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Lattice QCD
Lattice QCD is a well-established non- perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered. Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly nonlinear nature of the strong force and the large coupling constant at low energies. This formulation of QCD in discrete rather than continuous spacetime naturally introduces a momentum cut-off at the order 1/''a'', where ''a'' is the lattice spacing, which regularizes the theory. As a result, lattice QCD is mathematically well-defined. Most importantly, lattice QCD provides a framework for investigation of non-perturbative phenomena such as confinement and quark–gluon plasma formation, which are intractable by mean ... [...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] |
Supercomputer
A supercomputer is a type of computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2022, supercomputers have existed which can perform over 1018 FLOPS, so called Exascale computing, exascale supercomputers. For comparison, a desktop computer has performance in the range of hundreds of gigaFLOPS (1011) to tens of teraFLOPS (1013). Since November 2017, all of the TOP500, world's fastest 500 supercomputers run on Linux-based operating systems. Additional research is being conducted in the United States, the European Union, Taiwan, Japan, and China to build faster, more powerful and technologically superior exascale supercomputers. Supercomputers play an important role in the field of computational science, and are used for a wide range of computationally intensive tasks in various fields, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haar Measure
In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups. This Measure (mathematics), measure was introduced by Alfréd Haar in 1933, though its special case for Lie groups had been introduced by Adolf Hurwitz in 1897 under the name "invariant integral". Haar measures are used in many parts of mathematical analysis, analysis, number theory, group theory, representation theory, mathematical statistics, statistics, probability theory, and ergodic theory. Preliminaries Let (G, \cdot) be a locally compact space, locally compact Hausdorff space, Hausdorff topological group. The Sigma-algebra, \sigma-algebra generated by all open subsets of G is called the Borel algebra. An element of the Borel algebra is called a Borel set. If g is an element of G and S is a subset of G, then we define the left and right Coset, translates of S by ''g'' as follows: * Left ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Action (physics)
In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory. Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects. Action and the variational principle are used in Feynman's formulation of quantum mechanics and in general relativity. For systems with small values of action close to the Planck constant, quantum effects are significant. In the simple case of a single particle moving with a constant velocity (thereby undergoing uniform linear motion), the action is the momentum of the particle times the distance it moves, added up along its path; equivalently, action is the difference between the particle's kinetic energy and its potential energy, times the duration for which it has that amount of energy. More formally, action is a mathematical functional which takes the trajectory ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Function (quantum Field Theory)
In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism. They are the imaginary time versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics. Partition functions can rarely be solved for exactly, although free theories do admit such solutions. Instead, a perturbative approach is usually implemented, this being equivalent to summing over Feynman diagrams. Generating functional Scalar theories In a d-dimensional field theory with a real scalar field \phi and action S phi/math>, the partition function is defined in the path integral formalism as the functional : Z = \int \mathcal D\phi \ e^ where J(x) is a fictitious source current. It acts as a generating functional for arbitrary n-point correlation functions : G_n(x_1, \dots, x_n) = (-1)^n \frac \frac\bigg, _. The derivatives used here ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path Integral Formulation
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization. Unlike previous methods, the path integral allows one to easily change coordinates between very different canonical descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions of a certain type, these ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wick Rotation
In physics, Wick rotation, named after Italian physicist Gian Carlo Wick, is a method of finding a solution to a mathematical problem in Minkowski space from a solution to a related problem in Euclidean space by means of a transformation that substitutes an imaginary-number variable for a real-number variable. Wick rotations are useful because of an analogy between two important but seemingly distinct fields of physics: statistical mechanics and quantum mechanics. In this analogy, inverse temperature plays a role in statistical mechanics formally akin to imaginary time in quantum mechanics: that is, , where is time and is the imaginary unit (). More precisely, in statistical mechanics, the Gibbs measure describes the relative probability of the system to be in any given state at temperature , where is a function describing the energy of each state and is the Boltzmann constant. In quantum mechanics, the transformation describes time evolution, where is an operator descri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blue Gene
Blue Gene was an IBM project aimed at designing supercomputers that can reach operating speeds in the petaFLOPS (PFLOPS) range, with relatively low power consumption. The project created three generations of supercomputers, Blue Gene/L, Blue Gene/P, and Blue Gene/Q. During their deployment, Blue Gene systems often led the TOP500 and Green500 rankings of the most powerful and most power-efficient supercomputers, respectively. Blue Gene systems have also consistently scored top positions in the Graph500 list. The project was awarded the 2009 National Medal of Technology and Innovation. After Blue Gene/Q, IBM focused its supercomputer efforts on the OpenPower platform, using accelerators such as FPGAs and GPUs to address the diminishing returns of Moore's law. History A video presentation of the history and technology of the Blue Gene project was given at the Supercomputing 2020 conference. In December 1999, IBM announced a US$100 million research initiative for a five-year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proton
A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an electron (the proton-to-electron mass ratio). Protons and neutrons, each with a mass of approximately one Dalton (unit), dalton, are jointly referred to as ''nucleons'' (particles present in atomic nuclei). One or more protons are present in the Atomic nucleus, nucleus of every atom. They provide the attractive electrostatic central force which binds the atomic electrons. The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol ''Z''). Since each chemical element, element is identified by the number of protons in its nucleus, each element has its own atomic number, which determines the number of atomic electrons and consequently the chemical characteristi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Sign Problem
In applied mathematics, the numerical sign problem is the problem of numerically evaluating the integral of a highly oscillatory function of a large number of variables. Numerical methods fail because of the near-cancellation of the positive and negative contributions to the integral. Each has to be integrated to very high precision in order for their difference to be obtained with useful accuracy. The sign problem is one of the major unsolved problems in the physics of many-particle systems. It often arises in calculations of the properties of a quantum mechanical system with large number of strongly interacting fermions, or in field theories involving a non-zero density of strongly interacting fermions. Overview In physics the sign problem is typically (but not exclusively) encountered in calculations of the properties of a quantum mechanical system with large number of strongly interacting fermions, or in field theories involving a non-zero density of strongly interacting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aneesur Rahman
Aneesur Rahman (24 August 1927 – 6 June 1987) was an Indian-born American physicist who pioneered the application of computational methods to physical systems. His 1964 paper on liquid argon studied a system of 864 argon atoms on a CDC 3600 computer, using a Lennard-Jones potential. His algorithms still form the basis for many codes written today. Moreover, he worked on a wide variety of problems, such as the microcanonical ensemble approach to lattice gauge theory, which he invented with David J E Callaway. Aneesur Rahman was a native of Hyderabad, India. He earned his undergraduate degree in physics and mathematics from Cambridge University in England and his Ph.D. in theoretical physics from Louvain University in Belgium. In 1960, Dr. Rahman began a 25-year tenure as a physicist at the Argonne National Laboratory (Argonne, Ill.) (operated by the University of Chicago). In 1985, Dr. Rahman joined the faculty at the University of Minnesota as a professor of physics and fe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Callaway
David James Edward Callaway is a biological nanophysicist in the New York University School of Medicine, where he is professor and laboratory director. He was trained as a theoretical physicist by Richard Feynman, Kip Thorne, and Cosmas Zachos, and was previously an associate professor at the Rockefeller University after positions at CERN and Los Alamos National Laboratory. Callaway's laboratory discovered potential therapeutics for Alzheimer's disease based upon apomorphine after an earlier paper of his developed models of Alzheimer amyloid formation. He has also initiated the study of protein domain dynamics by neutron spin echo spectroscopy, providing a way to observe protein nanomachines in motion. Previous work includes the invention of the microcanonical ensemble approach to lattice gauge theory with Aneesur Rahman, work on the convexity of the effective potential of quantum field theory, work on Langevin dynamics in quantum field theory with John R. Klauder, a monograph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
