Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in quantum Monte Carlo techniques.

This book summarizes the results of research the authors have pursued in the past years on the problem of implementing Bell's notion of local causality in local physical theories and relating it to other important concepts and principles in the foundations of physics such as the Common Cause Principle, Bell's inequalities, the EPR (Einstein-Podolsky-Rosen) scenario, and various other locality and causality concepts. The book is intended for philosophers of science with an interest in the formal background of sciences, philosophers of physics and physicists working in foundation of physics.

This book presents the basic elements of theoretical physics in a highly accessible, captivating way for university students in the third year of a degree in physics. It covers analytical mechanics, thermodynamics and statistical physics, special and general relativity and non-relativistic quantum theory, fully developing the necessary mathematical methods beyond standard calculus. The central theme is scientific curiosity and the main focus is on the experimental meaning of all quantities and equations. Several recent verifications of General Relativity are presented, with emphasis on the physical effects - why they were predicted to exist and what signals they were seen to produce. Similarly, the basic reasons why superconductors have zero resistance and are perfect diamagnets are pinpointed. Quantum Eraser Experiments and Delayed Choice Experiments are described. Many statements of Quantum Theory are a challenge to common sense and some crucial predictions have often been considered hard to believe and have been tested experimentally. The book examines the EPR paradox, Bell states and teleportation. To show the beauty and richness of the subject, various topics from different areas of Physics are covered. These include: discrete quantum models and lattices (periodic and not), Casimir effect, Anyons, Fano Resonances, the Hanbury Brown and Twiss effect, the Aharonov-Bohm effect, the Meitner-Auger effect, Squeezed Light, the Rabi model, neutrino oscillations, aspects of Quantum Transport, Quantum Pumping, and Berry phases, black holes and cosmological problems.

The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kahler and Sasaki geometry.

The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical electrodynamics to current approaches to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics research, are presented and defended in an accessible format that avoids complex mathematics. Blending history, philosophy, and theoretical physics, this refreshing outlook on the nature of spacetime sheds light on one of the most thought-provoking topics in modern physics.

This thesis presents two production cross-section measurements of pairs of massive bosons using final states with leptons, made with the ATLAS detector at the Large Hadron Collider. The first measurement, performed using data collected in 2012 at center-of-mass energy s = 8 TeV, is the first fiducial and differential cross-section measurement of the production of the Higgs Boson when it decays to four charged leptons (electrons or muons). The second measurement is the first fiducial and inclusive production cross-section measurement of WZ pairs at center-of-mass energy s = 13 TeV using final states with three charged leptons. A significant portion of the thesis focuses on the methods used to identify electrons from massive boson decay-important for many flagship measurements-and on assessing the efficiency of these particle identification techniques. The chapter discussing the WZ pair cross-section measurement provides a detailed example of an estimate of lepton background in the context of an analysis with three leptons in the final state.

This advanced course, a sequel to the first volume of this lecture series on topos quantum theory, delves deeper into the theory, addressing further technical aspects and recent advances. These include, but are not limited to, the development of physical quantities and self-adjoint operators; insights into the quantization process; the description of an alternative, covariant version of topos quantum theory; and last but not least, the development of a new concept of spacetime. The book builds on the concepts introduced in the first volume (published as Lect. Notes Phys. 868), which presents the main building blocks of the theory and how it could provide solutions to interpretational problems in quantum theory, such as: What are the main conceptual issues in quantum theory? And how can these issues be solved within a new theoretical framework of quantum theory? These two volumes together provide a complete, basic course on topos quantum theory, offering a set of mathematical tools to readers interested in tackling fundamental issues in quantum theory in general, and in quantum gravity in particular. From the reviews of the first volume: The book is self-contained and can be used as a textbook or self-study manual teaching the usage of category theory and topos theory, in particular in theoretical physics or in investigating the foundations of quantum theory in mathematically rigorous terms. [The] book is a very welcome contribution. Frank Antonsen, Mathematical Reviews, December, 2013

Reproducing kernel Hilbert spaces have developed into an important tool in many areas, especially statistics and machine learning, and they play a valuable role in complex analysis, probability, group representation theory, and the theory of integral operators. This unique text offers a unified overview of the topic, providing detailed examples of applications, as well as covering the fundamental underlying theory, including chapters on interpolation and approximation, Cholesky and Schur operations on kernels, and vector-valued spaces. Self-contained and accessibly written, with exercises at the end of each chapter, this unrivalled treatment of the topic serves as an ideal introduction for graduate students across mathematics, computer science, and engineering, as well as a useful reference for researchers working in functional analysis or its applications.

This book presents a basic introduction to quantum mechanics. Depending on the choice of topics, it can be used for a one-semester or two-semester course. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. Wherever possible, examples are given to illustrate the underlying physics associated with the mathematical equations of quantum mechanics. To this end, connections are made with corresponding phenomena in classical mechanics and electromagnetism. The problems at the end of each chapter are intended to help students master the course material and to explore more advanced topics. Many calculations exploit the extraordinary capabilities of computer programs such as Mathematica, MatLab, and Maple. Students are urged to use these programs, just as they had been urged to use calculators in the past. The treatment of various topics is rather complete, in that most steps in derivations are included. Several of the chapters go beyond what is traditionally covered in an introductory course. The goal of the presentation is to provide the students with a solid background in quantum mechanics.

This thesis presents and discusses recent optical low-temperature experiments on disordered NbN, granular Al thin-films, and the heavy-fermion compound CeCoIn5, offering a unified picture of quantum-critical superconductivity. It provides a concise introduction to the respective theoretical models employed to interpret the experimental results, and guides readers through in-depth calculations supplemented with supportive figures in order to both retrace the interpretations and span the bridge between experiment and state-of-the art theory.

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.

This book gives an intermediate level treatment of quantum field theory, appropriate to a reader with a first degree in physics and a working knowledge of special relativity and quantum mechanics. It aims to give the reader some understanding of what QFT is all about, without delving deep into actual calculations of Feynman diagrams or similar. The author serves up a seven-course menu, which begins with a brief introductory Aperitif. This is followed by the Hors d'oeuvres, which set the scene with a broad survey of the Universe, its theoretical description, and how the ideas of QFT developed during the last century. In the next course, the Art of Cooking, the author recaps on some basic facts of analytical mechanics, relativity, quantum mechanics and also presents some nutritious "extras" in mathematics (group theory at the elementary level) and in physics (theory of scattering). After these preparations, the reader should have a good appetite for the Entrees - the central par t of the book where the Standard Model is described and explained. After Trou Normand, the restive pause including human stories about physicists and no formulas, the author serves the Dessert, devoted to supersymmetry (a very beautiful theory that is still awaiting a direct experimental confirmation), to general relativity and to the mystery of quantum gravity.

The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix.

This proceedings records the 31st International Colloquium on Group Theoretical Methods in Physics ("Group 31"). Plenary-invited articles propose new approaches to the moduli spaces in gauge theories (V. Pestun, 2016 Weyl Prize Awardee), the phenomenology of neutrinos in non-commutative space-time, the use of Hardy spaces in quantum physics, contradictions in the use of statistical methods on complex systems, and alternative models of supersymmetry. This volume's survey articles broaden the colloquia's scope out into Majorana neutrino behavior, the dynamics of radiating charges, statistical pattern recognition of amino acids, and a variety of applications of gauge theory, among others. This year's proceedings further honors Bertram Kostant (2016 Wigner Medalist), as well as S.T. Ali and L. Boyle, for their life-long contributions to the math and physics communities. The aim of the ICGTMP is to provide a forum for physicists, mathematicians, and scientists of related disciplines who develop or apply methods in group theory to share their research. The 31st ICGTMP was held in Rio de Janeiro, Brazil, from June 19th to June 25th, 2016. This was the first time that a colloquium of the prestigious and traditional ICGTMP series (which started in 1972 in Marseille, France) took place in South America. (The history of the colloquia can be found at http://icgtmp.blogs.uva.es/)

This thesis presents an experimental study of quantum memory based on cold atomic ensembles and discusses photonic entanglement. It mainly focuses on experimental research on storing orbital angular momentum, and introduces readers to methods for storing a single photon carried by an image or an entanglement of spatial modes. The thesis also discusses the storage of photonic entanglement using the Raman scheme as a step toward implementing high-bandwidth quantum memory. The storage of photonic entanglement is central to achieving long-distance quantum communication based on quantum repeaters and scalable linear optical quantum computation. Addressing this key issue, the findings presented in the thesis are very promising with regard to future high-speed and high-capacity quantum communications.

This thesis presents results crucial to the emerging field of indirect excitons. These specially designed quasiparticles give the unique opportunity to study fundamental properties of quantum degenerate Bose gases in semiconductors. Furthermore, indirect excitons allow for the creation of novel optoelectronic devices where excitons are used in place of electrons. Excitonic devices are explored for the development of advanced signal processing seamlessly coupled with optical communication. The thesis presents and describes the author's imaging experiments that led to the discovery of spin transport of excitons. The many firsts presented herein include the first studies of an excitonic conveyer, leading to the discovery of the dynamical localization-delocalization transition for excitons, and the first excitonic ramp and excitonic diode with no energy-dissipating voltage gradient.

Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.

The aim of this book is the pedagogical exploration of the basic principles of quantum-statistical thermodynamics as applied to various states of matter - ranging from rare gases to astrophysical matter with high-energy density. The reader will learn in this work that thermodynamics and quantum statistics are still the concepts on which even the most advanced research is operating - despite of a flood of modern concepts, classical entities like temperature, pressure, energy and entropy are shown to remain fundamental. The physics of gases, plasmas and high-energy density matter is still a growing field and even though solids and liquids dominate our daily life, more than 99 percent of the visible Universe is in the state of gases and plasmas and the overwhelming part of matter exists at extreme conditions connected with very large energy densities, such as in the interior of stars. This text, combining material from lectures and advanced seminars given by the authors over many decades, is a must-have introduction and reference for both newcomers and seasoned researchers alike.

Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.

Originally published in 1960, and written by the renowned German-American physicist Alfred Lande (1888-1976), this book challenges the view that the principles of wave-particle duality, complementarity and uncertainty are fundamental to micro-mechanics. Instead, the text sets out to reduce dualistic quantum phenomena to still more elementary general principles, such as symmetry, invariance and continuity. It thus develops the Bohr-Heisenberg account, resting on Born's statistical interpretation, into a unitary theory. Appendices are included. This book will be of value to anyone with an interest in quantum physics and the history of science.

This SpringerBrief covers the main scales of description of matter, starting at its finest level, the quantum scale, moving through ab-initio, molecular dynamics, coarse grained approaches, to finish at the scale of kinetic theory models that allows a nice compromise between the rich but expensive microscopic descriptions and the computationally cheap but sometimes too coarse macroscopic descriptions. The book addresses undergraduate and graduate students, as well as beginners in multi-scale modeling of materials.

By questioning the validity of some of our basic concepts, such as space, object, and causality, quantum physics contributes quite decisively to the dramatic changes now taking place in our world picture.This book is addressed not only to physicists at an early stage in their careers (the first or second year graduate student) but also to philosophers, as well as to all the senior physicists interested in the interpretation problem. Beginning with a chapter that could be described as ?philosophy for physicists,? it presents an in-depth analysis of present-day quantum mechanical concepts, an analysis of physicists and philosophers alike. Specifically, it first offers an extensive critical analysis of such topics as the Einstein, Podolsky, Rosen reality criterion, nonseparatability, the quantum measurement riddle, decoherence theory, consistent histories approaches and ontologically interpretable theories. All this then naturally leads to philosophical questions concerning, in particular, intersubjective agreement and the limit of realism. And a thorough examination of this whole material finally leads to the view that distinguishing between empirical reality and a veiled man-independent reality yields an acceptable answer to the perplexing question of how to interpret quantum physics. Veiled Reality offers nonspecialists, including students in physics, philosophy and the history of science, an accessible perspective on basic problems in the foundations of physics.

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.

This thesis represents a unique mix of theoretical work discussing the Lorentz theory of gravity and experimental work searching for supersymmetry with the Compact Muon Solenoid experiment at the Large Hadron Collider. It begins by reviewing a set of widely-discussed theoretical solutions to the cosmological constant problem, including a natural solution provided by the recently developed Lorentz gauge theory of gravity. The Schwartzschild metric, de Sitter space, and quantum versions of the theory are also discussed. The thesis then looks to supersymmetry for an alternative solution. The idea behind supersymmetry is reviewed and an experimental search for supersymmetry is presented. A major contribution was to estimate one of the most significant backgrounds in this search, which arises from top-antitop quark pair production or W boson production in association with multiple jets where the W boson decays into the hadronically-decaying tau leptons and neutrinos. This background was estimated through a novel method involving kinematically analogous events but including a well-measured muon. This search significantly extends limits on supersymmetric partners of gluons from previous searches.

This thesis reports on experiments in which the motion of a mechanical oscillator is measured with unprecedented precision. The position fluctuations of the oscillator-a glass nanostring-are measured with an imprecision that is sufficient to resolve its quantum zero-point motion within its thermal decoherence time. The concomitant observation of measurement back-action, in accordance with Heisenberg's uncertainty principle, verifies the principles of linear quantum measurements on a macroscopic mechanical object. The record of the measurement is used to perform feedback control so as to suppress both classical thermal motion and quantum measurement back-action. These results verify some of the central and long-standing predictions of quantum measurement theory applied to a macroscopic object. The act of measurement not only perturbs the subject of the measurement-the mechanical oscillator-but also changes the state of the light used to make the measurement. This prediction is verified by demonstrating that the optical field, after having interacted with the mechanical oscillator, contains quantum correlations that render its quadrature fluctuations smaller than those of the vacuum - i.e., the light is squeezed. Lastly, the thesis reports on some of the first feedback control experiments involving macroscopic objects in the quantum regime, together with an exploration of the quantum limit of feedback control. The book offers a pedagogical account of linear measurement theory, its realization via optical interferometry, and contains a detailed guide to precision optical interferometry..