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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 means ... [...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] |
Quenched Approximation
In lattice field theory, the quenched approximation is an approximation often used in lattice gauge theory in which the quantum loops of fermions in Feynman diagrams are neglected. Equivalently, the corresponding one-loop determinants are set to one. This approximation is often forced upon the physicists because the calculation with the Grassmann numbers is computationally very difficult in lattice gauge theory. In particular, quenched QED is quantum electrodynamics, QED without dynamical electrons, and quenched QCD is quantum chromodynamics, QCD without dynamical quarks. Recent calculations typically avoid the quenched approximation. References See also Lattice QCD Lattice field theory {{lattice-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distribution Function (physics)
:''This article describes the ''distribution function'' as used in physics. You may be looking for the related mathematical concepts of cumulative distribution function or probability density function.'' In molecular kinetic theory in physics, a system's distribution function is a function of seven variables, f(x,y,z,t;v_x,v_y,v_z), which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volume having approximately the velocity \mathbf=(v_x,v_y,v_z) near the position \mathbf=(x,y,z) and time t. The usual normalization of the distribution function is :n(x,y,z,t) = \int f \,dv_x \,dv_y \,dv_z, :N(t) = \int n \,dx \,dy \,dz, where, ''N'' is the total number of particles, and ''n'' is the number density of particles – the number of particles per unit volume, or the density divided by the mass of individual particles. A distribution function may be specialised with respect to a particular set of dimensions. E.g. t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Action (physics)
In physics, action is a scalar quantity describing how a physical system has dynamics (physics), changed over time. Action is significant because the equations of motion of the system can be derived through the principle of stationary action. In the simple case of a single particle moving with a constant velocity (uniform linear motion), the action is the momentum of the particle times the distance it moves, integral (mathematics), added up along its path; equivalently, action is twice the particle's kinetic energy times the duration for which it has that amount of energy. For more complicated systems, all such quantities are combined. More formally, action is a functional (mathematics), mathematical functional which takes the trajectory (also called path or history) of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths. Action has dimensional analysis, dimensions of energy × time or momentu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation Function (quantum Field Theory)
In quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products of field operators. They are a key object of study in quantum field theory where they can be used to calculate various observables such as S-matrix elements. Definition For a scalar field theory with a single field \phi(x) and a vacuum state , \Omega\rangle at every event (x) in spacetime, the n-point correlation function is the vacuum expectation value of the time-ordered products of n field operators in the Heisenberg picture G_n(x_1,\dots, x_n) = \langle \Omega, T\, \Omega\rangle. Here T\ is the time-ordering operator for which orders the field operators so that earlier time field operators appear to the right of later time field operators. By transforming the fields and states into the interaction picture, this is rewritten as G_n(x_1, \dots, x_n) = \frac, where , 0\rangle is the ground state of the free theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. The physicist Albert Einstein helped develop the idea of spacetime as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton's laws of physics described the motion of massive objects, while James Clerk Maxwell's electromagnetic models explained the properties of light. However, in 1905, Einstein based a work on special relativity on two postulates: * The laws of physics are invariant ... [...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. This transformation is also used to find solutions to problems in quantum mechanics and other areas. Overview Wick rotation is motivated by the observation that the Minkowski metric in natural units (with metric signature convention) :ds^2 = -\left(dt^2\right) + dx^2 + dy^2 + dz^2 and the four-dimensional Euclidean metric :ds^2 = d\tau^2 + dx^2 + dy^2 + dz^2 are equivalent if one permits the coordinate to take on imaginary values. The Minkowski metric becomes Euclidean when is restricted to the imaginary axis, and vice versa. Taking a problem expressed in Minkowski space with coordinates , and substituting sometimes yields a problem in real Euclidean coordinates wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension (mathematics), dimension, including the three-dimensional space and the ''Euclidean plane'' (dimension two). The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics. Ancient History of geometry#Greek geometry, Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the Greek mathematics, ancient Greek mathematician Euclid in his ''Elements'', with the great innovation of ''mathematical proof, proving'' all properties of the space as theorems, by starting from a few fundamental properties, called ''postulates'', which either were considered as eviden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blue Gene
Blue Gene is an IBM project aimed at designing supercomputers that can reach operating speeds in the petaFLOPS (PFLOPS) range, with 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. As of 2015, IBM seems to have ended the development of the Blue Gene family though no public announcement has been made. IBM's continuing efforts of the supercomputer scene seems to be concentrated around OpenPower, using accelerators such as FPGAs and GPUs to battle the end of Moore's law. History In December 1999, IBM announced a US$100 million research initiative for a five-year effort to build a mass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proton
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ratio). Protons and neutrons, each with masses of approximately one atomic mass unit, are jointly referred to as "nucleons" (particles present in atomic nuclei). One or more protons are present in the 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 element has a unique number of protons, each element has its own unique atomic number, which determines the number of atomic electrons and consequently the chemical characteristics of the element. The word ''proton'' is Greek for "first", and this name was given to the ... [...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 fermio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aneesur Rahman
Aneesur Rahman (24 August 1927 – 6 June 1987) 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 fellow at the University of Minnesota Super ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
