|
Variational Perturbation Theory
In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say :s=\sum_^\infty a_n g^n, into a convergent series in powers :s=\sum_^\infty b_n /(g^\omega)^n, where \omega is a critical exponent (the so-called index of "approach to scaling" introduced by Franz Wegner). This is possible with the help of variational parameters, which are determined by optimization order by order in g. The partial sums are converted to convergent partial sums by a method developed in 1992. Most perturbation expansions in quantum mechanics are divergent for any small coupling strength g. They can be made convergent by VPT (for details see the first textbook cited below). The convergence is exponentially fast. After its success in quantum mechanics, VPT has been developed further to become an important mathematical tool in quantum field theory with its anomalous dimensions. Applications focus on the theory of critic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Physics
''Annals of Physics'' is a monthly peer-reviewed scientific journal covering all aspects of physics. It was established in 1957 and is published by Elsevier. The editor-in-chief is Neil Turok (University of Edinburgh School of Physics and Astronomy). Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 2.73. References External links * Physics journals Monthly journals Publications established in 1957 English-language journals Elsevier academic journals {{physics-journal-stub ... [...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 Review ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hagen Kleinert
Hagen Kleinert (born 15 June 1941) is professor of theoretical physics at the Free University of Berlin, Germany (since 1968)Honorary Doctorat the West University of Timișoaraandat thin Bishkek. He is alsHonorary Memberof th For his contributions to particle and solid state physics he wathe Max Born Prize 2008 witMedal His contribution to thmemorial volumecelebrating the 100th birthday of Lev Davidovich Landau earned him the Majorana Prize 2008 with Medal. He is married to Dr. Annemarie Kleinert since 1974 with whom he has a soMichael Kleinert Publications Kleinert has written ~420 papers on mathematical physics and the physics of elementary particles, nuclei, solid state systems, liquid crystals, biomembranes, microemulsions, polymers, and the theory of financial markets. He has written several books on theoretical physics, the most notable of which, ''Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets,'' has been published in five edition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Phenomena
In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking. Critical phenomena take place in second order phase transitions, although not exclusively. The critical behavior is usually different from the mean-field approximation which is valid away from the phase transition, since the latter neglects correlations, which become increasingly important as the system approaches the critical point where the correlation length diverges. Many properties of the critical behavior of a system can be derived in the framework of the renormalization group. In order to expl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review D
Physical may refer to: *Physical examination In a physical examination, medical examination, or clinical examination, a medical practitioner examines a patient for any possible medical signs or symptoms of a medical condition. It generally consists of a series of questions about the pati ..., a regular overall check-up with a doctor * ''Physical'' (Olivia Newton-John album), 1981 ** "Physical" (Olivia Newton-John song) * ''Physical'' (Gabe Gurnsey album) * "Physical" (Alcazar song) (2004) * "Physical" (Enrique Iglesias song) (2014) * "Physical" (Dua Lipa song) (2020) *"Physical (You're So)", a 1980 song by Adam & the Ants, the B side to " Dog Eat Dog" * ''Physical'' (TV series), an American television series See also {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anomalous Scaling Dimension
In theoretical physics, the scaling dimension, or simply dimension, of a local operator in a quantum field theory characterizes the rescaling properties of the operator under spacetime dilations x\to \lambda x. If the quantum field theory is scale invariant, scaling dimensions of operators are fixed numbers, otherwise they are functions of the distance scale. Scale-invariant quantum field theory In a scale invariant quantum field theory, by definition each operator ''O'' acquires under a dilation x\to \lambda x a factor \lambda^, where \Delta is a number called the scaling dimension of ''O''. This implies in particular that the two point correlation function \langle O(x) O(0)\rangle depends on the distance as (x^2)^. More generally, correlation functions of several local operators must depend on the distances in such a way that \langle O_1(\lambda x_1) O_2(\lambda x_2)\ldots\rangle= \lambda^\langle O_1(x_1) O_2(x_2)\ldots\rangle Most scale invariant theories are also confo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Series
In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots where ''an'' represents the coefficient of the ''n''th term and ''c'' is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, ''c'' (the ''center'' of the series) is equal to zero, for instance when considering a Maclaurin series. In such cases, the power series takes the simpler form \sum_^\infty a_n x^n = a_0 + a_1 x + a_2 x^2 + \dots. Beyond their role in mathematical analysis, power series also occur in combinatorics as generating functions (a kind of formal power series) and in electronic engineering (under the name of the Z-transform). The familiar decimal notation for real numbers can also be viewed as an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory (quantum Mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system. Approximate Hamiltonians Perturbation theory is an important tool for de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics Letters A
''Physics Letters'' was a scientific journal published from 1962 to 1966, when it split in two series now published by Elsevier: *''Physics Letters A'': condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. *''Physics Letters B'': nuclear physics, theoretical nuclear physics, experimental high-energy physics, theoretical high-energy physics, and astrophysics. ''Physics Letters B'' is part of the SCOAP3 initiative. References See also * List of periodicals published by Elsevier This is a list of scientific, technical and general interest periodicals published by Elsevier or one of its imprints or subsidiary companies. Both printed items and electronic publications are included in this list. A B C D E F G ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
