Most textbooks explain quantum mechanics as a story where each step follows naturally from the one preceding it. However, the development of quantum mechanics was exactly the opposite. It was a zigzag route, full of personal disputes where scientists were forced to abandon well-established classical concepts and to explore new and imaginative pathways. Some of the explored routes were successful in providing new mathematical formalisms capable of predicting experiments at the atomic scale. However, even such successful routes were painful enough, so that relevant scientists like Albert Einstein and Erwin Schroedinger decided not to support them. In this book, the authors demonstrate the huge practical utility of another of these routes in explaining quantum phenomena in many different research fields. Bohmian mechanics, the formulation of the quantum theory pioneered by Louis de Broglie and David Bohm, offers an alternative mathematical formulation of quantum phenomena in terms of quantum trajectories. Novel computational tools to explore physical scenarios that are currently computationally inaccessible, such as many-particle solutions of the Schroedinger equation, can be developed from it.

This is a collection of essays based on lectures that author has given on various occasions on foundation of quantum theory, symmetries and representation theory, and the quantum theory of the superworld created by physicists. The lectures are linked by a unifying theme: how the quantum world and superworld appear under the lens of symmetry and supersymmetry.

In the world of ultra-small times and distances such as the Planck length and Planck time, physicists believe no measurements are possible and so the structure of spacetime itself is an unkown that has to be first understood. There have been suggestions (Volovich hypothesis) that world geometry at such energy regimes is non-archimedian and some of the lectures explore the consequences of such a hypothesis.

Ultimately, symmetries and supersymmetries are described by the representation of groups and supergroups. The author's interest in representation is a lifelong one and evolved slowly, and owes a great deal to conversations and discussions he had with George Mackey and Harish-Chandra. The book concludes with a retrospective look at these conversations.

In this book, the problem of electron and hole transport is approached from the point of view that a coherent and consistent physical theory can be constructed for transport phenomena. Along the road readers will visit some exciting citadels in theoretical physics as the authors guide them through the strong and weak aspects of the various theoretical constructions. Our goal is to make clear the mutual coherence and to put each theoretical model in an appropriate perspective. The mere fact that so many partial solutions have been proposed to describe transport, be it in condensed matter, fluids, or gases, illustrates that we are entering a world of physics with a rich variety of phenomena. Theoretical physics always seeks to provide a unifying picture. By presenting this tour of many very inventive attempts to build such a picture, it is hoped that the reader will be inspired and encouraged to help find the unifying principle behind the many faces of transport.

How much knowledge can we gain about a physical system and to what degree can we control it? In quantum optical systems, such as ion traps or neutral atoms in cavities, single particles and their correlations can now be probed in a way that is fundamentally limited only by the laws of quantum mechanics. In contrast, quantum many-body systems pose entirely new challenges due to the enormous number of microscopic parameters and their small length- and short time-scales.
This thesis describes a new approach to probing quantum many-body systems at the level of individual particles: Using high-resolution, single-particle-resolved imaging and manipulation of strongly correlated atoms, single atoms can be detected and manipulated due to the large length and time-scales and the precise control of internal degrees of freedom. Such techniques lay stepping stones for the experimental exploration of new quantum many-body phenomena and applications thereof, such as quantum simulation and quantum information, through the design of systems at the microscopic scale and the measurement of previously inaccessible observables.

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics-one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

Quantum field theory, which started with Paul Diraca (TM)s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity.

Quantum Field Theory: A Modern Perspective presents Professor Naira (TM)s view of certain topics in field theory loosely knit together as it grew out of courses on field theory and particle physics taught at Columbia University and the City College of CUNY. The first few chapters, up to Chapter 12, contain material that generally goes into any course on quantum field theory, although there are a few nuances of presentation which readers may find to be different from other books. This first part of the book can be used for a general course on field theory, omitting, perhaps, the last three sections in Chapter 3, the last two in Chapter 8 and sections 6 and 7 in Chapter 10. The remaining chapters cover some of the more modern developments over the last three decades, involving topological and geometricalfeatures. The introduction given to the mathematical basis of this part of the discussion is necessarily brief and should be accompanied by books on the relevant mathematical topics as indicated in the bibliography. Professor Nair also concentrates on developments pertinent to a better understanding of the standard model. There is no discussion of supersymmetry, supergravity, developments in field theory inspired by string theory, etc. There is also no detailed discussion of the renormalization group. Each of these topics would require a book in its own right to do justice to the topic. Quantum Field Theory: A Modern Perspective serves as a portal to so many more topics of detailed and ongoing research, referring readers to more detailed treatments for many specific topics. The book also contains extensive references, providing readers a more comprehensive perspective on the literature and the historical development of the subject.

V. Parameswaran Nair is Professor of Physics at City College of The City University of New York (CUNY). Professor Nair has held Visiting Professorships at The Abdus Salam International Center for Theoretical Physics, Rockefeller University, Institute for Advanced Study at Princeton, and Massachusetts Institute of Technology.

This thesis reports on major steps towards the realization of scalable quantum networks. It addresses the experimental implementation of a deterministic interaction mechanism between flying optical photons and a single trapped atom. In particular, it demonstrates the nondestructive detection of an optical photon. To this end, single rubidium atoms are trapped in a three-dimensional optical lattice at the center of an optical cavity in the strong coupling regime. Full control over the atomic state - its position, its motion, and its electronic state - is achieved with laser beams applied along the resonator and from the side. When faint laser pulses are reflected from the resonator, the combined atom-photon state acquires a state-dependent phase shift. In a first series of experiments, this is employed to nondestructively detect optical photons by measuring the atomic state after the reflection process. Then, quantum bits are encoded in the polarization of the laser pulse and in the Zeeman state of the atom. The state-dependent phase shift mediates a deterministic universal quantum gate between the atom and one or two successively reflected photons, which is used to generate entangled atom-photon, atom-photon-photon, and photon-photon states out of separable input states.

This thesis reports a major breakthrough in discovering the superconducting mechanism in CeCoIn5, the "hydrogen atom" among heavy fermion compounds. By developing a novel theoretical formalism, the study described herein succeeded in extracting the crucial missing element of superconducting pairing interaction from scanning tunneling spectroscopy experiments. This breakthrough provides a theoretical explanation for a series of puzzling experimental observations, demonstrating that strong magnetic interactions provide the quantum glue for unconventional superconductivity. Additional insight into the complex properties of strongly correlated and topological materials was provided by investigating their non-equilibrium charge and spin transport properties. The findings demonstrate that the interplay of magnetism and disorder with strong correlations or topology leads to complex and novel behavior that can be exploited to create the next generation of spin electronics and quantum computing devices.

This thesis elucidates electron correlation effects in topological matter whose electronic states hold nontrivial topological properties robust against small perturbations. In addition to a comprehensive introduction to topological matter, this thesis provides a new perspective on correlated topological matter. The book comprises three subjects, in which electron correlations in different forms are considered. The first focuses on Coulomb interactions for massless Dirac fermions. Using a perturbative approach, the author reveals emergent Lorentz invariance in a low-energy limit and discusses how to probe the Lorentz invariance experimentally. The second subject aims to show a principle for synthesizing topological insulators with common, light elements. The interplay between the spin-orbit interaction and electron correlation is considered, and Hund's rule and electron filling are consequently found to play a key role for a strong spin-orbit interaction important for topological insulators. The last subject is classification of topological crystalline insulators in the presence of electron correlation. Unlike non-interacting topological insulators, such two- and three-dimensional correlated insulators with mirror symmetry are demonstrated to be characterized, respectively, by the Z4 and Z8 group by using the bosonization technique and a geometrical consideration.

Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many areas of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which is equally applied to all these areas is given by quantum field theory. This book provides an overview of the basic ideas and concepts of the method of nonequilibrium Green's functions, written by the leading experts and presented in a way accessible to non-specialists and graduate students. It is complemented by invited review papers on modern applications of the method to a variety of topics, such as optics and quantum transport in semiconductors; superconductivity; strong field effects, QCD, and state-of-the-art computational concepts - from Green's functions to quantum Monte Carlo and time-dependent density functional theory.The proceedings have been selected for coverage in:* Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)

Optical solitons in fibers are a beautiful example of how an abstract mathematical concept has had an impact on new information transmission technologies. The concept of all-optical data transmission with optical soliton systems is now setting the standard for the most advanced transmission systems. The book deals with the motion of light waves in optical fibers, the evolution of light wavepackets, optical information transfer, all-optical soliton transmission systems, the control of optical solitons, polarization effects, dispersion-managed solitons, WDM transmission, soliton lasers, all-optical switching and other applications. This book is a must for all researchers and graduate students active in the field of optical data transmission.

The revised edition of this established work presents an extended overview of recent applications of symmetry to the description of atomic nuclei, including a pedagogical introduction to symmetry concepts using simple examples. Following a historical overview of the applications of symmetry in nuclear physics, attention turns to more recent progress in the field. Special emphasis is placed on the introduction of neutron-proton and boson-fermion degrees of freedom. Their combination leads to a supersymmetric description of pairs and quartets of nuclei. Expanded and updated throughout, the book now features separate chapters on the nuclear shell model and the interacting boson model, the former including discussion of recent results on seniority in a single-j shell. Both theoretical aspects and experimental signatures of dynamical (super)symmetries are carefully discussed. This book focuses on nuclear structure physics, but its broad scope makes it suitable for final-year or post-graduate students and researchers interested in understanding the power and beauty of symmetry methods in physics. Review of the 1st Edition: "The subject of this book, symmetries in physical systems, with particular focus on atomic nuclei, is of the utmost importance in modern physical science. In contrast to most treatments, frequently characterized by fearsome formalism, this book leads the reader step-by-step, in an easily understandable way, through this fascinating field...this book is remarkably accessible to both theorists and experimentalists. Indeed, I view it as essential reading for experimental nuclear structure physicists. This is one of the finest volumes on this subject I have ever encountered." Prof. R.F. Casten, Yale University

This thesis reports the measurement of muon neutrino and antineutrino disappearance and electron neutrino and antineutrino appearance in a muon neutrino and antineutrino beam using the T2K experiment. It describes a result in neutrino physics that is a pioneering indication of charge-parity (CP) violation in neutrino oscillation; the first to be obtained from a single experiment. Neutrinos are some of the most abundant-but elusive-particles in the universe, and may provide a promising place to look for a potential solution to the puzzle of matter/antimatter imbalance in the observable universe. It has been firmly established that neutrinos can change flavour (or 'oscillate'), as recognised by the 2015 Nobel Prize. The theory of neutrino oscillation allows for neutrinos and antineutrinos to oscillate differently (CP violation), and may provide insights into why our universe is matter-dominated. Bayesian statistical methods, including the Markov Chain Monte Carlo fitting technique, are used to simultaneously optimise several hundred systematic parameters describing detector, beam, and neutrino interaction uncertainties as well as the six oscillation parameters.

The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.Besides its obvious practical use, this theory is attractive also because it satisfies the aesthetic need in a beautiful formula which is so inherent to mathematics.The second edition is up-to-date and differs from the first one considerably. One third of the book (five chapters) is completely new and the rest is refreshed and edited.

Simulation of materials at the atomistic level is an important tool in studying microscopic structures and processes. The atomic interactions necessary for the simulations are correctly described by Quantum Mechanics, but the size of systems and the length of processes that can be modelled are still limited. The framework of Gaussian Approximation Potentials that is developed in this thesis allows us to generate interatomic potentials automatically, based on quantum mechanical data. The resulting potentials offer several orders of magnitude faster computations, while maintaining quantum mechanical accuracy. The method has already been successfully applied for semiconductors and metals.

This book describes the phenomena that arise from the interaction between quantum systems and their environment. Since the first edition appeared in 1996, the concepts of decoherence have become firmly established experimentally and are now widely used in the literature. The major consequences of decoherence are the emergence of "classicality", superselection rules, the border line between microscopic and macroscopic behavior, the emergence of classical spacetime, and the appearance of quantum jumps. Most of the new developments in this rapidly evolving field are discussed in this second edition: chaos theory, quantum information, neuroscience, primordial fluctuations in cosmology, black holes and string theory, experimental tests, and interpretational issues. While the major part of the book is concerned with environmental decoherence derived from a universal Schrödinger equation, later chapters address complementary or competing approaches, such as consistent histories, open system dynamics, algebraic methods, and collapse models.

This invaluable book consists of problems in nonrelativistic quantum mechanics together with their solutions. Most of the problems have been tested in class. The degree of difficulty varies from very simple to research-level. The problems illustrate certain aspects of quantum mechanics and enable the students to learn new concepts, as well as providing practice in problem solving.The book may be used as an adjunct to any of the numerous books on quantum mechanics and should provide students with a means of testing themselves on problems of varying degrees of difficulty. It will be useful to students in an introductory course if they attempt the simpler problems. The more difficult problems should prove challenging to graduate students and may enable them to enjoy problems at the forefront of quantum mechanics.

A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

The main unique feature of Nonrelativistic Quantum Mechanics is its discussion of Hilbert space and rigged Hilbert space. This invaluable book is suitable for advanced undergraduate students as well as graduate students.

Based on eight extensive lectures selected from those given at the renowned Chris Engelbrecht Summer School in Theoretical Physics in South Africa, this text on the theoretical foundations of quantum information processing and communication covers an array of topics, including quantum probabilities, open systems, and non-Markovian dynamics and decoherence. It also addresses quantum information and relativity as well as testing quantum mechanics in high energy physics. Because these self-contained lectures discuss topics not typically covered in advanced undergraduate courses, they are ideal for post-graduate students entering this field of research. Some of the lectures are written at a more introductory level while others are presented as tutorials that survey recent developments and results in various subfields.

The subject of this book is the new field of squeezing in quantum fields. This general area includes all types of systems in which quantum fluctuations are reduced below those in the normal vacuum state. The book covers the main currently known techniques of generating squeezed photon fields, together with some treatment of matter field squeezing. Both theory and experiments are covered, together with applications to communications and measurement. The chapters of the book are written by the foremost international experts in the field, and their coverage extends from general introductory material, to the most recent developments.