Statistical Methods in Quantum Optics 2 - Non-Classical Fields continues the development of the methods used in quantum optics to treat open quantum systems and their fluctuations. Its early chapters build upon the phase-space methods introduced in the first volume Statistical Methods in Quantum Optics 1 - Matter Equations and Fokker-Planck Equations the difficulties these methods face in treating non-classical light are exposed, where the regime of large fluctuations failure of the system size expansion is shown to be particularly problematic. Cavity QED is adopted as a natural vehicle for extending quantum noise theory into this regime. In response to the issues raised, the theory of quantum trajectories is presented as a universal approach to the treatment of fluctuations in open quantum systems.

This book presents its material at a level suitable for beginning researchers or students in an advanced course in quantum optics, or a course in quantum mechanics or statistical physics that deals with open quantum systems. The text is complemented by exercises and interspersed notes that point the reader to side issues or a deeper exploration of the material presented."

This thesis breaks new ground in the physics of photonic circuits for quantum optical applications. The photonic circuits are based either on ridge waveguides or photonic crystals, with embedded quantum dots providing the single qubit, quantum optical emitters. The highlight of the thesis is the first demonstration of a spin-photon interface using an all-waveguide geometry, a vital component of a quantum optical circuit, based on deterministic single photon emission from a single quantum dot. The work makes a further important contribution to the field by demonstrating the effects and limitations that inevitable disorder places on photon propagation in photonic crystal waveguides, a further key component of quantum optical circuits. Overall the thesis offers a number of highly novel contributions to the field; those on chip circuits may prove to be the only means of scaling up the highly promising quantum-dot-based quantum information technology.

Rob Clifton was one of the most brilliant and productive researchers in the foundations and philosophy of quantum theory, who died tragically at the age of 38. Jeremy Butterfield and Hans Halvorson collect fourteen of his finest papers here, drawn from the latter part of his career (1995-2002), all of which combine exciting philosophical discussion with rigorous mathematical results.
Many of these papers break wholly new ground, either conceptually or technically. Others resolve a vague controversy intoa precise technical problem, which is then solved; still others solve an open problem that had been in the air for soem time. All of them show scientific and philosophical creativity of a high order, genuinely among the very best work in the field.
The papers are grouped into four Parts. First come four papers about the modal interpretation of quantum mechanics. Part II comprises three papers on the foundations of algebraic quantum field theory, with an emphasis on entanglement and nonlocality. The two papers in Part III concern the concept of a particle in relativistic quantum theories. One paper analyses localization; the other analyses the Unruh effect (Rindler quanta) using the algebraic approach to quantum theory. Finally, Part IV contains striking new results about such central issues as complementarity, Bohr's reply to the EPR argument, and no hidden variables theorems; and ends with a philosophical survey of the field of quantum information. The volume includes a full bibliography of Clifton's publications.
Quantum Entanglements offers inspiration and substantial reward to graduates and professionals in the foundations of physics, with a background in philosophy, physics, or mathematics.

This book demonstrates that fundamental concepts and methods from phenomenological particle physics can be derived rigorously from well-defined general assumptions in a mathematically clean way. Starting with the Wightman formulation of relativistic quantum field theory, the perturbative formulation of quantum electrodynamics is derived avoiding the usual formalism based on the canonical commutation relations. A scattering formalism based on the local-observables approach is developed, directly yielding expressions for the observable inclusive cross-sections without having to introduce the S-matrix. Neither ultraviolet nor infrared regularizations are required in this approach. Although primarily intended for researchers working in this field, anyone with a basic working knowledge of relativistic quantum field theory can benefit from this book.

This book is based on the analysis of canonical commutation relations (CCRs) and their possible deformations. In light of the recent interest on PT-quantum mechanics, the author presents a special deformed version of the CCRs, and discusses the consequences of this deformation both from a mathematical side, and for its possible applications to physics. These include the analysis of several non self-adjoint Hamiltonians, a novel view to the position and momentum operators, and a general approach to compute path integrals and transition probabilities using the so-called bi-coherent states. The book is meant for researchers and is also suited for advanced students. It can be used as a gentle introduction to some delicate aspects in functional analysis and in quantum mechanics for non self-adjoint observables.

This book provides a comprehensive overview of the field of Higgs boson physics. It offers the first in-depth review of the complete results in connection with the discovery of the Higgs boson at CERN's Large Hadron Collider and based on the full dataset for the years 2011 to 2012. The fundamental concepts and principles of Higgs physics are introduced and the important searches prior to the advent of the Large Hadron Collider are briefly summarized. Lastly, the discovery and first mensuration of the observed particle in the course of the CMS experiment are discussed in detail and compared to the results obtained in the ATLAS experiment.

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this second volume, the authors show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies. Along with a systematic reworking of the Batalin-Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory.

The rapid increase in capabilities at neutron and x-ray scattering sources has resulted in a wealth of highly accurate data on liquids, allowing for the testing of sophisticated models pertinent to the microscopic dynamics. This book, written with the experimentalist in the field of liquids in mind, is a practical guide on how to infer the maximum amount of information from the data using a minimum number of parameters, employing a fail-safe framework that ensures that pitfalls are avoided and that small differences between various liquids can be uncovered. Also, it details excitations for a range of liquids, covering simple fluids, colloids, mixtures, metals and superfluids. Results are interpreted in words rather than in equations, bringing to the fore new links between these fluids and between spontaneous fluctuations involving thousands of atoms down to those involving just a few. By providing a review of scattering results in the field of liquids, and placing various liquids in context, the book gives an overview for the graduate student and the postdoc entering the field, and a refresher course, based on modern results, for established experimentalists. Moreover, in re-establishing the connection between the large-scale properties of liquids, and their underlying collision sequences, the book directly ties experimental results to the most important open questions in the field. It is hoped that the book will inspire theorists to take up the challenges it poses.

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Optically Polarized Atoms is addressed at upper-level undergraduate and graduate students involved in research in atomic, molecular, and optical Physics. It will also be useful to researchers practicing in this field. It gives an intuitive, yet sufficiently detailed and rigorous introduction to light-atom interactions with a particular emphasis on the symmetry aspects of the interaction, especially those associated with the angular momentum of atoms and light. The book will enable readers to carry out practical calculations on their own, and is richly illustrated with examples drawn from current research topics, such as resonant nonlinear magneto-optical effects. The book comes with a software package for a variety of atomic-physics calculations and further interactive examples that is freely downloadable from the book's web page, as well as additional materials (such as power-point presentations) available to instructors who adopt the text for their courses.

The purpose of this book is to initiate a new discipline, namely a formalized epistemological method drawn from the cognitive strategies practised in the most effective among the modern scientific disciplines, as well as from general philosophical thinking. Indeed, what is lacking in order to improve our knowledge and our domination of the modes which nowadays are available for the generation and communication of knowledge, thoroughly and rapidly and with precision and detail? It is a systematic explication of the epistemological essence encrypted in the specialized languages and algorithms of the major modern scientific approaches, a systematic cross-referencing of the explicated results, and a final elaboration of a new coherent whole.

Quantum mechanics, like a diver, can take us down to the level of the very first actions of our conceptualization of reality. And starting from there, it can induce an explicit understanding of certain fundamental features of the new scientific thinking.

A formalized epistemology should not be mistaken for a crossdisciplinary or a multidisciplinary project. The latter projects are designed to offer to nonspecialists access to information, to results obtained inside specialized disciplines, as well as a certain understanding of these results; whereas a formalized epistemology should equip anyone with a framework for conceptualizing himself in whatever domain and direction he or she might choose. A formalized epistemology should not be mistaken either for an approach belonging to the modern cognitive sciences. These try to establish as neutrally as possible descriptions of how the human body-and-mind work spontaneously when knowledge isgenerated; whereas a method of conceptualization should establish what conceptual-operational deliberate procedures have to be applied in order to represent and to achieve processes of generation of knowledge optimized accordingly to any definite aims.

This book addresses philosophers of science, physicists, mathematicians, logicians, computer scientists, researchers in cognitive sciences, and biologists, as well as any intellectual who is interested in scientific and philosophical thinking.

This thesis makes significant advances towards an understanding of superconductivity in the cuprate family of unconventional, high-temperature superconductors. Even though the high-temperature superconductors were discovered over 35 years ago, there is not yet a general consensus on an acceptable theory of superconductivity in these materials. One of the early proposals suggested that collective magnetic excitations of the conduction electrons could lead them to form pairs, which in turn condense to form the superconducting state at a critical temperature Tc. Quantitative calculations of Tc using experimental data were, however, not available to verify the applicability of this magnetic mechanism. In this thesis, the author constructed an angle-resolved photoemission apparatus that could provide sufficiently accurate data of the electronic excitation spectra of samples in the normal state, data which was furthermore unusually devoid of any surface contamination. The author also applied the Bethe-Salpeter method to his uncommonly pristine and precise normal state data, and was able to predict the approximate superconducting transition temperatures of different samples. This rare combination of experiment with sophisticated theoretical calculations leads to the conclusion that antiferromagnetic correlations are a viable candidate for the pairing interaction in the cuprate superconductors.

Modern nuclear physics is a well developed branch of physical science, with wide-ranging applications of its results in engineering and industry. At the same time, the development of a consistent theory of nuclei and nuclear processes presents certain problems. It is well known that the most important aim of nuclear physics is the study of nuclear structure and the explanation of properties on the basis of the interaction between nucleons which constitute nuclei. Difficulties of a modern theory of the nucleus are caused by both an insufficient knowledge of nuclear interactions and the multi particle character of nuclear systems. Experimental data on nuclear interactions do not contradict the hypothesis of the pair character of nuclear forces. However, the absence of rigorous meth ods of calculations of many particle nuclear systems with strong interaction makes it necessary to use macroscopic nuclear models to describe particular nuclear properties. Nuclear models have been developed in different ways, and the models themselves have been modified and complicated. In spite of the visible discrepancy, different models of the nucleus significantly supple ment one another. The development of nuclear models has led to considerable progress in the understanding of atomic nuclei. The current results of theo retical nuclear physics are reported in numerous scientific papers. The most important and relevant experimental and theoretical results can be found in many monographs, the best of which are written by well-known experts in the field."

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 reviewed.

Modern techniques from quantum field theory are applied in this work to the description of ultracold quantum gases. This leads to a unified description of many phenomena including superfluidity for bosons and fermions, classical and quantum phase transitions, different dimensions, thermodynamic properties and few-body phenomena as bound state formation or the Efimov effect. The non-perturbative treatment with renormalization group flow equations can account for all known limiting cases by solving one single equation. It improves previous results quantitatively and brings qualitatively new insights. As an example, new quantum phase transitions are found for fermions with three spin states. Ultracold atomic gases can be seen as an interesting model for features of high energy physics and for condensed matter theory. The research reported in this thesis helps to solve the difficult complexity problem in modern theoretical physics.

This book investigates Lorentzian structures in the four-dimensional space-time, supplemented either by a covector field of the time-direction or by a scalar field of the global time. Furthermore, it proposes a new metrizable model of gravity. In contrast to the usual General Relativity theory, where all ten components of the symmetric pseudo-metric are independent variables, the gravity model presented here essentially depends only on a single four-covector field, and is restricted to have only three-independent components. However, the author proves that the gravitational field, governed by the proposed model and generated by some massive body, resting and spherically symmetric in some coordinate system, is given by a pseudo-metric that coincides with the well known Schwarzschild metric from General Relativity. The Maxwell equations and electrodynamics are also investigated in the framework of the proposed model. In particular, the covariant formulation of electrodynamics of moving dielectrics and para/diamagnetic media is derived.

This book addresses novel electronic and thermoelectronic properties arising from topological spin textures as well as topologically non-trivial electronic structures. In particular, it focuses on a unique topological spin texture, i.e., spin hedgehog lattice, emerging in a chiral magnet and explore its novel properties which are distinct from the conventional skyrmion lattice, and discusses the possibility of realizing high-temperature quantum anomalous Hall effect through quantum confinement effect in topological semimetal. This book benefits students and researchers working in the field of condensed matter physics, through providing comprehensive understanding of the current status and the outlook in the field of topological magnets.

Atomic Physics provides a concise treatment of atomic physics and a basis to prepare for work in other disciplines that are underpinned by atomic physics such as chemistry, biology and several aspects of engineering science. The focus is mainly on atomic structure since this is what is primarily responsible for the physical properties of atoms. After a brief introduction to some basic concepts, the perturbation theory approach follows the hierarchy of interactions starting with the largest. The other interactions of spin, and angular momentum of the outermost electrons with each other, the nucleus and external magnetic fields are treated in order of descending strength. A spectroscopic perspective is generally taken by relating the observations of atomic radiation emitted or absorbed to the internal energy levels involved. X-ray spectra are then discussed in relation to the energy levels of the innermost electrons. Finally, a brief description is given of some modern, laser based, spectroscopic methods for the high resolution study of the nest details of atomic structure.

This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schroedinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.

The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory.

Intended for beginning graduate students, this text takes the reader from the familiar coordinate representation of quantum mechanics to the modern algebraic approach, emphasizing symmetry principles throughout. After an introduction to the basic postulates and techniques, the book discusses time-independent perturbation theory, angular momentum, identical particles, scatteering theory, and time-dependent perturbation theory. The whole is rounded off with several lectures on relativistic quantum mechanics and on many-body theory.

This thesis describes the first demonstration of a cooperative optical non-linearity based on Rydberg excitation. Whereas in conventional non-linear optics the non-linearity arises directly from the interaction between light and matter, in a cooperative process it is mediated by dipole-dipole interactions between light-induced excitations. For excitation to high Rydberg states where the electron is only weakly bound, the dipole-dipole interactions are extremely large and long range, enabling an enormous enhancement of the non-linear effect. Consequently, cooperative non-linear optics using Rydberg excitations opens a new era for quantum optics enabling large single photon non-linearity to be accessible in free space for the first time. The thesis describes the theoretical underpinnings of the non- linear effect, the pioneering experimental results and implications for experiments in the single photon regime.

This book discusses particle physics and relativistic local field theory that is the main theoretical tool for analyzing particle physics. It is helpful for the professional physicist and to the serious graduate student of physics.