This book deals with a variety of problems in Physics and Engineering where the large deviation principle of probability finds application. Large deviations is a branch of probability theory dealing with approximate computation of the probabilities of rare events. It contains applications of the LDP to pattern recognition problems like analysis of the performance of the EM algorithm for optimal parameter estimation in the presence of weak noise, analysis and control of non-Abelian gauge fields in the presence of noise, and quantum gravity wherein we are concerned with perturbation to the quadratic component of the Einstein-Hilbert Hamiltonian caused by higher order nonlinear terms in the position fields and their effect on the Gibbs statistics and consequently quantum probabilities of events computed using the quantum Gibbs state. The reader will also find in this book applications of LDP to quantum filtering theory as developed by Belavkin based on the celebrated Hudson-Parthasarathy quantum stochastic calculus. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).

This thesis contains three breakthrough results in condensed matter physics. Firstly, broken reflection symmetry in the hidden-order phase of the heavy-fermion material URu2Si2 is observed for the first time. This represents a significant advance in the understanding of this enigmatic material which has long intrigued the condensed matter community due to its emergent long range order exhibited at low temperatures (the so-called "hidden order"). Secondly and thirdly, a novel collective mode (the chiral spin wave) and a novel composite particle (the chiral exciton) are discovered in the three dimensional topological insulator Bi2Se3. This opens up new avenues of possibility for the use of topological insulators in photonic, optoelectronic, and spintronic devices. These discoveries are facilitated by using low-temperature polarized Raman spectroscopy as a tool for identifying optically excited collective modes in strongly correlated electron systems and three-dimensional topological insulators.

Quantum Machine Learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. Paring down the complexity of the disciplines involved, it focuses on providing a synthesis that explains the most important machine learning algorithms in a quantum framework. Theoretical advances in quantum computing are hard to follow for computer scientists, and sometimes even for researchers involved in the field. The lack of a step-by-step guide hampers the broader understanding of this emergent interdisciplinary body of research. Quantum Machine Learning sets the scene for a deeper understanding of the subject for readers of different backgrounds. The author has carefully constructed a clear comparison of classical learning algorithms and their quantum counterparts, thus making differences in computational complexity and learning performance apparent. This book synthesizes of a broad array of research into a manageable and concise presentation, with practical examples and applications.

This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

Many fundamental theories of modern physics can be considered as descriptions of dynamical systems subjected to constraints. The study of these constrained dynamical systems, and in particular the problems of formulating them as quantum systems, has many profound links with geometry. These links were explored in the Symposium on Geometry and Gravity held at the Newton Institute in 1994. This book, which arose from a conference held during that symposium, is a collection of papers devoted to problems such as Chern-Simons theory, sigma-models, gauge invariance and loop quantization, general relativity and the notion of time, and quantum gravity. They present a lively, varied and topical perspective on this important branch of theoretical physics from some of the leading authorities in the subject, and will be of value to theoretical physicists and mathematicians interested in the latest advances.

This monograph covers the concept of cartesian tensors with the needs and interests of physicists, chemists and other physical scientists in mind. After introducing elementary tensor operations and rotations, spherical tensors, combinations of tensors are introduced, also covering Clebsch-Gordan coefficients. After this, readers from the physical sciences will find generalizations of the results to spinors and applications to quantum mechanics.

Quantum cosmology has gradually emerged as the focus of devoted research, mostly within the second half of last century. As we entered the 21st century, the subject is still very much alive. The outcome of results and templates for investigation have been enlarged, some very recent and fascinating. Hence this book, where the authors bequeath some of their views, as they believe this current century is the one where quantum cosmology will be fully accomplished.Though some aspects are not discussed (namely, supersymmetry or loop structures), there are perhaps a set of challenges that in the authors' opinion remain, some since the dawn of quantum mechanics and applications to cosmology. Others could have been selected, at the readers' discretion and opinion. The authors put herewith a chart and directions to explore, some of which they have worked on or aimed to work more, in the twilight of their current efforts. Their confidence is that someone will follow in their trails, venturing in discovering the proper answer, by being able to formulate the right questions beforehand. The authors' shared foresight is that such discoveries, from those formulations, will be attained upon endorsing the routes within the challenges herewith indicated.

Quantum Mechanics II: Advanced Topics offers a comprehensive exploration of the state-of-the-art in various advanced topics of current research interest. A follow-up to the authors' introductory book Quantum Mechanics I: The Fundamentals, this book expounds basic principles, theoretical treatment, case studies, worked-out examples and applications of advanced topics including quantum technologies. A thoroughly revised and updated this unique volume presents an in-depth and up-to-date progress on the growing topics including latest achievements on quantum technology. In the second edition six new chapters are included and the other ten chapters are extensively revised. Features Covers classical and quantum field theories, path integral formalism and supersymmetric quantum mechanics. Highlights coherent and squeezed states, Berry's phase, Aharonov-Bohm effect and Wigner function. Explores salient features of quantum entanglement and quantum cryptography. Presents basic concepts of quantum computers and the features of no-cloning theorem and quantum cloning machines. Describes the theory and techniques of quantum tomography, quantum simulation and quantum error correction. Introduces other novel topics including quantum versions of theory of gravity, cosmology, Zeno effect, teleportation, games, chaos and steering. Outlines the quantum technologies of ghost imaging, detection of weak amplitudes and displacements, lithography, metrology, teleportation of optical images, sensors, batteries and internet. Contains several worked-out problems and exercises in each chapter. Quantum Mechanics II: Advanced Topics addresses various currently emerging exciting topics of quantum mechanics. It emphasizes the fundamentals behind the latest cutting-edge developments to help explain the motivation for deeper exploration. The book is a valuable resource for graduate students in physics and engineering wishing to pursue research in quantum mechanics.

This book surveys some of the important research work carried out by Indian scientists in the field of pure and applied probability, quantum probability, quantum scattering theory, group representation theory and general relativity. It reviews the axiomatic foundations of probability theory by A.N. Kolmogorov and how the Indian school of probabilists and statisticians used this theory effectively to study a host of applied probability and statistics problems like parameter estimation, convergence of a sequence of probability distributions, and martingale characterization of diffusions. It will be an important resource to students and researchers of Physics and Engineering, especially those working with Advanced Probability and Statistics.

This book provides a tutorial on quantum communication networks. The authors discuss current paradigm shifts in communication networks that are needed to add computing and storage to the simple transport ideas of prevailing networks. They show how these 'softwarized' solutions break new grounds to reduce latency and increase resilience. The authors discuss how even though these solutions have inherent problems due to introduced computing latency and energy consumption, the problems can be solved by hybrid classical-quantum communication networks. The book brings together quantum networking, quantum information theory, quantum computing, and quantum simulation.

Offers a whistle-stop tour through the early part of the 20th century when the founding fathers of quantum theory forever altered the frontiers of human thought Provides an example-filled interpretation of the theory, its applications, and its pinnacle in quantum field theory (QFT), so crucial in shaping ideas about the nature of reality Separates fact from speculation regarding quantum physics' ability to provide a starting point for philosophical queries into ultimate understanding and the limits of science

- Covers both continuum differential equation approach and matrix algebra. - Refined lecture notes, tested on students for over 30 years.

Key features: Presents the first elementary introduction to quantum geometry Explores how to understand quantum geometry without prior knowledge beyond bachelor level physics and mathematics. Contains exercises, problems and solutions to supplement and enhance learning

This book is a wide-ranging survey of the physics of out-of-equilibrium systems of correlated electrons, ranging from the theoretical, to the numerical, computational and experimental aspects. It starts from basic approaches to non-equilibrium physics, such as the mean-field approach, then proceeds to more advanced methods, such as dynamical mean-field theory and master equation approaches. Lastly, it offers a comprehensive overview of the latest advances in experimental investigations of complex quantum materials by means of ultrafast spectroscopy.

Quantum mechanics has shown unprecedented success as a physical theory, but it has forced a new view on the description of physical reality. In recent years, important progress has been achieved both in the theory of open quantum systems and in the experimental realization and control of such systems. A great deal of the new results is concerned with the characterization and quantification of quantum memory effects. From this perspective, the 684. WE-Heraeus-Seminar has brought together scientists from different communities, both theoretical and experimental, sharing expertise on open quantum systems, as well as the commitment to the understanding of quantum mechanics. This book consists of many contributions addressing the diversified physics community interested in foundations of quantum mechanics and its applications and it reports about recent results in open quantum systems and their connection with the most advanced experiments testing quantum mechanics.

This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail. The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan's Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory. The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.

Quantum field theory is the application of quantum mechanics to systems with infinitely many degrees of freedom. This 2007 textbook presents quantum field theoretical applications to systems out of equilibrium. It introduces the real-time approach to non-equilibrium statistical mechanics and the quantum field theory of non-equilibrium states in general. It offers two ways of learning how to study non-equilibrium states of many-body systems: the mathematical canonical way and an easy intuitive way using Feynman diagrams. The latter provides an easy introduction to the powerful functional methods of field theory, and the use of Feynman diagrams to study classical stochastic dynamics is considered in detail. The developed real-time technique is applied to study numerous phenomena in many-body systems. Complete with numerous exercises to aid self-study, this textbook is suitable for graduate students in statistical mechanics and condensed matter physics.

Unified Field Theory was an expression first used by Einstein in his attempt to unify general relativity with electromagnetism. Unified Field Theory and Occam's Razor attempts to provide real answers to foundational questions related to this unification and should be of high interest to innovative scientists. A diverse group of contributing authors approach an old problem with an open-mindedness that presents a new and fresh perspective. The following topics are discussed in detail in the hope of a fruitful dialogue with all who are interested in this subject:This highly original book brings together theoretical researchers and experimentalists specialized in the areas of mathematics and epistemology, theoretical and experimental physics, engineering, and technology. For years they have worked independently on topics related to the foundations and unity of physics and have had numerous overlapping ideas in terms of using Clifford algebra and spinors. Within the book, new technology applications are outlined and theoretical results are complemented by interpretations of experimental data.

Features: Includes over 104 codes in OOPs python, all of which can be used either as a standalone program or integrated with any other main program without any issues. Every parameter in the input, output and execution has been provided while keeping both beginner and advanced users in mind. The output of every program is explained thoroughly with detailed examples. A detailed mathematical commenting is done along side the code which enhances clarity about the flow and working of the code

It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrodinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.

- integrates contemporary science, philosophy, and psychoanalysis - first book on the market to discuss more than one area of contemporary science in relation to psychoanalysis

- integrates contemporary science, philosophy, and psychoanalysis - first book on the market to discuss more than one area of contemporary science in relation to psychoanalysis