Interacting Electrons

Theory and Computational Approaches

Author: Richard M. Martin,Lucia Reining,David M. Ceperley

Publisher: Cambridge University Press

ISBN: 1316558568

Category: Science

Page: N.A

View: 5382

Recent progress in the theory and computation of electronic structure is bringing an unprecedented level of capability for research. Many-body methods are becoming essential tools vital for quantitative calculations and understanding materials phenomena in physics, chemistry, materials science and other fields. This book provides a unified exposition of the most-used tools: many-body perturbation theory, dynamical mean field theory and quantum Monte Carlo simulations. Each topic is introduced with a less technical overview for a broad readership, followed by in-depth descriptions and mathematical formulation. Practical guidelines, illustrations and exercises are chosen to enable readers to appreciate the complementary approaches, their relationships, and the advantages and disadvantages of each method. This book is designed for graduate students and researchers who want to use and understand these advanced computational tools, get a broad overview, and acquire a basis for participating in new developments.
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Electronic Structure

Basic Theory and Practical Methods

Author: Richard M. Martin

Publisher: Cambridge University Press

ISBN: 9780521782852

Category: Science

Page: 624

View: 1899

Important graduate textbook in condensed matter physics by highly regarded physicist.
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Atomic and Electronic Structure of Solids

Author: Efthimios Kaxiras

Publisher: Cambridge University Press

ISBN: 9780521523394

Category: Science

Page: 676

View: 3916

Graduate-level textbook for physicists, chemists and materials scientists.
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Quantum Monte Carlo Approaches for Correlated Systems

Author: Federico Becca,Sandro Sorella

Publisher: Cambridge University Press

ISBN: 1108547311

Category: Science

Page: N.A

View: 1574

Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to state-of-the-art quantum Monte Carlo techniques relevant for applications in correlated systems. Providing a clear overview of variational wave functions, and featuring a detailed presentation of stochastic samplings including Markov chains and Langevin dynamics, which are developed into a discussion of Monte Carlo methods. The variational technique is described, from foundations to a detailed description of its algorithms. Further topics discussed include optimisation techniques, real-time dynamics and projection methods, including Green's function, reptation and auxiliary-field Monte Carlo, from basic definitions to advanced algorithms for efficient codes, and the book concludes with recent developments on the continuum space. Quantum Monte Carlo Approaches for Correlated Systems provides an extensive reference for students and researchers working in condensed matter theory or those interested in advanced numerical methods for electronic simulation.
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Electronic Structure Calculations for Solids and Molecules

Theory and Computational Methods

Author: Jorge Kohanoff

Publisher: Cambridge University Press

ISBN: 1139453483

Category: Science

Page: N.A

View: 5943

Electronic structure problems are studied in condensed matter physics and theoretical chemistry to provide important insights into the properties of matter. This 2006 graduate textbook describes the main theoretical approaches and computational techniques, from the simplest approximations to the most sophisticated methods. It starts with a detailed description of the various theoretical approaches to calculating the electronic structure of solids and molecules, including density-functional theory and chemical methods based on Hartree-Fock theory. The basic approximations are thoroughly discussed, and an in-depth overview of recent advances and alternative approaches in DFT is given. The second part discusses the different practical methods used to solve the electronic structure problem computationally, for both DFT and Hartree-Fock approaches. Adopting a unique and open approach, this textbook is aimed at graduate students in physics and chemistry, and is intended to improve communication between these communities. It also serves as a reference for researchers entering the field.
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Field Theory of Non-Equilibrium Systems

Author: Alex Kamenev

Publisher: Cambridge University Press

ISBN: 1139500295

Category: Science

Page: N.A

View: 4216

The physics of non-equilibrium many-body systems is one of the most rapidly expanding areas of theoretical physics. Traditionally used in the study of laser physics and superconducting kinetics, these techniques have more recently found applications in the study of dynamics of cold atomic gases, mesoscopic and nano-mechanical systems. The book gives a self-contained presentation of the modern functional approach to non-equilibrium field-theoretical methods. They are applied to examples ranging from biophysics to the kinetics of superfluids and superconductors. Its step-by-step treatment gives particular emphasis to the pedagogical aspects, making it ideal as a reference for advanced graduate students and researchers in condensed matter physics.
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Introduction to Computational Materials Science

Fundamentals to Applications

Author: Richard LeSar

Publisher: Cambridge University Press

ISBN: 1107328144

Category: Technology & Engineering

Page: N.A

View: 8610

Emphasising essential methods and universal principles, this textbook provides everything students need to understand the basics of simulating materials behaviour. All the key topics are covered from electronic structure methods to microstructural evolution, appendices provide crucial background material, and a wealth of practical resources are available online to complete the teaching package. Modelling is examined at a broad range of scales, from the atomic to the mesoscale, providing students with a solid foundation for future study and research. Detailed, accessible explanations of the fundamental equations underpinning materials modelling are presented, including a full chapter summarising essential mathematical background. Extensive appendices, including essential background on classical and quantum mechanics, electrostatics, statistical thermodynamics and linear elasticity, provide the background necessary to fully engage with the fundamentals of computational modelling. Exercises, worked examples, computer codes and discussions of practical implementations methods are all provided online giving students the hands-on experience they need.
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Nonequilibrium Many-Body Theory of Quantum Systems

A Modern Introduction

Author: Gianluca Stefanucci,Robert van Leeuwen

Publisher: Cambridge University Press

ISBN: 1107354579

Category: Science

Page: N.A

View: 9636

The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics.
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Theory and Applications of Computational Chemistry

The First Forty Years

Author: Clifford E. Dykstra

Publisher: Gulf Professional Publishing

ISBN: 9780444519047

Category: Science

Page: 1308

View: 5233

Computational chemistry is a means of applying theoretical ideas using computers and a set of techniques for investigating chemical problems within which common questions vary from molecular geometry to the physical properties of substances. Theory and Applications of Computational Chemistry: The First Forty Years is a collection of articles on the emergence of computational chemistry. It shows the enormous breadth of theoretical and computational chemistry today and establishes how theory and computation have become increasingly linked as methodologies and technologies have advanced. Written by the pioneers in the field, the book presents historical perspectives and insights into the subject, and addresses new and current methods, as well as problems and applications in theoretical and computational chemistry. Easy to read and packed with personal insights, technical and classical information, this book provides the perfect introduction for graduate students beginning research in this area. It also provides very readable and useful reviews for theoretical chemists. * Written by well-known leading experts * Looks at problems and applications in theoretical and computational chemistry * Is the perfect introduction to the field for young scientists
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Materials Modelling Using Density Functional Theory

Properties and Predictions

Author: Feliciano Giustino

Publisher: Oxford University Press

ISBN: 0199662436

Category: Science

Page: 286

View: 2724

This book is an introduction to the modern quantum theory of materials, and primarily addresses seniorundergraduate and first-year graduate students in the physical and chemical sciences, and in materials science and engineering. As advanced materials are becoming ubiquitous in every aspect of our life, the use of quantum mechanics to understand, predict, and design new materials is experiencing a fast-paced growth in academic and industrial research.Following this trend, atomistic materials modelling is becoming an important component of undergraduate science education, however there is still no book on this subject written primarily for anundergraduate readership. The book explains the fundamental ideas of density functional theory, and how this theory can be used as a powerful method for explaining and even predicting the properties of materials with stunning accuracy. This book can be used either as a complement to the quantum theory of materials, or as a primer in modern techniques of computational materials modelling using quantum mechanics.
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Advanced Theories and Computational Approaches to the Electronic Structure of Molecules

Author: C.E. Dykstra

Publisher: Springer Science & Business Media

ISBN: 9789027718105

Category: Science

Page: 248

View: 2136

That there have been remarkable advances in the field of molecular electronic structure during the last decade is clear not only to those working in the field but also to anyone else who has used quantum chemical results to guide their own investiga tions. The progress in calculating the electronic structures of molecules has occurred through the truly ingenious theoretical and methodological developments that have made computationally tractable the underlying physics of electron distributions around a collection of nuclei. At the same time there has been consider able benefit from the great advances in computer technology. The growing sophistication, declining costs and increasing accessibi lity of computers have let theorists apply their methods to prob lems in virtually all areas of molecular science. Consequently, each year witnesses calculations on larger molecules than in the year before and calculations with greater accuracy and more com plete information on molecular properties. We can surely anticipate continued methodological develop ments of real consequence, and we can also see that the advance in computational capability is not about to slow down. The recent introduction of array processors, mUltiple processors and vector machines has yielded a tremendous acceleration of many types of computation, including operations typically performed in quantum chemical studies. Utilizing such new computing power to the ut most has required some new ideas and some reformulations of existing methods.
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Quantum Statistical Mechanics

Author: Leo P. Kadanoff

Publisher: CRC Press

ISBN: 0429972849

Category: Science

Page: 224

View: 2881

Green's Function Methods in Equilibrium and Nonequilibrium Problems
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Multiconfigurational Quantum Chemistry

Author: Björn O. Roos,Roland Lindh,Per Ãke Malmqvist,Valera Veryazov,Per-Olof Widmark

Publisher: John Wiley & Sons

ISBN: 1119277884

Category: Science

Page: 240

View: 5001

The first book to aid in the understanding of multiconfigurational quantum chemistry, Multiconfigurational Quantum Chemistry demystifies a subject that has historically been considered difficult to learn. Accessible to any reader with a background in quantum mechanics and quantum chemistry, the book contains illustrative examples showing how these methods can be used in various areas of chemistry, such as chemical reactions in ground and excited states, transition metal and other heavy element systems. The authors detail the drawbacks and limitations of DFT and coupled-cluster based methods and offer alternative, wavefunction-based methods more suitable for smaller molecules.
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Molecular Electronic-Structure Theory

Author: Trygve Helgaker,Poul Jorgensen,Jeppe Olsen

Publisher: John Wiley & Sons

ISBN: 1119019559

Category: Science

Page: 944

View: 859

Ab initio quantum chemistry has emerged as an important tool in chemical research and is appliced to a wide variety of problems in chemistry and molecular physics. Recent developments of computational methods have enabled previously intractable chemical problems to be solved using rigorous quantum-mechanical methods. This is the first comprehensive, up-to-date and technical work to cover all the important aspects of modern molecular electronic-structure theory. Topics covered in the book include: * Second quantization with spin adaptation * Gaussian basis sets and molecular-integral evaluation * Hartree-Fock theory * Configuration-interaction and multi-configurational self-consistent theory * Coupled-cluster theory for ground and excited states * Perturbation theory for single- and multi-configurational states * Linear-scaling techniques and the fast multipole method * Explicity correlated wave functions * Basis-set convergence and extrapolation * Calibration and benchmarking of computational methods, with applications to moelcular equilibrium structure, atomization energies and reaction enthalpies. Molecular Electronic-Structure Theory makes extensive use of numerical examples, designed to illustrate the strengths and weaknesses of each method treated. In addition, statements about the usefulness and deficiencies of the various methods are supported by actual examples, not just model calculations. Problems and exercises are provided at the end of each chapter, complete with hints and solutions. This book is a must for researchers in the field of quantum chemistry as well as for nonspecialists who wish to acquire a thorough understanding of ab initio molecular electronic-structure theory and its applications to problems in chemistry and physics. It is also highly recommended for the teaching of graduates and advanced undergraduates.
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Atoms in Molecules

A Quantum Theory

Author: Richard F. W. Bader

Publisher: Oxford University Press on Demand

ISBN: 9780198558651

Category: Science

Page: 438

View: 6517

The molecular structure hypothesis - that a molecule is a collection of atoms linked by a network of bonds - was forged in the crucible of nineteenth century experimental chemistry and has continued to serve as the principal means of ordering and classifying the observations of chemistry. There is a difficulty with the hypothesis, however, in that it is not related directly to the physics which governs the motions of the nuclei and electrons that make up the atoms and the bonds. It isthe purpose of this important book - now available in paperback for the first time - to show that a theory can be developed to underpin the molecular structure hypothesis - that the atoms in a molecule are real, with properties predicted and defined by the laws of quantum mechanics can be incorporated into the resulting theory - a theory of atoms in molecules. The book is aimed at those scientists responsible for performing the experiments and collecting the observations on the properties ofmatter at the atomic level, in the belief that the transformation of qualitative concepts into a qualitative theory will serve to deepen our understanding of chemistry.
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Recent Progress In Orbital-free Density Functional Theory

Author: Wang Yan Alexander,Wesolowski Tomasz A

Publisher: World Scientific

ISBN: 9814436747

Category: Science

Page: 464

View: 780

This is a comprehensive overview of state-of-the-art computational methods based on orbital-free formulation of density functional theory completed by the most recent developments concerning the exact properties, approximations, and interpretations of the relevant quantities in density functional theory.The book is a compilation of contributions stemming from a series of workshops which had been taking place since 2002. It not only chronicles many of the latest developments but also summarises some of the more significant ones. The chapters are mainly reviews of sub-domains but also include original research.
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Quantum Theory from First Principles

An Informational Approach

Author: Giacomo Mauro D'Ariano,Giulio Chiribella,Paolo Perinotti

Publisher: Cambridge University Press

ISBN: 1107043425

Category: Science

Page: 400

View: 6039

Quantum theory is the soul of theoretical physics. It is not just a theory of specific physical systems, but rather a new framework with universal applicability. This book shows how we can reconstruct the theory from six information-theoretical principles, by rebuilding the quantum rules from the bottom up. Step by step, the reader will learn how to master the counterintuitive aspects of the quantum world, and how to efficiently reconstruct quantum information protocols from first principles. Using intuitive graphical notation to represent equations, and with shorter and more efficient derivations, the theory can be understood and assimilated with exceptional ease. Offering a radically new perspective on the field, the book contains an efficient course of quantum theory and quantum information for undergraduates. The book is aimed at researchers, professionals, and students in physics, computer science and philosophy, as well as the curious outsider seeking a deeper understanding of the theory.
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Ab Initio Molecular Dynamics

Basic Theory and Advanced Methods

Author: Dominik Marx,Jürg Hutter

Publisher: Cambridge University Press

ISBN: 9781139477192

Category: Science

Page: N.A

View: 9428

Ab initio molecular dynamics revolutionized the field of realistic computer simulation of complex molecular systems and processes, including chemical reactions, by unifying molecular dynamics and electronic structure theory. This book provides the first coherent presentation of this rapidly growing field, covering a vast range of methods and their applications, from basic theory to advanced methods. This fascinating text for graduate students and researchers contains systematic derivations of various ab initio molecular dynamics techniques to enable readers to understand and assess the merits and drawbacks of commonly used methods. It also discusses the special features of the widely used Car–Parrinello approach, correcting various misconceptions currently found in research literature. The book contains pseudo-code and program layout for typical plane wave electronic structure codes, allowing newcomers to the field to understand commonly used program packages and enabling developers to improve and add new features in their code.
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Computational Atomic Physics

Electron and Positron Collisions with Atoms and Ions

Author: Klaus Bartschat

Publisher: Springer

ISBN: 3642610102

Category: Science

Page: 249

View: 2574

Computational Atomic Physics deals with computational methods for calculating electron (and positron) scattering from atoms and ions, including elastic scattering, excitation, and ionization processes. Each chapter is divided into abstract, theory, computer program with sample input and output, summary, suggested problems, and references. An MS-DOS diskette is included, which holds 11 programs covering the features of each chapter and therefore contributing to a deeper understanding of the field. Thus the book provides a unique practical application of advanced quantum mechanics.
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Quantum Theory of Many-Body Systems

Techniques and Applications

Author: Alexandre Zagoskin

Publisher: Springer

ISBN: 3319070495

Category: Technology & Engineering

Page: 280

View: 5653

This text presents a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green’s functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory and the Matsubara, Keldysh and Nambu-Gor'kov formalism, as well as an introduction to Feynman path integrals. This new edition contains an introduction to the methods of theory of one-dimensional systems (bosonization and conformal field theory) and their applications to many-body problems. Intended for graduate students in physics and related fields, the aim is not to be exhaustive, but to present enough detail to enable the student to follow the current research literature, or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout their volume and which therefore provides an ideal testing ground for many-body theories.
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