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R-matrix
The term R-matrix has several meanings, depending on the field of study. The term R-matrix is used in connection with the Yang–Baxter equation. This is an equation which was first introduced in the field of statistical mechanics, taking its name from independent work of C. N. Yang and R. J. Baxter. The classical R-matrix arises in the definition of the classical Yang–Baxter equation. In quasitriangular Hopf algebra, the R-matrix is a solution of the Yang–Baxter equation. The numerical modeling of diffraction gratings in optical science can be performed using the R-matrix propagation algorithm. R-matrix method in quantum mechanics There is a method in computational quantum mechanics for studying scattering known as the R-matrix. This method was originally formulated for studying resonances in nuclear scattering by Wigner and Eisenbud. Using that work as a basis, an R-matrix method was developed for electron, positron and photon scattering by atoms. This approac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantemol
Quantemol Ltd is based in University College London initiated by Professor Jonathan Tennyson (physicist), Jonathan Tennyson FRS and Dr. Daniel Brown in 2004. The company initially developed a unique software tool, #Quantemol-N, Quantemol-N, which provides full accessibility to the highly sophisticated UK molecular R-matrix codes, used to model electron polyatomic molecule interactions. Since then Quantemol has widened to further types of simulation, with Plasma (physics), plasmas and industrial plasma tools, in #Quantemol-VT, Quantemol-VT in 2013 and launched in 2016 a sustainable database #Quantemol-DB, Quantemol-DB, representing the chemical and radiative transport properties of a wide range of plasmas. Quantemol-N The Quantemol-N software system has been developed to simplify use of UK Molecular R-matrix Codes, UK R-matrix codes. It provides an interface for non specialists to perform ab initio electron-molecule scattering calculations. Quantemol-N calculates a variety of ob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
UK Molecular R-matrix Codes
The UK Molecular R-Matrix codes are a set of software routines used to calculate the effects of collision of electrons with atoms and molecules. The R-matrix method is used in computational quantum mechanics to study scattering of positrons and electrons by atomic and molecular targets. The fundamental idea was originally introduced by Eugene Wigner Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his con ... and Leonard Eisenbud in the 1940s. The method works by fixed nuclei approximation, where the molecule's nuclei are considered fixed when collision occurs and the electronic part of the problem is solved. This information is then plugged into calculations which take into account nuclear motion. The UK Molecular R-Matrix codes were developed by the Collaborative Computational Project Q (CC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasitriangular Hopf Algebra
In mathematics, a Hopf algebra, ''H'', is quasitriangularMontgomery & Schneider (2002), p. 72 if there exists an invertible element, ''R'', of H \otimes H such that :*R \ \Delta(x)R^ = (T \circ \Delta)(x) for all x \in H, where \Delta is the coproduct on ''H'', and the linear map T : H \otimes H \to H \otimes H is given by T(x \otimes y) = y \otimes x, :*(\Delta \otimes 1)(R) = R_ \ R_, :*(1 \otimes \Delta)(R) = R_ \ R_, where R_ = \phi_(R), R_ = \phi_(R), and R_ = \phi_(R), where \phi_ : H \otimes H \to H \otimes H \otimes H, \phi_ : H \otimes H \to H \otimes H \otimes H, and \phi_ : H \otimes H \to H \otimes H \otimes H, are algebra morphisms determined by :\phi_(a \otimes b) = a \otimes b \otimes 1, :\phi_(a \otimes b) = a \otimes 1 \otimes b, :\phi_(a \otimes b) = 1 \otimes a \otimes b. ''R'' is called the R-matrix. As a consequence of the properties of quasitriangularity, the R-matrix, ''R'', is a solution of the Yang–Baxter equation (and so a module ''V'' of ''H'' c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene Wigner
Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles". A graduate of the Technical University of Berlin, Wigner worked as an assistant to Karl Weissenberg and Richard Becker at the Kaiser Wilhelm Institute in Berlin, and David Hilbert at the University of Göttingen. Wigner and Hermann Weyl were responsible for introducing group theory into physics, particularly the theory of symmetry in physics. Along the way he performed ground-breaking work in pure mathematics, in which he authored a number of mathematical theorems. In particular, Wigner's theorem is a cornerstone in the mathematical formulation of quantum mechanics. He is also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yang–Baxter Equation
In physics, the Yang–Baxter equation (or star–triangle relation) is a consistency equation which was first introduced in the field of statistical mechanics. It depends on the idea that in some scattering situations, particles may preserve their momentum while changing their quantum internal states. It states that a matrix R, acting on two out of three objects, satisfies :(\check\otimes \mathbf)(\mathbf\otimes \check)(\check\otimes \mathbf) =(\mathbf\otimes \check)(\check \otimes \mathbf)(\mathbf\otimes \check) In one dimensional quantum systems, R is the scattering matrix and if it satisfies the Yang–Baxter equation then the system is integrable. The Yang–Baxter equation also shows up when discussing knot theory and the braid groups where R corresponds to swapping two strands. Since one can swap three strands two different ways, the Yang–Baxter equation enforces that both paths are the same. It takes its name from independent work of C. N. Yang from 1968, and R. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Science
Atomic, molecular, and optical physics (AMO) is the study of matter-matter and light-matter interactions; at the scale of one or a few atoms and energy scales around several electron volts. The three areas are closely interrelated. AMO theory includes classical, semi-classical and quantum treatments. Typically, the theory and applications of emission, absorption, scattering of electromagnetic radiation (light) from excited atoms and molecules, analysis of spectroscopy, generation of lasers and masers, and the optical properties of matter in general, fall into these categories. Atomic and molecular physics Atomic physics is the subfield of AMO that studies atoms as an isolated system of electrons and an atomic nucleus, while molecular physics is the study of the physical properties of molecules. The term ''atomic physics'' is often associated with nuclear power and nuclear bombs, due to the synonymous use of ''atomic'' and ''nuclear'' in standard English. However, physi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Eisenbud
David Eisenbud (born 8 April 1947 in New York City) is an American mathematician. He is a professor of mathematics at the University of California, Berkeley and Director of the Mathematical Sciences Research Institute (MSRI); he previously served as Director of MSRI from 1997 to 2007. Biography Eisenbud is the son of mathematical physicist Leonard Eisenbud, who was a student and collaborator of the renowned physicist Eugene Wigner. Eisenbud received his Ph.D. in 1970 from the University of Chicago, where he was a student of Saunders Mac Lane and, unofficially, James Christopher Robson. He then taught at Brandeis University from 1970 to 1997, during which time he had visiting positions at Harvard University, Institut des Hautes Études Scientifiques (IHÉS), University of Bonn, and Centre national de la recherche scientifique (CNRS). He joined the staff at MSRI in 1997, and took a position at Berkeley at the same time. From 2003 to 2005 Eisenbud was President of the American M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MOLPRO
MOLPRO is a software package used for accurate ''ab initio'' quantum chemistry calculations. It is developed by Peter Knowles at Cardiff University and Hans-Joachim Werner at Universität Stuttgart in collaboration with other authors. The emphasis in the program is on highly accurate computations, with extensive treatment of the electron correlation problem through the multireference configuration interaction, coupled cluster and associated methods. Integral-direct local electron correlation methods reduce the increase of the computational cost with molecular size. Accurate ab initio calculations can then be performed for larger molecules. With new explicitly correlated methods the basis set limit can be very closely approached. History Molpro was designed and maintained by Wilfried Meyer and Peter Pulay Peter Pulay (born September 20, 1941, in Veszprém, Hungary) is a theoretical chemist. He is the Roger B. Bost Distinguished Professor of Chemistry in the Department of Chemis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
