Continued advances in the precision manufacturing of new structures at the nanometer scale have provided unique opportunities for device physics. This book sets out to summarize those elements of classical mechanics most applicable for scientists and engineers studying device physics. Supplementary MATLAB (R) materials are available for all figures generated numerically.

Recent work in quantum information science has produced a revolution in our understanding of quantum entanglement. Scientists now view entanglement as a physical resource with many important applications. These range from quantum computers, which would be able to compute exponentially faster than classical computers, to quantum cryptographic techniques, which could provide unbreakable codes for the transfer of secret information over public channels. These important advances in the study of quantum entanglement and information touch on deep foundational issues in both physics and philosophy. This interdisciplinary volume brings together fourteen of the world's leading physicists and philosophers of physics to address the most important developments and debates in this exciting area of research. It offers a broad spectrum of approaches to resolving deep foundational challenges - philosophical, mathematical, and physical - raised by quantum information, quantum processing, and entanglement. This book is ideal for historians, philosophers of science and physicists.

In this thesis we discuss the construction of an effective field theory (EFT) for non-relativistic Majorana fermions, show how to use it to calculate observables in a thermal medium, and derive the effects of these thermal particles on the CP asymmetry. The methods described in this thesis allow a systematic and effective description of the non-relativistic dynamics of a heavy Majorana fermion at finite temperature. The CP asymmetry is studied for hierarchical and nearly degenerate heavy-neutrino masses and the analysis includes the treatment of lepton-flavor effects. Heavy Majorana neutrinos are involved in many scenarios of physics beyond the standard model and, in the leptogenesis framework, they are at the root of the baryon asymmetry in the Universe. Besides simplifying exist in g results, the EFT approach provides useful tools for addressing even more involved observables. Indeed, taken together, the approach and the material presented here represent an important step toward a systematic improvement of our knowledge of the CP asymmetry in heavy-neutrino decays at finite temperature.

Strong Interactions in Spacelike and Timelike Domains: Dispersive Approach provides the theoretical basis for the description of the strong interactions in the spacelike and timelike domains. The book primarily focuses on the hadronic vacuum polarization function, R-ratio of electron-positron annihilation into hadrons, and the Adler function, which govern a variety of the strong interaction processes at various energy scales. Specifically, the book presents the essentials of the dispersion relations for these functions, recaps their perturbative calculation, and delineates the dispersively improved perturbation theory. The book also elucidates the peculiarities of the continuation of the spacelike perturbative results into the timelike domain, which is indispensable for the studies of electron-positron annihilation into hadrons and the related processes.

This work provides a convincing motivation for and introduction to magnon-based computing. The challenges faced by the conventional semiconductor-transistor-based computing industry are contrasted with the many exciting avenues for developing spin waves (or magnons) as a complementary technology wherein information can be encoded, transmitted, and operated upon: essential ingredients for any computing paradigm. From this general foundation, one particular operation is examined: phase conjugation via four-wave-mixing (FWM). The author constructs an original theory describing the generation of a phase conjugate mirror with the remarkable property that any incident spin wave will be reflected back along the same direction of travel. After establishing a theoretical framework, the careful design of the experiment is presented, followed by the demonstration of a magnetic phase conjugate mirror using four-wave mixing for the first time. The thesis concludes with an investigation into the unexpected fractal behaviour observed arising from the phase conjugate mirror - a result that is testament to the richness and vibrancy of these highly nonlinear spin wave systems.

With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras

This book is written with the view of providing learners a fast track into the modern applications of quantum physics. It is designed as a book of Problems and Solutions, consisting of more than 200 exercises with explicitly worked out solutions.Focusing on modern research topics, the problems are designed to suit recent developments such as graphene, topological materials, spintronics, and quantum computation and information (QCI). Categorized into eight chapters, the book first introduces QM for undergraduates with an emphasis on the Dirac formalism and its representation in the form of matrices and functions. Chapter 2 is dedicated to spin physics, where the spinor formalism is increasingly relevant to research on spintronics, graphene, topological systems, Dirac, Weyl, and all branches of quantum information sciences. Chapter 3 deals with second quantization and its applications in nanoscience and condensed matter physics. Building on the foundations of the previous two chapters, Chapter 4 expounds on the non-equilibrium Green's Function (NEGF) - a modern topic with problems designed to suit applications in nanoscale electronic and spintronics systems. Chapter 5 covers gauge fields and topology, with a modern emphasis on applications in new materials such as graphene and topological systems. Chapter 6 comprises numerous advanced sub-topics in condensed matter physics as well as conventional topics such as band structures and entanglement entropy. Chapter 7 extends to cross-disciplinary and miscellaneous physics, where the topics are not necessarily quantum by nature, but deal with issues that have inspired the development of quantum mechanics and quantum fields. Lastly, the book caters to quantum computation with a preamble on the QM foundations of spin, projection, measurement and density matrices which underpin applications in quantum gates, quantum teleportation and entanglement.Readers can expect a handy and effective guide in mastering problem solving techniques in frontier applications of quantum physics.

Our understanding of nature, and in particular of physics and the laws governing it, has changed radically since the days of the ancient Greek natural philosophers. This book explains how and why these changes occurred, through landmark experiments as well as theories that - for their time - were revolutionary. The presentation covers Mechanics, Optics, Electromagnetism, Thermodynamics, Relativity Theory, Atomic Physics and Quantum Physics. The book places emphasis on ideas and on a qualitative presentation, rather than on mathematics and equations. Thus, although primarily addressed to those who are studying or have studied science, it can also be read by non-specialists. The author concludes with a discussion of the evolution and organization of universities, from ancient times until today, and of the organization and dissemination of knowledge through scientific publications and conferences.

Path integrals provide a powerful method for describing quantum phenomena. This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories. The authors start by deriving path integrals for particles moving in curved space and their supersymmetric generalizations. They then discuss the regularization schemes essential to constructing and computing these path integrals. This topic is used to introduce regularization and renormalization in quantum field theories in a wider context. These methods are then applied to discuss and calculate anomalies in quantum field theory. Such anomalies provide enormous constraints in the search for physical theories of elementary particles, quantum gravity and string theories. An advanced text for researchers and graduate students of quantum field theory and string theory, the first part is also a stand-alone introduction to path integrals in quantum mechanics.

The energy momentum tensor (EMT) is one of the most fundamental observables in physics. Recently, a novel method to define EMT on the basis of the gradient-flow formalism has been proposed. It turned out that the EMT operator can be constructed even on the lattice with the method, which enables non-perturbative computations. This approach has been successfully applied to the analyses on thermodynamic quantities. This book presents the study on spatial EMT distributions around static charges via the gradient flow in lattice simulations based on SU(3) Yang-Mills theory. Static charges are employed as probes to explore complex quantum systems, and EMT then characterizes the response of vacuum as well as hot medium under the existence of the charges, which significantly provides profound and novel insights into the non-perturbative phenomena, such as the confinement of quarks. In addition, the book treats the study on the EMT distribution around a magnetic vortex in the Abelian-Higgs model, which is compared with the lattice result. These achievements open up various future studies for revealing non-trivial aspects of the strong interaction. The book also includes well-organized reviews on general properties of EMT, lattice gauge theory and the gradient-flow formalism with its application to the definition of EMT. They are useful for students and young researchers as a brief introduction to this field.

In topological quantum materials, quantum effects emerge at macroscopic scales and are robust to continuous changes in a material's state. This striking synergy between quantum and topological properties is of great interest for both fundamental research and emerging technologies, especially in the fields of electronics and quantum information. This edition of the book presents a wealth of topological quantum materials, bringing together burgeoning research from different areas: topological insulators, transition metal dichalcogenides, Weyl semimetals, and unconventional and topological superconductors. The realization of the application potential of topological quantum materials requires understanding their properties at a fundamental level. This brings us back to the discovery of topological phases of matter, which earned the Nobel Prize in Physics in 2016. This book explores the connection between pioneering work on topological phases of matter and a flurry of activity that followed. The topics covered include the quantum anomalous and spin Hall effects, emergent axion electrodynamics and topological magnetoelectric effects, Weyl nodes and surface Fermi arcs, weak antilocalization, induced triplet superconductivity, Majorana fermion modes, and the fractional Josephson effect.

The book describes state-of-the-art advances in simulators and emulators for quantum computing. It introduces the main concepts of quantum computing, defining q-bits, explaining the parallelism behind any quantum computation, describing measurement of the quantum state of information and explaining the process of quantum bit entanglement, collapsed state and cloning. The book reviews the concept of quantum unitary, binary and ternary quantum operators as well as the computation implied by each operator. It provides details of the quantum processor, providing its architecture, which is validated via execution simulation of some quantum instructions.

Semiconductor quantum dots represent one of the fields of solid state physics that have experienced the greatest progress in the last decade. Recent years have witnessed the discovery of many striking new aspects of the optical response and electronic transport phenomena. This book surveys this progress in the physics, optical spectroscopy and application-oriented research of semiconductor quantum dots. It focuses especially on excitons, multi-excitons, their dynamical relaxation behaviour and their interactions with the surroundings of a semiconductor quantum dot. Recent developments in fabrication techniques are reviewed and potential applications discussed. This book will serve not only as an introductory textbook for graduate students but also as a concise guide for active researchers.

This book introduces readers to scattering from a practical/numerical point of view. The focus is on basic aspects like single scattering, multiple scattering, and whether inhomogeneous boundary conditions or inhomogeneous scatterers have to be taken into account. The powerful T-matrix approach is explained in detail and used throughout the book, and iterative solution methods are discussed. In addition, the book addresses appropriate criteria for estimating the accuracy of numerical results, as well as their importance for practical applications. Python code is provided with each chapter, and can be freely used and modified by readers. Moreover, numerous scattering results for different configurations are provided for benchmarking purposes. The book will be particularly valuable for those readers who plan to develop their own scattering code, and wish to test the correct numerical implementation of the underlying mathematics.

The relaxation of isolated quantum many-body systems is a major unsolved problem of modern physics, which is connected to many fundamental questions. However, realizations of quantum many-body systems which are both well isolated from their environment and accessible to experimental study are scarce. In recent years, the field has experienced rapid progress, partly attributed to ultra-cold atoms. This book presents the experimental study of a relaxation phenomenon occurring in a one-dimensional bosonic Josephson junction. The system consists of two 1D quasi Bose-Einstein condensates of 87Rb, magnetically trapped on an atom chip. Using radio-frequency dressing, the author deforms a single harmonic trap, in which the atoms are initially condensed, into a double-well potential and realizes a splitting of the wave function. A large spatial separation and a tilt of the double-well enable the preparation of a broad variety of initial states by precisely adjusting the initial population and relative phase of the two wave packets, while preserving the phase coherence. By re-coupling the two wave packets, the author investigates tunneling regimes such as Josephson (plasma) oscillations and macroscopic quantum self-trapping. In both regimes, the tunneling dynamics exhibits a relaxation to a phase-locked equilibrium state contradicting theoretical predictions. The experimental results are supported with an empirical model that allows quantitative discussions according to various experimental parameters. These results illustrate how strongly the non-equilibrium dynamics differ from the equilibrium one, which is well described by thermodynamics and statistical physics.

The concepts of the Electron Statistics (ES) and the ES dependent electronic properties are basic pillars in semiconductor electronics and this first-of-its-kind book deals with the said concepts in doping superlattices (SLs), quantum well, quantum wire and quantum dot SLs, effective mass SLs, SLs with graded interfaces and Fibonacci SLs under different physical conditions respectively. The influences of intense radiation and strong electric fields under said concepts have been considered together with the heavily doped SLs in this context on the basis of newly formulated the electron energy spectra in all the cases. We have suggested experimental determinations of the Einstein relation for the Diffusivity-Mobility ratio, the Debye screening length, Elastic Constants and the content of this book finds 25 different applications in the arena of nanoscience and nanotechnology.This book contains hundred open research problems which form the integral part of the text and are useful for both PhD aspirants and researchers. It is written for post graduate students of various departments of different academic organizations, engineers and professionals in the fields of solid state electronics, materials science, solid state sciences, nano-science, nanotechnology and nano materials in general.

In the mid-1980's, Abhay Ashtekar discovered a reformulation of general relativity in terms of what are now called the "new variables". This led to a rapid series of developments, and in 1990 Carlo Rovelli and Lee Smolin published a paper entitled "Loop representation of quantum general relativity", in which, among other things, it was shown that there is a space of solutions to the constraint equations of quantum gravity consisting of link invariants. The discovery of relations between quantum gravity and the theory of knots and links came as quite a surprise, since the topics had been regarded as quite remote from each other. This volume is the proceedings of a workshop held in 1993 at the University of California at Riverside. The purpose of the workshop was to bring together researchers in knot theory and quantum gravity and form more bridges between the two subjects. Most of the talks were given by researchers whose work has significance for both subjects. This volume contains expository papers as well as new results, and should serve as a guide for mathematicians and physicists seeking to understand this rapidly developing area of research.

This book presents a comprehensive mathematical study of the operators behind the Born-Jordan quantization scheme. The Schroedinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born-Jordan scheme is used. Thus, Born-Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born-Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.

This new edition of a well-received textbook provides a concise introduction to both the theoretical and experimental aspects of quantum information at the graduate level. While the previous edition focused on theory, the book now incorporates discussions of experimental platforms. Several chapters on experimental implementations of quantum information protocols have been added: implementations using neutral atoms, trapped ions, optics, and solidstate systems are each presented in its own chapter. Previous chapters on entanglement, quantum measurements, quantum dynamics, quantum cryptography, and quantum algorithms have been thoroughly updated, and new additions include chapters on the stabilizer formalism and the Gottesman-Knill theorem as well as aspects of classical and quantum information theory. To facilitate learning, each chapter starts with a clear motivation to the topic and closes with exercises and a recommended reading list. Quantum Information Processing: Theory and Implementation will be essential to graduate students studying quantum information as well as and researchers in other areas of physics who wish to gain knowledge in the field.

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.

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.