The mathematical structure of gauge theory is a union of many modern algebraic concepts. The book provides the background to understand gauge theory and use it in computational chemistry. It introduces two powerful methods used in modern computational chemistry: The Diffusion Monte Carlo algorithm and Ring Polymer Molecular Dynamics. Gauge theory is used to derive a convergent version of the ground state probability amplitude approach for the simulation of excited states. Contains some recent advances in theoretical and computational chemistry. Clear, coherently written explanation of the various background mathematical concepts. Accessible to undergraduate students with many exercises for readers to achieve mastery of the subjects.
The mathematical structure of gauge theory is a union of many modern algebraic concepts. The book provides the background to understand gauge theory and use it in computational chemistry. It introduces two powerful methods used in modern computational chemistry: The Diffusion Monte Carlo algorithm and Ring Polymer Molecular Dynamics. Gauge theory is used to derive a convergent version of the ground state probability amplitude approach for the simulation of excited states. Contains some recent advances in theoretical and computational chemistry. Clear, coherently written explanation of the various background mathematical concepts. Accessible to undergraduate students with many exercises for readers to achieve mastery of the subjects.
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.
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.
Monte Carlo methods have been very prominent in computer simulation of various systems in physics, chemistry, biology, and materials science. This book focuses on the discussion and path-integral quantum Monte Carlo methods in many-body physics and provides a concise but complete introduction to the Metropolis algorithm and its applications in these two techniques. To explore the schemes in clarity, several quantum many-body systems are analysed and studied in detail. The book includes exercises to help digest the materials covered. It can be used as a tutorial to learn the discussion and path-integral Monte Carlo or a recipe for developing new research in the reader's own area. Two complete Java programs, one for the discussion Monte Carlo of 4He clusters on a graphite surface and the other for the path-integral Monte Carlo of cold atoms in a potential trap, are ready for download and adoption.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
An impressively comprehensive textbook adopting a phenomenological approach to quantum physics. The chapters cover everything from basic definitions of key concepts to detailed discussions of the underlying theoretical framework, walking students step-by-step through the necessary mathematics and drawing clear connections between the theory and the most important modern research applications including quantum optics, fluids, nanophysics, entanglement, information, and relativity. With this book, students and researchers will have access to hundreds of real-world examples, exercises, and illustrations to support and expand their understanding. Instructors can tailor the content to suit the length and level of their course and will have access to an online solutions manual with fully worked solutions to all 300+ exercises in the book. Other online resources include Python simulations, additional exercises, and detailed appendices.