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This book deals with applications of quantum mechanical techniques to areas outside of quantum mechanics, socalled quantumlike modeling. Research in this area has grown over the last 15 years. But even already more than 50 years ago, the interaction between Physics Nobelist Pauli and the psychologist Carl Jung in the 1950's on seeking to find analogous uses of the complementarity principle from quantum mechanics in psychology needs noting. This book does NOT want to advance that society is quantum mechanical! The macroscopic world is manifestly not quantum mechanical. But this rules not out that one can use concepts and the mathematical apparatus from quantum physics in a macroscopic environment. A mainstay ingredient of quantum mechanics, is 'quantum probability' and this tool has been proven to be useful in the mathematical modelling of decision making. In the most basic experiment of quantum physics, the double slit experiment, it is known (from the works of A. Khrennikov) that the law of total probability is violated. It is now well documented that several decision making paradoxes in psychology and economics (such as the Ellsberg paradox) do exhibit this violation of the law of total probability. When data is collected with experiments which test 'nonrational' decision making behaviour, one can observe that such data often exhibits a complex noncommutative structure, which may be even more complex than if one considers the structure allied to the basic two slit experiment. The community exploring quantumlike models has tried to address how quantum probability can help in better explaining those paradoxes. Research has now been published in very high standing journals on resolving some of the paradoxes with the mathematics of quantum physics. The aim of this book is to collect the contributions of world's leading experts in quantum like modeling in decision making, psychology, cognition, economics, and finance.
Quantumlike models  mathematical formalism of quantum theory  quantum probability  decision making  psychology  cognition  emotions
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Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the bigdata analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum manybody physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for nonspecialists on quantum physics to understand tensor network algorithms and the related mathematics.
Physics  Physics  Quantum physics  Quantum optics  Statistical physics  Machine learning  Elementary particles (Physics)  Quantum field theory
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With this graduatelevel primer, the principles of the standard model of particle physics receive a particular skillful, personal and enduring exposition by one of the great contributors to the field.In 2013 the late Prof. Altarelli wrote: The discovery of the Higgs boson and the nonobservation of new particles or exotic phenomena have made a big step towards completing the experimental confirmation of the standard model of fundamental particle interactions. It is thus a good moment for me to collect, update and improve my graduate lecture notes on quantum chromodynamics and the theory of electroweak interactions, with main focus on collider physics. I hope that these lectures can provide an introduction to the subject for the interested reader, assumed to be already familiar with quantum field theory and some basic facts in elementary particle physics as taught in undergraduate courses.
elementary particles  quantum field theory  string theory
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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 KochenSpecker, Free Will, and Bell Theorems, the KadisonSinger conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.
Quantum physics  Mathematical physics  Matrix theory  Algebra
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This open access textbook takes the reader stepbystep through the concepts of mechanics in a clear and detailed manner. Mechanics is considered to be the core of physics, where a deep understanding of the concepts is essential in understanding all branches of physics. Many proofs and examples are included to help the reader grasp the fundamentals fully, paving the way to deal with more advanced topics. After solving all of the examples, the reader will have gained a solid foundation in mechanics and the skills to apply the concepts in a variety of situations. The book is useful for undergraduate students majoring in physics and other science and engineering disciplines. It can also be used as a reference for more advanced levels.
Physics  Mechanics  Mechanical engineering  Elementary particles (Physics)  Quantum field theory
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Traditional approaches to cognitive psychology correspond with a classical view of logic and probability theory. More specifically, one typically assumes that cognitive processes of human thought are founded on the Boolean structures of classical logic, while the probabilistic aspects of these processes are based on the Kolmogorovian structures of classical probability theory. However, growing experimental evidence indicates that the models founded on classical structures systematically fail when human decisions are at stake. These experimental deviations from classical behavior have been called `paradoxes’, `fallacies’, `effects’ or `contradictions’, depending on the specific situation where they appear. But, they involve a broad spectrum of cognitive and social science domains, ranging from conceptual combination to decision making under uncertainty, behavioral economics, and linguistics. This situation has constituted a serious drawback to the development of various disciplines, like cognitive science, linguistics, artificial intelligence, economic modeling and behavioral finance. A different approach to cognitive psychology, initiated two decades ago, has meanwhile matured into a new domain of research, called ‘quantum cognition’. Its main feature is the use of the mathematical formalism of quantum theory as modeling tool for these cognitive situations where traditional classically based approaches fail. Quantum cognition has recently attracted the interest of important journals and editing houses, academic and funding institutions, popular science and media. Specifically, within a quantum cognition approach, one assumes that human decisions do not necessarily obey the rules of Boolean logic and Kolmogorovian probability, and can on the contrary be modeled by the quantummechanical formalism. Different concrete quantumtheoretic models have meanwhile been developed that successfully represent the cognitive situations that are classically problematical, by explaining observed deviations from classicality in terms of genuine quantum effects, such as `contextuality’, `emergence’, `interference’, `superposition’, `entanglement’ and `indistinguishability’. In addition, the validity of these quantum models is convincingly confirmed by new experimental tests. We also stress that, since the use of a quantumtheoretic framework is mainly for modeling purposes, the identification of quantum structures in cognitive processes does not presuppose (without being incompatible with it) the existence of microscopic quantum processes in the human brain. In this Research Topic, we review the major achievements that have been obtained in quantum cognition, by providing an accurate picture of the stateoftheart of this emerging discipline. Our overview does not pretend to be either complete or exhaustive. But, we aim to introduce psychologists and social scientists to this challenging new research area, encouraging them, at the same time, to consider its promising results. It is our opinion that, if continuous progress in this domain can be realized, quantum cognition can constitute an important breakthrough in cognitive psychology, and potentially open the way towards a new scientific paradigm in social science.
human cognition  decisionmaking  Cognitive fallacies  Human perception  social networks  mathematical modeling  quantum structures  Quantum cognition paradigm
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The QM/MM method, short for quantum mechanical/molecular mechanical, is a highly versatile approach for the study of chemical phenomena, combining the accuracy of quantum chemistry to describe the region of interest with the efficiency of molecular mechanical potentials to represent the remaining part of the system. Originally conceived in the 1970s by the influential work of the the Nobel laureates Martin Karplus, Michael Levitt and Arieh Warshel, QM/MM techniques have evolved into one of the most accurate and general approaches to investigate the properties of chemical systems via computational methods. Whereas the first applications have been focused on studies of organic and biomolecular systems, a large variety of QM/MM implementations have been developed over the last decades, extending the range of applicability to address research questions relevant for both solution and solidstate chemistry as well. Despite approaching their 50th anniversary in 2022, the formulation of improved QM/MM methods is still an active field of research, with the aim to (i) extend the applicability to address an even broader range of research questions in chemistry and related disciplines, and (ii) further push the accuracy achieved in the QM/MM description beyond that of established formulations. While being a highly successful approach on its own, the combination of the QM/MM strategy with other established theoretical techniques greatly extends the capabilities of the computational approaches. For instance the integration of a suitable QM/MM technique into the highly successful MonteCarlo and molecular dynamics simulation protocols enables the description of the chemical systems on the basis of an ensemble that is in part constructed on a quantummechanical basis. This eBook presents the contributions of a recent Research Topic published in Frontiers in Chemistry, that highlight novel approaches as well as advanced applications of QM/MM method to a broad variety of targets. In total 2 review articles and 10 original research contributions from 48 authors are presented, covering 12 different countries on four continents. The range of research questions addressed by the individual contributions provide a lucid overview on the versatility of the QM/MM method, and demonstrate the general applicability and accuracy that can be achieved for different problems in chemical sciences. Together with the development of improved algorithms to enhance the capabilities of quantum chemical methods and the continuous advancement in the capacities of computational resources, it can be expected that the impact of QM/MM methods in chemical sciences will be further increased already in the near future.
Hybrid Quantum Mechanical/Molecular Mechanical  QM/MM  Quantum Chemistry  Ab initio/First Principles  Density Functional Theory  Empirical Potentials  Molecular Mechanics  Force Field
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This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft.Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory.The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle.This framework elegantly explains  and automatically cures  the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.
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With the emergence of Systems Biology, there is a greater realization that the whole behavior of a living system may not be simply described as the sum of its elements. To represent a living system using mathematical principles, practical quantities with units are required. Quantities are not only the bridge between mathematical description and biological observations; they often stand as essential elements similar to genome information in genetics. This important realization has greatly rejuvenated research in the area of Quantitative Biology. Because of the increased need for precise quantification, a new era of technological development has opened. For example, spatiotemporal highresolution imaging enables us to track single molecule behavior in vivo. Clever artificial control of experimental conditions and molecular structures has expanded the variety of quantities that can be directly measured. In addition, improved computational power and novel algorithms for analyzing theoretical models have made it possible to investigate complex biological phenomena. This research topic is organized on two aspects of technological advances which are the backbone of Quantitative Biology: (i) visualization of biomolecules, their dynamics and function, and (ii) generic technologies of model optimization and numeric integration. We have also included articles highlighting the need for new quantitative approaches to solve some of the longstanding cell biology questions. In the first section on visualizing biomolecules, four cuttingedge techniques are presented. Ichimura et al. provide a review of quantum dots including their basic characteristics and their applications (for example, single particle tracking). Horisawa discusses a quick and stable labeling technique using click chemistry with distinct advantages compared to fluorescent protein tags. The relatively small physical size, stability of covalent bond and simple metabolic labeling procedures in living cells provides this type of technology a potential to allow longterm imaging with least interference to protein function. Obien et al. review strategies to control microelectrodes for detecting neuronal activity and discuss techniques for higher resolution and quality of recordings using monolithic integration with onchip circuitry. Finally, the original research article by Amariei et al. describes the oscillatory behavior of metabolites in bacteria. They describe a new method to visualize the periodic dynamics of metabolites in large scale cultures populations. These four articles contribute to the development of quantitative methods visualizing diverse targets: proteins, electrical signals and metabolites. In the second section of the topic, we have included articles on the development of computational tools to fully harness the potential of quantitative measurements through either calculation based on specific model or validation of the model itself. Kimura et al. introduce optimization procedures to search for parameters in a quantitative model that can reproduce experimental data. They present four examples: transcriptional regulation, bacterial chemotaxis, morphogenesis of tissues and organs, and cell cycle regulation. The original research article by Sumiyoshi et al. presents a general methodology to accelerate stochastic simulation efforts. They introduce a method to achieve 130 times faster computation of stochastic models by applying GPGPU. The strength of such accelerated numerical calculation are sometimes underestimated in biology; faster simulation enables multiple runs and in turn improved accuracy of numerical calculation which may change the final conclusion of modeling study. This also highlights the need to carefully assess simulation results and estimations using computational tools.
imaging  data visualization  fluorescence chemistry  quantum dot  model optimization  numerical integration  GPGPU  molecular crowding  cell division
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This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 2527, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the lightmatter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into postquantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize postquantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on postquantum cryptography.
Mathematical and Computational Engineering  Data Structures and Information Theory  Quantum Computing  Systems and Data Security  Mathematical and Computational Engineering Applications  Data and Information Security  Cryptography for Quantum Computers  Postquantum Cryptography  Number Theory  Representation Theory  Quantum Physics  Security Modelling  Open Access  Maths for engineers  Algorithms & data structures  Information theory  Mathematical theory of computation  Computer security  Network security
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