Markov Chain Monte Carlo Methods In Quantum Field Theories
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Markov Chain Monte Carlo Methods In Quantum Field Theories
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Author : Anosh Joseph
language : en
Publisher: Springer Nature
Release Date : 2020-04-16
Markov Chain Monte Carlo Methods In Quantum Field Theories written by Anosh Joseph and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-16 with Science categories.
This primer is a comprehensive collection of analytical and numerical techniques that can be used to extract the non-perturbative physics of quantum field theories. The intriguing connection between Euclidean Quantum Field Theories (QFTs) and statistical mechanics can be used to apply Markov Chain Monte Carlo (MCMC) methods to investigate strongly coupled QFTs. The overwhelming amount of reliable results coming from the field of lattice quantum chromodynamics stands out as an excellent example of MCMC methods in QFTs in action. MCMC methods have revealed the non-perturbative phase structures, symmetry breaking, and bound states of particles in QFTs. The applications also resulted in new outcomes due to cross-fertilization with research areas such as AdS/CFT correspondence in string theory and condensed matter physics. The book is aimed at advanced undergraduate students and graduate students in physics and applied mathematics, and researchers in MCMC simulations and QFTs. At the end of this book the reader will be able to apply the techniques learned to produce more independent and novel research in the field.
Monte Carlo Methods In Quantum Problems
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Author : M.H. Kalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Monte Carlo Methods In Quantum Problems written by M.H. Kalos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Monte Carlo methods have been a tool of theoretical and computational scientists for many years. In particular, the invention and percolation of the algorithm of Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller sparked a rapid growth of applications to classical statistical mechanics. Although proposals for treatment of quantum systems had been made even earlier, only a few serious calculations had heen carried out. Ruch calculations are generally more consuming of computer resources than for classical systems and no universal algorithm had--or indeed has yet-- emerged. However, with advances in techniques and in sheer computing power, Monte Carlo methods have been used with considerable success in treating quantum fluids and crystals, simple models of nuclear matter, and few-body nuclei. Research at several institutions suggest that they may offer a new approach to quantum chemistry, one that is independent of basis ann yet capable of chemical accuracy. That. Monte Carlo methods can attain the very great precision needed is itself a remarkable achievement. More recently, new interest in such methods has arisen in two new a~as. Particle theorists, in particular K. Wilson, have drawn attention to the rich analogy between quantum field theoty and statistical mechanics and to the merits of Monte Carlo calculations for lattice gauge theories. This has become a rapidly growing sub-field. A related development is associated with lattice problems in quantum physics, particularly with models of solid state systems. The~ is much ferment in the calculation of various one-dimensional problems such as the'Hubbard model.
Quantum Monte Carlo Methods
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Author : James Gubernatis
language : en
Publisher: Cambridge University Press
Release Date : 2016-06-02
Quantum Monte Carlo Methods written by James Gubernatis and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-02 with Computers categories.
The first textbook to provide a pedagogical examination of the major algorithms used in quantum Monte Carlo simulations.
Lattice Quantum Chromodynamics
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Author : Francesco Knechtli
language : en
Publisher: Springer
Release Date : 2016-10-20
Lattice Quantum Chromodynamics written by Francesco Knechtli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Science categories.
This book provides an overview of the techniques central to lattice quantum chromodynamics, including modern developments. The book has four chapters. The first chapter explains the formulation of quarks and gluons on a Euclidean lattice. The second chapter introduces Monte Carlo methods and details the numerical algorithms to simulate lattice gauge fields. Chapter three explains the mathematical and numerical techniques needed to study quark fields and the computation of quark propagators. The fourth chapter is devoted to the physical observables constructed from lattice fields and explains how to measure them in simulations. The book is aimed at enabling graduate students who are new to the field to carry out explicitly the first steps and prepare them for research in lattice QCD.
Statistical Approach To Quantum Field Theory
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Author : Andreas Wipf
language : en
Publisher: Springer Nature
Release Date : 2021-10-25
Statistical Approach To Quantum Field Theory written by Andreas Wipf and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Science categories.
This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.
Quantum Monte Carlo Methods In Physics And Chemistry
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Author : M.P. Nightingale
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-12-31
Quantum Monte Carlo Methods In Physics And Chemistry written by M.P. Nightingale and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-31 with Mathematics categories.
This book contains lectures on the basic theory and applications of quantum Monte Carlo methods, with contributions written by authorities in the field. Although tutorial in nature, it includes current developments. Both continuum systems and lattice models are covered. The applications include atomic, molecular, and solid state physics, statistical and low-temperature physics, and nuclear structure. Suitable for Ph.D. students and beyond.
Quantum Monte Carlo Methods In Condensed Matter Physics
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Author : Masuo Suzuki
language : en
Publisher: World Scientific
Release Date : 1993
Quantum Monte Carlo Methods In Condensed Matter Physics written by Masuo Suzuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
This book reviews recent developments of quantum Monte Carlo methods and some remarkable applications to interacting quantum spin systems and strongly correlated electron systems. It contains twenty-two papers by thirty authors. Some of the features are as follows. The first paper gives the foundations of the standard quantum Monte Carlo method, including some recent results on higher-order decompositions of exponential operators and ordered exponentials. The second paper presents a general review of quantum Monte Carlo methods used in the present book. One of the most challenging problems in the field of quantum Monte Carlo techniques, the negative-sign problem, is also discussed and new methods proposed to partially overcome it. In addition, low-dimensional quantum spin systems are studied. Some interesting applications of quantum Monte Carlo methods to fermion systems are also presented to investigate the role of strong correlations and fluctuations of electrons and to clarify the mechanism of high-c superconductivity. Not only thermal properties but also quantum-mechanical ground-state properties have been studied by the projection technique using auxiliary fields. Further, the Haldane gap is confirmed by numerical calculations. Active researchers in the forefront of condensed matter physics as well as young graduate students who want to start learning the quantum Monte Carlo methods will find this book useful.
Statistical Field Theory Volume 2 Strong Coupling Monte Carlo Methods Conformal Field Theory And Random Systems
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Author : Claude Itzykson
language : en
Publisher: Cambridge University Press
Release Date : 1991-03-29
Statistical Field Theory Volume 2 Strong Coupling Monte Carlo Methods Conformal Field Theory And Random Systems written by Claude Itzykson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-03-29 with Mathematics categories.
Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.
Quantum Monte Carlo Approaches For Correlated Systems
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Author : Federico Becca
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-30
Quantum Monte Carlo Approaches For Correlated Systems written by Federico Becca and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-30 with Science categories.
A comprehensive introduction to state-of-the-art quantum Monte Carlo techniques for applications in strongly-interacting systems. Including variational wave functions, stochastic samplings, the variational technique, optimisation techniques, real-time dynamics and projection methods and recent developments on the continuum space. An extensive resource for students and researchers.
Probabilistic Methods In Quantum Field Theory And Quantum Gravity
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Author : P. H. Damgaard
language : en
Publisher: Springer Science & Business Media
Release Date : 1990
Probabilistic Methods In Quantum Field Theory And Quantum Gravity written by P. H. Damgaard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
The meeting encompassed all Euclidean quantum field theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Contributors examine the space-time discretized lattice field theories, and present optimized techniques that combine features of ordinary"