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Quantum Information Processing With Finite Resources

Author: Marco Tomamichel
Publisher: Springer
ISBN: 3319218913
Size: 15.55 MB
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This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.

Noncommutative Geometry And Optimal Transport

Author: Pierre Martinetti
Publisher: American Mathematical Soc.
ISBN: 1470422972
Size: 41.74 MB
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The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. It is a generalization of Riemannian geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of states on an algebra. It also has an intriguing echo in physics, for it yields a metric interpretation for the Higgs field. In the 1990s, Rieffel noticed that this distance is a noncommutative version of the Wasserstein distance of order 1 in the theory of optimal transport. More exactly, this is a noncommutative generalization of Kantorovich dual formula of the Wasserstein distance. Connes distance thus offers an unexpected connection between an ancient mathematical problem and the most recent discovery in high energy physics. The meaning of this connection is far from clear. Yet, Rieffel's observation suggests that Connes distance may provide an interesting starting point for a theory of optimal transport in noncommutative geometry. This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.

Supersymmetry And Noncommutative Geometry

Author: Wim Beenakker
Publisher: Springer
ISBN: 3319247980
Size: 25.63 MB
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In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far.The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model.This book is intended for mathematical/theoretical physicists with an interest in the applications of noncommutative geometry to supersymmetric field theories.

Formality Theory

Author: Chiara Esposito
Publisher: Springer
ISBN: 3319092901
Size: 45.63 MB
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This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.

Effective Evolution Equations From Quantum Dynamics

Author: Niels Benedikter
Publisher: Springer
ISBN: 3319248987
Size: 59.30 MB
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These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.

Networks Of Networks The Last Frontier Of Complexity

Author: Gregorio D'Agostino
Publisher: Springer
ISBN: 3319035185
Size: 34.27 MB
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The present work is meant as a reference to provide an organic and comprehensive view of the most relevant results in the exciting new field of Networks of Networks (NetoNets). Seminal papers have recently been published posing the basis to study what happens when different networks interact, thus providing evidence for the emergence of new, unexpected behaviors and vulnerabilities. From those seminal works, the awareness on the importance understanding Networks of Networks (NetoNets) has spread to the entire community of Complexity Science. The reader will benefit from the experience of some of the most well-recognized leaders in this field. The contents have been aggregated under four headings; General Theory, Phenomenology, Applications and Risk Assessment. The reader will be impressed by the different applications of the general paradigm that span from physiology, to financial risk, to transports. We are currently making the first steps to reduce the distance between the language and the way of thinking of the two communities of experts in real infrastructures and the complexity scientists. Although this path may prove to be long, it is extremely promising, both in extending our understanding of complex systems and in finding concrete applications that can enhance the life quality of millions of people.

Pic Microcontroller And Embedded Systems

Author: Muhammad Ali Mazidi
Publisher: Microdigitaled
ISBN: 9780997925999
Size: 70.50 MB
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The PIC microcontroller from Microchip is one of the most widely used 8-bit microcontrollers in the world. In this book, the authors use a step-by-step and systematic approach to show the programming of the PIC18 chip. Examples in both Assembly language and C show how to program many of the PIC18 features such as timers, serial communication, ADC, and SPI.

100 Years Of Radar

Author: Gaspare GALATI
Publisher: Springer
ISBN: 3319005847
Size: 24.69 MB
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This book offers fascinating insights into the key technical and scientific developments in the history of radar, from the first patent, taken out by Hülsmeyer in 1904, through to the present day. Landmark events are highlighted and fascinating insights provided into the exceptional people who made possible the progress in the field, including the scientists and technologists who worked independently and under strict secrecy in various countries across the world in the 1930s and the big businessmen who played an important role after World War II. The book encourages multiple levels of reading. The author is a leading radar researcher who is ideally placed to offer a technical/scientific perspective as well as a historical one. He has taken care to structure and write the book in such a way as to appeal to both non-specialists and experts. The book is not sponsored by any company or body, either formally or informally, and is therefore entirely unbiased. The text is enriched by approximately three hundred images, most of which are original and have been accessed by detailed searches in the archives.

Tensor Categories And Endomorphisms Of Von Neumann Algebras

Author: Marcel Bischoff
Publisher: Springer
ISBN: 3319143018
Size: 60.60 MB
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C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).

Attracted To Conflict Dynamic Foundations Of Destructive Social Relations

Author: Robin R. Vallacher
Publisher: Springer Science & Business Media
ISBN: 3642352804
Size: 46.79 MB
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Conflict is inherent in virtually every aspect of human relations, from sport to parliamentary democracy, from fashion in the arts to paradigmatic challenges in the sciences, and from economic activity to intimate relationships. Yet, it can become among the most serious social problems humans face when it loses its constructive features and becomes protracted over time with no obvious means of resolution. This book addresses the subject of intractable social conflict from a new vantage point. Here, these types of conflict represent self-organizing phenomena, emerging quite naturally from the ongoing dynamics in human interaction at any scale—from the interpersonal to the international. Using the universal language and computational framework of nonlinear dynamical systems theory in combination with recent insights from social psychology, intractable conflict is understood as a system locked in special attractor states that constrain the thoughts and actions of the parties to the conflict. The emergence and maintenance of attractors for conflict can be described by means of formal models that incorporate the results of computer simulations, experiments, field research, and archival analyses. Multi-disciplinary research reflecting these approaches provides encouraging support for the dynamical systems perspective. Importantly, this text presents new views on conflict resolution. In contrast to traditional approaches that tend to focus on basic, short-lived cause-effect relations, the dynamical perspective emphasizes the temporal patterns and potential for emergence in destructive relations. Attractor deconstruction entails restoring complexity to a conflict scenario by isolating elements or changing the feedback loops among them. The creation of a latent attractor trades on the tendency toward multi-stability in dynamical systems and entails the consolidation of incongruent (positive) elements into a coherent structure. In the bifurcation scenario, factors are identified that can change the number and types of attractors in a conflict scenario. The implementation of these strategies may hold the key to unlocking intractable conflict, creating the potential for constructive social relations.