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The following timeline starts with the invention of the modern computer in the late interwar period.
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.
Nicholas Constantine Metropolis was a Greek-American physicist.
In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice.
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.
Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution of the quantum many-body problem. The diverse flavors of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem.
In physics, the Fermi–Pasta–Ulam–Tsingou (FPUT) problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi–Pasta–Ulam–Tsingou recurrence – instead of the expected ergodic behavior. This came as a surprise, as Enrico Fermi, certainly, expected the system to thermalize in a fairly short time. That is, it was expected for all vibrational modes to eventually appear with equal strength, as per the equipartition theorem, or, more generally, the ergodic hypothesis. Yet here was a system that appeared to evade the ergodic hypothesis. Although the recurrence is easily observed, it eventually became apparent that over much, much longer time periods, the system does eventually thermalize. Multiple competing theories have been proposed to explain the behavior of the system, and it remains a topic of active research.
The kinetic Monte Carlo (KMC) method is a Monte Carlo method computer simulation intended to simulate the time evolution of some processes occurring in nature. Typically these are processes that occur with known transition rates among states. It is important to understand that these rates are inputs to the KMC algorithm, the method itself cannot predict them.
Path integral Monte Carlo (PIMC) is a quantum Monte Carlo method used to solve quantum statistical mechanics problems numerically within the path integral formulation. The application of Monte Carlo methods to path integral simulations of condensed matter systems was first pursued in a key paper by John A. Barker.
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.
Aneesur Rahman 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.
The Wolff algorithm, named after Ulli Wolff, is an algorithm for Monte Carlo simulation of the Ising model and Potts model in which the unit to be flipped is not a single spin but a cluster of them. This cluster is defined as the set of connected spins sharing the same spin states, based on the Fortuin-Kasteleyn representation.
David Matthew Ceperley is a theoretical physicist in the physics department at the University of Illinois Urbana-Champaign or UIUC. He is a world expert in the area of Quantum Monte Carlo computations, a method of calculation that is generally recognised to provide accurate quantitative results for many-body problems described by quantum mechanics.
Subir Sachdev is Herchel Smith Professor of Physics at Harvard University specializing in condensed matter. He was elected to the U.S. National Academy of Sciences in 2014, and received the Lars Onsager Prize from the American Physical Society and the Dirac Medal from the ICTP in 2018. He was a co-editor of the Annual Review of Condensed Matter Physics from 2017-2019.
Berni Julian Alder was a German-born American physicist specialized in statistical mechanics, and a pioneer of computational modelling of matter.
Franz Joachim Wegner is emeritus professor for theoretical physics at the University of Heidelberg.
The following is a timeline of scientific computing, also known as computational science.
The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of mathematics.
This is a timeline of key developments in computational mathematics.
The KBD algorithm is a cluster update algorithm designed for the fully frustrated Ising model in two dimensions, or more generally any two dimensional spin glass with frustrated plaquettes arranged in a checkered pattern. It is discovered in 1990 by Daniel Kandel, Radel Ben-Av, and Eytan Domany, and generalized by P. D. Coddington and L. Han in 1994. It is the inspiration for cluster algorithms used in quantum monte carlo simulations.
Replica cluster move in condensed matter physics refers to a family of non-local cluster algorithms used to simulate spin glasses. It is an extension of the Swendsen-Wang algorithm in that it generates non-trivial spin clusters informed by the interaction states on two replicas instead of just one. It is different from the replica exchange method, as it performs a non-local update on a fraction of the sites between the two replicas at the same temperature, while parallel tempering directly exchanges all the spins between two replicas at different temperature. However, the two are often used alongside to achieve state-of-the-art efficiency in simulating spin-glass models.