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Field Theory Of Condensed Matter And Ultracold Gases - Volume 1
This book provides a pedagogical introduction to the concepts and methods of quantum field theory necessary for the study of condensed matter and ultracold atomic gases. After a thorough discussion of the basic methods of field theory and many-body physics (functional integrals, perturbation theory, Feynman diagrams, correlation functions and linear response theory, symmetries and their consequences, etc.), the book covers a wide range of topics, from electron gas and Fermi-liquid theory to superfluidity and superconductivity, magnetic instabilities in electron systems, and dynamical mean-field theory of Mott transition. The focus is on the study of model Hamiltonians, where the microscopic physics and characteristic energy scales are encoded into a few effective parameters, rather than first-principle methods which start from a realistic Hamiltonian at the microscopic level and then make material-specific predictions. The reader is expected to be familiar with elementary quantum mechanics and statistical physics, and some acquaintance with condensed-matter physics and ultracold gases may also be useful. No prior knowledge of field theory or many-body problem is required.
Quantum Mechanics
This book provides the reader with a contemporary and comprehensive introduction to Quantum Mechanics. It is suitable for beginners as well as for more advanced university students. Quantum mechanics is presented in a pedagogical fashion, with a clear logical organization. The various concepts and methods are introduced first in elementary terms, and later developed into more precise formulations. Systematic studies of approximation methods and the discussion of a wide class of physical applications follow. Part I of the book, together with the opening sections of Part II, provide adequate material for an introductory course of one semester at most universities. The rest of the book might be...
Finite Fields, with Applications to Combinatorics
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
Quantum Probability for Probabilists
In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical stochastic calculus and martingale theory, tries to provide an introduction to this rapidly expanding field in a way which should be accessible to probabilists familiar with the Ito integral. It can also, on the other hand, provide a means of access to the methods of stochastic calculus for physicists familiar with Fock space analysis. For this second edition, the author has added about 30 pages of new material, mostly on quantum stochastic integrals.
Artificial Intelligence for Communications and Networks
This two-volume set LNICST 396 and 397 constitutes the post-conference proceedings of the Third EAI International Conference on Artificial Intelligence for Communications and Networks, AICON 2021, held in September 2021. Due to COVID-19 pandemic the conference was held virtually. The 79 full papers were carefully reviewed and selected from 159 submissions. The papers are organized in topical sections on Artificial Intelligence in Wireless Communications and Satellite Communications; Artificial Intelligence in Electromagnetic Signal Processing; Artificial Intelligence Application in Wireless Caching and Computing; Artificial Intelligence Application in Computer Network.
Problems In Solid State Physics With Solutions
This book provides a practical approach to consolidate one's acquired knowledge or to learn new concepts in solid state physics through solving problems. It contains 300 problems on various subjects of solid state physics. The problems in this book can be used as homework assignments in an introductory or advanced course on solid state physics for undergraduate or graduate students.It can also serve as a desirable reference book to solve typical problems and grasp mathematical techniques in solid state physics. In practice, it is more fascinating and rewarding to learn a new idea or technique through solving challenging problems rather than through reading only. In this aspect, this book is not a plain collection of problems but it presents a large number of problem-solving ideas and procedures, some of which are valuable to practitioners in condensed matter physics.
Quantum Mechanics with Applications to Nanotechnology and Information Science
Quantum mechanics transcends and supplants classical mechanics at the atomic and subatomic levels. It provides the underlying framework for many subfields of physics, chemistry and materials science, including condensed matter physics, atomic physics, molecular physics, quantum chemistry, particle physics, and nuclear physics. It is the only way we can understand the structure of materials, from the semiconductors in our computers to the metal in our automobiles. It is also the scaffolding supporting much of nanoscience and nanotechnology. The purpose of this book is to present the fundamentals of quantum theory within a modern perspective, with emphasis on applications to nanoscience and na...
Conformal Invariance and Critical Phenomena
This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators. Numerical methods for matrix diagonalization are described as well as finite-size scaling techniques and their conformal extensions. Many exercises are included. Applications treat the Ising, Potts, chiral Potts, Yang-Lee, percolation and XY models, the XXZ chain, linear polymers, tricritical points, conformal turbulence, surface criticality and profiles, defect lines and aperiodically modulated systems, persistent currents and dynamical scaling. The vicinity of the critical point is studied culminating in the exact solution of the two-dimensional Ising model at the critical temperature in a magnetic field. Relevant experimental results are also reviewed.
Quark-Gluon Plasma: Theoretical Foundations
The purpose of this volume is to trace the development of the theoretical understanding of quark-gluon plasma, both in terms of the equation of state and thermal correlation functions and in terms of its manifestation in high energy nuclear collisions. Who among us has not wondered how tall a mountain is on a neutron star, what happens when matter is heated and compressed to higher and higher densities, what happens when an object falls into a black hole, or what happened eons ago in the early universe? The study of quark-gluon plasma is related in one way or another to these and other thought provoking questions. Oftentimes the most eloquent exposition is given in the original papers. To th...
English Vocabulary in Use Elementary with Answers
"Vocabulary tests to accompany the popular English Vocabulary in Use Elementary second edition. Test Your English Vocabulary in Use Elementary 2nd edition can be used on its own or with the companion volume English Vocabulary in Use Elementary 2nd edition. It is a handy book of tests covering the vocabulary practised in English Vocabulary in Use Elementary 2nd edition." -- Publisher description.
