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1 De Nittis, Giuseppe Linear Response Theory I10402 2017 eBook  
2 Prodan, Emil A Computational Non-commutative Geometry Program for Disordered Topological Insulators I10352 2017 eBook  
3 Bru, J.-B Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory I10275 2017 eBook  
4 Busch, Paul Quantum Measurement I09266 2016 eBook  
5 Lieb, Elliott H Condensed Matter Physics and Exactly Soluble Models I11519 2004 eBook  
6 Lieb, E.H Statistical Mechanics I11351 2004 eBook  
7 Buttkus, Burkhard Spectral Analysis and Filter Theory in Applied Geophysics I11158 2000 eBook  
8 Hamhalter, J Quantum Measure Theory I10731 2003 eBook  
9 Pavsic, M The Landscape of Theoretical Physics: A Global View I10575 2002 eBook  
10 Gupta, Ved Prakash The Functional Analysis of Quantum Information Theory I08428 2015 eBook  
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TitleLinear Response Theory : An Analytic-Algebraic Approach
Author(s)De Nittis, Giuseppe;Lein, Max
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionX, 138 p : online resource
Abstract NoteThis book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3???5: the relevant von Neumann algebras, noncommutative $L^p$- and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and Kubo-Streda formulas. The book closes with a chapter about possible future developments and applications of the theory to periodic light conductors. The book addresses a wide audience of mathematical physicists, focusing on the conceptual aspects rather than technical details and making algebraic methods accessible to analysts
ISBN,Price9783319567327
Keyword(s)1. CONDENSED MATTER 2. CONDENSED MATTER PHYSICS 3. EBOOK 4. EBOOK - SPRINGER 5. FUNCTIONAL ANALYSIS 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. PHYSICS
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TitleA Computational Non-commutative Geometry Program for Disordered Topological Insulators
Author(s)Prodan, Emil
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionX, 118 p. 19 illus. in color : online resource
Abstract NoteThis work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons??? dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the concept of non-commutative Brillouin torus, and a list of known formulas for various physical response functions is presented. In the second part, auxiliary algebras are introduced and a canonical finite-volume approximation of the non-commutative Brillouin torus is developed. Explicit numerical algorithms for computing generic correlation functions are discussed. In the third part upper bounds on the numerical errors are derived and it is proved that the canonical-finite volume approximation converges extremely fast to the thermodynamic limit. Convergence tests and various applications concludes the presentation. The book is intended for graduate students and researchers in numerical and mathematical physics
ISBN,Price9783319550237
Keyword(s)1. CONDENSED MATTER 2. CONDENSED MATTER PHYSICS 3. EBOOK 4. EBOOK - SPRINGER 5. FUNCTIONAL ANALYSIS 6. K-THEORY 7. Mathematical Methods in Physics 8. MATHEMATICAL PHYSICS 9. PHYSICS
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TitleLieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory
Author(s)Bru, J.-B;de Siqueira Pedra, W
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionVII, 109 p : online resource
Abstract NoteLieb-Robinson bounds for multi-commutators are effective mathematical tools to handle analytic aspects of infinite volume dynamics of non-relativistic quantum particles with short-range, possibly time-dependent interactions. In particular, the existence of fundamental solutions is shown for those (non-autonomous) C*-dynamical systems for which the usual conditions found in standard theories of (parabolic or hyperbolic) non-autonomous evolution equations are not given. In mathematical physics, bounds on multi-commutators of an order higher than two can be used to study linear and non-linear responses of interacting particles to external perturbations. These bounds are derived for lattice fermions, in view of applications to microscopic quantum theory of electrical conduction discussed in this book. All results also apply to quantum spin systems, with obvious modifications. In order to make the results accessible to a wide audience, in particular to students in mathematics with little Physics background, basics of Quantum Mechanics are presented, keeping in mind its algebraic formulation. The C*-algebraic setting for lattice fermions, as well as the celebrated Lieb-Robinson bounds for commutators, are explained in detail, for completeness
ISBN,Price9783319457840
Keyword(s)1. CONDENSED MATTER 2. CONDENSED MATTER PHYSICS 3. EBOOK 4. EBOOK - SPRINGER 5. FUNCTIONAL ANALYSIS 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. PHYSICS 9. QUANTUM COMPUTERS 10. Quantum Information Technology, Spintronics 11. SPINTRONICS
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TitleQuantum Measurement
Author(s)Busch, Paul;Lahti, Pekka;Pellonp????, Juha-Pekka;Ylinen, Kari
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2016.
DescriptionXII, 542 p. 7 illus., 2 illus. in color : online resource
Abstract NoteThis is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann???s classic treatise with this title. Fundamental non-classical features of quantum mechanics???indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality???are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4. Foundations discusses a selection of foundational topics (quantum-classical contrast, Bell nonlocality, measurement limitations, measurement problem, operational axioms) from a measurement theoretic perspective. The book is addressed to physicists, mathematicians and philosophers of physics with an interest in the mathematical and conceptual foundations of quantum physics, specifically from the perspective of measurement theory
ISBN,Price9783319433899
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. FUNCTIONAL ANALYSIS 4. History and Philosophical Foundations of Physics 5. MATHEMATICAL PHYSICS 6. PHYSICS 7. QUANTUM COMPUTERS 8. Quantum Information Technology, Spintronics 9. QUANTUM PHYSICS 10. SPINTRONICS
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TitleCondensed Matter Physics and Exactly Soluble Models : Selecta of Elliott H. Lieb
Author(s)Lieb, Elliott H;Nachtergaele, Bruno;Solovej, Jan Philip;Yngvason, Jakob
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2004.
DescriptionIX, 675 p : online resource
Abstract NoteThe first part of this book contains E. Lieb's fundamental contributions to the mathematical theory of Condensed Matter Physics. Often considered the founding father of the field, E. Lieb demonstrates his ability to select the most important issues and to formulate them as well-defined mathematical problems and, finally, to solve them. The second part presents Lieb's work on integrable models. His groundbreaking articles helped to establish Exactly Soluble Models as a flourishing research field in its own right. The papers collected in this volume have also been carefully annotated by the editors
ISBN,Price9783662063903
Keyword(s)1. Atomic, Molecular, Optical and Plasma Physics 2. ATOMS 3. Condensed materials 4. CONDENSED MATTER 5. CONDENSED MATTER PHYSICS 6. EBOOK 7. EBOOK - SPRINGER 8. FUNCTIONAL ANALYSIS 9. Mathematical Methods in Physics 10. Phase transformations (Statistical physics) 11. PHYSICS 12. Quantum Gases and Condensates
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TitleStatistical Mechanics : Selecta of Elliott H. Lieb
Author(s)Lieb, E.H;Nachtergaele, Bruno;Solovej, Jan Philip;Yngvason, Jakob
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2004.
DescriptionX, 508 p : online resource
Abstract NoteIn Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with realistic forces. Elliott Lieb is a mathematical physicist who meets the challenge of statistical mechanics head on, taking nothing for granted and not being content until the purported consequences have been shown, by rigorous analysis, to follow from the premises. The present volume contains a selection of his contributions to the field, in particular papers dealing with general properties of Coulomb systems, phase transitions in systems with a continuous symmetry, lattice crystals, and entropy inequalities. It also includes work on classical thermodynamics, a discipline that, despite many claims to the contrary, is logically independent of statistical mechanics and deserves a rigorous and unambiguous foundation of its own. The articles in this volume have been carefully annotated by the editors
ISBN,Price9783662100189
Keyword(s)1. COMPLEX SYSTEMS 2. CONDENSED MATTER 3. CONDENSED MATTER PHYSICS 4. DYNAMICAL SYSTEMS 5. EBOOK 6. EBOOK - SPRINGER 7. FUNCTIONAL ANALYSIS 8. Mathematical Methods in Physics 9. PHYSICS 10. STATISTICAL PHYSICS 11. Statistical Physics and Dynamical Systems 12. THERMODYNAMICS
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TitleSpectral Analysis and Filter Theory in Applied Geophysics
Author(s)Buttkus, Burkhard
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2000.
DescriptionXV, 667 p : online resource
Abstract NoteThis book is intended to be an introduction to the fundamentals and methods of spectral analysis and filter theory and their appli?? cations in geophysics. The principles and theoretical basis of the various methods are described, their efficiency and effectiveness eval?? uated, and instructions provided for their practical application. Be?? sides the conventional methods, newer methods arediscussed, such as the spectral analysis ofrandom processes by fitting models to the ob?? served data, maximum-entropy spectral analysis and maximum-like?? lihood spectral analysis, the Wiener and Kalman filtering methods, homomorphic deconvolution, and adaptive methods for nonstation?? ary processes. Multidimensional spectral analysis and filtering, as well as multichannel filters, are given extensive treatment. The book provides a survey of the state-of-the-art of spectral analysis and fil?? ter theory. The importance and possibilities ofspectral analysis and filter theory in geophysics for data acquisition, processing and eval?? uation are illustrated with practical examples from various fields of applied geophysics. Although this book was planned primarily as a textbook for a course on the analysis of geophysical time?? series, it may also be of interest to scientists and engineers who process other digital data. It provides a comprehensive discussion of the theoretical fundamen?? tals and a compilation of the extensive literature on the subject. I hope that I have succeeded in presenting the various principles and methods of time-series analysis comprehensively and without error. Comments on errors or suggestions for improvements are welcome
ISBN,Price9783642570162
Keyword(s)1. Astronomy, Observations and Techniques 2. Astronomy???Observations 3. ASTROPHYSICS 4. Astrophysics and Astroparticles 5. EBOOK 6. EBOOK - SPRINGER 7. FUNCTIONAL ANALYSIS 8. GEOLOGY 9. GEOPHYSICS 10. Geophysics and Environmental Physics 11. Geophysics/Geodesy 12. Observations, Astronomical
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TitleQuantum Measure Theory
Author(s)Hamhalter, J
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2003.
DescriptionVIII, 410 p : online resource
ISBN,Price9789401701198
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. FUNCTIONAL ANALYSIS 4. OPERATOR THEORY 5. QUANTUM PHYSICS
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TitleThe Landscape of Theoretical Physics: A Global View : From Point Particles to the Brane World and Beyond in Search of a Unifying Principle
Author(s)Pavsic, M
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2002.
DescriptionXXII, 374 p : online resource
Abstract NoteToday many important directions of research are being pursued more or less independently of each other. These are, for instance, strings and mem branes, induced gravity, embedding of spacetime into a higher dimensional space, the brane world scenario, the quantum theory in curved spaces, Fock Schwinger proper time formalism, parametrized relativistic quantum the ory, quantum gravity, wormholes and the problem of ???time machines???, spin and supersymmetry, geometric calculus based on Clifford algebra, various interpretations of quantum mechanics including the Everett interpretation, and the recent important approach known as ???decoherence???. A big problem, as I see it, is that various people thoroughly investigate their narrow field without being aware of certain very close relations to other fields of research. What we need now is not only to see the trees but also the forest. In the present book I intend to do just that: to carry out a first approximation to a synthesis of the related fundamental theories of physics. I sincerely hope that such a book will be useful to physicists. From a certain viewpoint the book could be considered as a course in the oretical physics in which the foundations of all those relevant fundamental theories and concepts are attempted to be thoroughly reviewed. Unsolved problems and paradoxes are pointed out. I show that most of those ap proaches have a common basis in the theory of unconstrained membranes. The very interesting and important concept of membrane space, the tensor calculus in and functional transformations in are discussed
ISBN,Price9780306471360
Keyword(s)1. Associative rings 2. Associative Rings and Algebras 3. EBOOK 4. EBOOK - SPRINGER 5. Elementary particles (Physics) 6. Elementary Particles, Quantum Field Theory 7. FUNCTIONAL ANALYSIS 8. MATHEMATICAL PHYSICS 9. QUANTUM FIELD THEORY 10. QUANTUM PHYSICS 11. Rings (Algebra) 12. Theoretical, Mathematical and Computational Physics
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TitleThe Functional Analysis of Quantum Information Theory : A Collection of Notes Based on Lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter
Author(s)Gupta, Ved Prakash;Mandayam, Prabha;Sunder, V.S
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2015.
DescriptionXI, 139 p : online resource
Abstract NoteThis book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann???s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring???s dilation theorem for completely positive maps and Kirchberg???s theorem on tensor products of C*-algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrix-valued random variables in the quantum information setting
ISBN,Price9783319167183
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. FUNCTIONAL ANALYSIS 4. Mathematical Methods in Physics 5. MATHEMATICAL PHYSICS 6. PHYSICS 7. QUANTUM COMPUTERS 8. Quantum computing 9. QUANTUM PHYSICS
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