. It was taken over by the American Physical Society (formed in 1899) in 1913. In 1970, ''Physical Review'' was subdivided into ''Physical Review A'', ''B'', ''C'', and ''D''. At that time, section ''A'' was subtitled ''Physical Review A: General Physics''. In 1990, a process was started to split this journal into two, resulting in the creation of '' Physical Review E'' in 1993. Hence, in 1993, ''Physical Review A'' changed its statement of scope to ''Atomic, Molecular and Optical Physics.'' In January 2007, the section of ''Physical Review E'' that published papers on classical optics was merged into ''Physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Mathematical Physics
The ''Journal of Mathematical Physics'' is a peer-reviewed journal published monthly by the American Institute of Physics devoted to the publication of papers in mathematical physics. The journal was first published bimonthly beginning in January 1960; it became a monthly publication in 1963. The current editor is Jan Philip Solovej from University of Copenhagen The University of Copenhagen (, KU) is a public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia, after Uppsala University. .... Its 2018 Impact Factor is 1.355 Abstracting and indexing This journal is indexed by the following services: 2013. References External ...
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Potential Energy
In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity or those in a spring. The term ''potential energy'' was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to the ancient Greek philosopher Aristotle's concept of Potentiality and Actuality, ''potentiality''. Common types of potential energy include gravitational potential energy, the elastic potential energy of a deformed spring, and the electric potential energy of an electric charge and an electric field. The unit for energy in the International System of Units (SI) is the joule (symbol J). Potential energy is associated with forces that act on a body in a way that the total Work (physics), work done by these forces on the body depends only on the initial and final positions of the b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruijsenaars–Schneider Model
Ruijsenaars–Schneider models (short RS models) are relativistic generalizations of Calogero–Moser–Sutherland models (short CMS models), which are closely connected with relativistic field theories like the Sine-Gordon model. RS models are named after Simon N. M. Ruijsenaars and Herbert Schneider. Both of them introduced the classical models in 1986 and Ruijsenaars introduced the quantum models in 1987. Description For N particles on the real line \mathbb, the Hamiltonian of the RS model is given by: : H =mc^2\sum_^N\cosh\left(\frac\right)\prod_f(x_i-x_j). Different potentials Potential generally refers to a currently unrealized ability, in a wide variety of fields from physics to the social sciences. Mathematics and physics * Scalar potential, a scalar field whose gradient is a given vector field * Vector potential ... lead to different RS models, which the four types most often considered being: * Type I/rational: *: f(x)^2 =1+\left(\frac\right)^2. * Type II/h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scattering
In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called ''diffuse reflections'' and unscattered reflections are called ''specular'' (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, a pioneer in light scattering research, noted the connecti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-body Systems
The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of many interacting particles. Terminology ''Microscopic'' here implies that quantum mechanics has to be used to provide an accurate description of the system. ''Many'' can be anywhere from three to infinity (in the case of a practically infinite, homogeneous or periodic system, such as a crystal), although three- and four-body systems can be treated by specific means (respectively the Faddeev and Faddeev–Yakubovsky equations) and are thus sometimes separately classified as few-body systems. Explanation of the problem In general terms, while the underlying physical laws that govern the motion of each individual particle may (or may not) be simple, the study of the collection of particles can be extremely complex. In such a quantum system, the repeated interactions between particles create quantum correlations, or entanglement. As a consequen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soliton
In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is , in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets. Its remarkable stability can be traced to a balanced cancellation of nonlinear and dispersive effects in the medium.Dispersive effects are a property of certain systems where the speed of a wave depends on its frequency. Solitons were subsequently found to provide stable solutions of a wide class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described in 1834 by John Scott Russell who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the " Wave of Translation". The Korteweg–de Vries equation was later formulated to model such waves, and the term "soliton" was coined by Zabu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Spectrum
In the physical sciences, the term ''spectrum'' was introduced first into optics by Isaac Newton in the 17th century, referring to the range of colors observed when white light was dispersed through a prism. Soon the term referred to a plot of light intensity or power as a function of frequency or wavelength, also known as a ''spectral density plot''. Later it expanded to apply to other waves, such as sound waves and sea waves that could also be measured as a function of frequency (e.g., noise spectrum, sea wave spectrum). It has also been expanded to more abstract "signals", whose power spectrum can be analyzed and processed. The term now applies to any signal that can be measured or decomposed along a continuous variable, such as energy in electron spectroscopy or mass-to-charge ratio in mass spectrometry. Spectrum is also used to refer to a graphical representation of the signal as a function of the dependent variable. Etymology Electromagnetic spectrum Elect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
