In virtue of its features, Bohm's quantum potential introduces interesting and relevant perspectives towards a satisfactory geometrodynamic description of quantum processes. This book makes a comprehensive state-of-the-art review of some of the most significant elements and results about the geometrodynamic picture determined by the quantum potential in various contexts. Above all, the book explores the perspectives about the fundamental arena subtended by the quantum potential, the link between the geometry associated to the quantum potential and a fundamental quantum vacuum. After an analysis of the geometry subtended by the quantum potential in the different fields of quantum physics (the non-relativistic domain, the relativistic domain, the relativistic quantum field theory, the quantum gravity domain and the canonical quantum cosmology), in the second part of the book, a recent interpretation of Bohm's quantum potential in terms of a more fundamental entity called quantum entropy, the approach of the symmetryzed quantum potential and the link between quantum potential and quantum vacuum are analysed, also in the light of the results obtained by the author.

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

This book provides an interdisciplinary perspective on one of the most fascinating and important open questions in science: What is quantum mechanics talking about? Quantum theory is perhaps our best confirmed physical theory. However, despite its great empirical effectiveness and the subsequent technological developments that it gave rise to in the 20th century, from the interpretation of the periodic table of elements to CD players, holograms and quantum state teleportation, it stands even today without a universally accepted interpretation. The novelty of the book comes from the multiple viewpoints and subjects investigated by a group of researchers from Europe and North and South America.

This volume contains the proceedings of the First Ukrainian-French Romanian School "Algebraic and Geometric Methods in Mathematical Physics," held in Kaciveli, Crimea (Ukraine) from 1 September ti1114 September 1993. The School was organized by the generous support of the Ministry of Research and Space of France (MRE), the Academy of Sciences of Ukraine (ANU), the French National Center for Scientific Research (CNRS) and the State Committee for Science and Technologies of Ukraine (GKNT). Members of the International Scientific Committee were: J.-M. Bony (paris), A. Boutet de Monvel-Berthier (Paris, co-chairman), P. Cartier (paris), V. Drinfeld (Kharkov), V. Georgescu (Paris), J.L. Lebowitz (Rutgers), V. Marchenko (Kharkov, co-chairman), V.P. Maslov (Moscow), H. Mc-Kean (New-York), Yu. Mitropolsky (Kiev), G. Nenciu (Bucharest, co-chairman), S. Novikov (Moscow), G. Papanicolau (New-York), L. Pastur (Kharkov), J.-J. Sansuc (Paris). The School consisted of plenary lectures (morning sessions) and special sessions. The plenary lectures were intended to be accessible to all participants and plenary speakers were invited by the scientific organizing committee to give reviews of their own field of interest. The special sessions were devoted to a variety of more concrete and technical questions in the respective fields. According to the program the plenary lectures included in the volume are grouped in three chapters. The fourth chapter contains short communications."

Zeta regularization is a method to treat the divergent quantities appearing in several areas of mathematical physics and, in particular, in quantum field theory; it is based on the fascinating idea that a finite value can be ascribed to a formally divergent expression via analytic continuation with respect to a complex regulating parameter.This book provides a thorough overview of zeta regularization for the vacuum expectation values of the most relevant observables of a quantized, neutral scalar field in Minkowski spacetime; the field can be confined to a spatial domain, with suitable boundary conditions, and an external potential is possibly present. Zeta regularization is performed in this framework for both local and global observables, like the stress-energy tensor and the total energy; the analysis of their vacuum expectation values accounts for the Casimir physics of the system. The analytic continuation process required in this setting by zeta regularization is deeply linked to some integral kernels; these are determined by the fundamental elliptic operator appearing in the evolution equation for the quantum field. The book provides a systematic illustration of these connections, devised as a toolbox for explicit computations in specific configurations; many examples are presented. A comprehensive account is given of the existing literature on this subject, including the previous work of the authors.The book will be useful to anyone interested in a mathematically sound description of quantum vacuum effects, from graduate students to scientists working in this area.

This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas that appeared in Hamiltonian mechanics, optics and hydrodynamics under different names. In addition, some interesting applications of the general theory of vortices are discussed in the book such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics. The investigation of families of trajectories of Hamiltonian systems can be reduced to problems of multidimensional ideal fluid dynamics. For example, the well-known Hamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested in mathematical physics, mechanics, and the theory of differential equations.

Gives a fresh and modern approach to the field. It is a textbook on the principles of the theory, its mathematical framework and its first applications. It constantly refers to modern and practical developments, tunneling microscopy, quantum information, Bell inequalities, quantum cryptography, Bose-Einstein condensation and quantum astrophysics. The book also contains 92 exercises with their solutions.

This edited volume explores the philosophical implications of quantum mechanics. It features papers from venues of the International Ontology Congress (IOC) up to 2016. IOC is a worldwide platform for dialogue and reflection on the interactions between science and philosophy. The collection features philosophers as well as physicists, including David Albert, Harvey Brown, Jeffrey Bub, Otavio Bueno, James Cushing, Steven French, Victor Gomez-Pin, Carl Hoefer, Simon Kochen, Peter Lewis, Tim Maudlin, Peter Mittlestatedt, Roland Omnes, Juha Saatsi, Albert Sole, David Wallace, and Anton Zeilinger. Since the early days of quantum mechanics, philosophers have studied the subject with growing technical skill and fruitfulness. Their efforts have unveiled intellectual bridges between physics and philosophy. These connections have helped fuel the contemporary debate about the scope and limits of realism and understanding in the interpretation of physical theories and scientific theories in general. The philosophical analysis of quantum mechanics is now one of the most sophisticated and productive areas in contemporary philosophy, as the papers in this collection illustrate.

The work presented in this PhD dissertation is the first search at CMS for Higgs bosons produced in association with top quarks (ttH) in a final state consisting of only jets. The results presented in this book uncover a new class of ttH events that will help us elucidate our understanding of the Yukawa sector interactions between the Higgs boson and the top quark. Despite this being the most common decay signature for ttH, a large contamination of SM backgrounds makes it the most challenging for extracting a signal from data. The PhD thesis presents many sophisticated tools and techniques that were developed in order to overcome these challenges. These tools pave the way for future analyses to investigate other standard model and beyond-standard model physics.

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.

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

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

"Stochastic Processes in Quantum Physics" addresses the question 'What is the mathematics needed for describing the movement of quantum particles', and shows that it is the theory of stochastic (in particular Markov) processes and that a relativistic quantum particle has pure-jump sample paths while sample paths of a non-relativistic quantum particle are continuous. Together with known techniques, some new stochastic methods are applied in solving the equation of motion and the equation of dynamics of relativistic quantum particles. The problem of the origin of universes is discussed as an application of the theory. The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level, and some selected chapters can be used as (sub-)textbooks for advanced courses on stochastic processes, quantum theory and theoretical chemistry.

We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets - important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets.

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

A sequel to the well received book, Quantum Mechanics by T Y Wu, this book carries on where the earlier volume ends. This present volume follows the generally pedagogic style of Quantum Mechanics. The scope ranges from relativistic quantum mechanics to an introduction to quantum field theory with quantum electrodynamics as the basic example and ends with an exposition of important issues related to the standard model. The book presents the subject in basic and easy-to-grasp notions which will enhance the purpose of this book as a useful textbook in the area of relativistic quantum mechanics and quantum electrodynamics.

This is an introductory book dealing with collective phenomena in many-body systems. A gas of bosons or fermions can show oscillations of various types of density. These are described by different combinations of field variables. Especially delicate is the competition of these variables. In superfluid 3He, for example, the atoms can be attracted to each other by molecular forces, whereas they are repelled from each other at short distance due to a hardcore repulsion. The attraction gives rise to Cooper pairs, and the repulsion is overcome by paramagnon oscillations. The combination is what finally led to the discovery of superfluidity in 3He. In general, the competition between various channels can most efficiently be studied by means of a classical version of the Hubbard-Stratonovich transformation.A gas of electrons is controlled by the interplay of plasma oscillations and pair formation. In a system of rod- or disc-like molecules, liquid crystals are observed with directional orientations that behave in unusual five-fold or seven-fold symmetry patterns. The existence of such a symmetry was postulated in 1975 by the author and K Maki. An aluminium material of this type was later manufactured by Dan Shechtman which won him the 2014 Nobel prize. The last chapter presents some solvable models, one of which was the first to illustrate the existence of broken supersymmetry in nuclei.

Quantum information science has found great experimental success by exploiting single photons. To date, however, the majority of quantum optical experiments use large-scale (bulk) optical elements bolted down to an optical bench, an approach that ultimately limits the complexity and stability of the quantum circuits required for quantum science and technology. The realization of complex optical schemes involving large numbers of elements requires the introduction of waveguide technology to achieve the desired scalability, stability and miniaturization of the device. This thesis reports on surprising findings in the field of integrated devices for quantum information. Here the polarization of the photon is shown to offer a suitable degree of freedom for encoding quantum information in integrated systems. The most important results concern: the quantum interference of polarization entangled photons in an on-chip directional coupler; the realization of a Controlled-NOT (CNOT) gate operating with polarization qubits; the realization of a quantum walk of bosons and fermions in an ordered optical lattice and the quantum simulation of Anderson localization of bosons and fermions simulated by polarization entangled photons in a disordered quantum walk. The findings presented in this thesis represent an important step towards the integration of a complete quantum photonic experiment in a chip.

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.

Quantum Systems in Physics, Chemistry and Biology, Theory, Interpretation, and Results, Volume 78, the latest release in the Advances in Quantum Chemistry series presents surveys of current topics in this rapidly developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology. It features detailed reviews written by leading international researchers.

The theoretical foundations of the Standard Model of elementary particles relies on the existence of the Higgs boson, a particle which has been revealed for the first time by the experiments run at the Large Hadron Collider (LHC) in 2012. As the Higgs boson is an unstable particle, its search strategies were based on its decay products. In this thesis, Francesco Pandolfi conducted a search for the Higgs boson in the H ZZ l + l - qq Decay Channel with 4.6 fb -1 of 7 TeV proton-proton collision data collected by the Compact Muon Solenoid (CMS) experiment. The presence of jets in the final state poses a series of challenges to the experimenter: both from a technical point of view, as jets are complex objects and necessitate of ad-hoc reconstruction techniques, and from an analytical one, as backgrounds with jets are copious at hadron colliders, therefore analyses must obtain high degrees of background rejection in order to achieve competitive sensitivity. This is accomplished by following two directives: the use of an angular likelihood discriminant, capable of discriminating events likely to originate from the decay of a scalar boson from non-resonant backgrounds, and by using jet parton flavor tagging, selecting jets compatible with quark hadronization and discarding jets more likely to be initiated by gluons. The events passing the selection requirements in 4.6 fb -1 of data collected by the CMS detector are examined, in the search of a possible signal compatible with the decay of a heavy Higgs boson. The thesis describes the statistical tools and the results of this analysis. This work is a paradigm for studies of the Higgs boson with final states with jets. The non-expert physicists will enjoy a complete and eminently readable description of a proton-proton collider analysis. At the same time, the expert reader will learn the details of the searches done with jets at CMS.

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

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

Based on the Fourth International Conference on Quantum Communication, Measurement and Computing, this volume brings together scientists working in the interdisciplinary fields of quantum communication science and technology. Topics include quantum information theory, quantum computing, stochastic processes and filtering, and quantum measurement theory

The behaviour of electrons in systems without periodicity is one of the most fascinating areas in solid-state physics, and the last 25 years have seen an enormous increase in research in this field. This has given rise to many new ideas for understanding electronic states in disordered systems, especially the study of the degenerate electron gas in which electron-electron interactions are important. This book provides a much needed survey of these advances. In the first part of the book, the authors discuss impurity bands in three dimensions. Attention is focused on the regime in which the electrons are spatially localized rather than free, so that an interesting interplay of localization and interaction arises. In the second part of the book, they look at the outstanding features of the two-dimensional systems, explaining how these make the localization problem special and interesting. The authors have provided a clear outline of the theoretical picture for the chosen materials and description heuristic. Each chapter is self-contained, allowing readers to pursue their special interests.