Format: Paperback / softback, 304 pages, height x width: 235x155 mm, 40 Tables, color; 34 Illustrations,
color; 40 Illustrations, black and white; XII, 304 p. 74 illus., 34 illus. in color.
Series: Undergraduate Lecture Notes in Physics
Pub. Date: 23-Jan-2023
ISBN-13: 9783031161643
In this undergraduate textbook, now in its 2nd edition, the author develops the quantum theory from first principles based on very simple experiments: a photon traveling through beam splitters to detectors, an electron moving through magnetic fields, and an atom emitting radiation. From the physical description of these experiments follows a natural mathematical description in terms of matrices and complex numbers. The first part of the book examines how experimental facts force us to let go of some deeply held preconceptions and develops this idea into a description of states, probabilities, observables, and time evolution. The quantum mechanical principles are illustrated using applications such as gravitational wave detection, magnetic resonance imaging, atomic clocks, scanning tunneling microscopy, and many more. The first part concludes with an overview of the complete quantum theory. The second part of the book covers more advanced topics, including the concept of entanglement, the process of decoherence or how quantum systems become classical, quantum computing and quantum communication, and quantum particles moving in space. Here, the book makes contact with more traditional approaches to quantum physics. The remaining chapters delve deeply into the idea of uncertainty relations and explore what the quantum theory says about the nature of reality. The book is an ideal accessible introduction to quantum physics, tested in the classroom, with modern examples and plenty of end-of-chapter exercises.
Chapter 1: Three simple experiments.- The purpose of physical theories.- A laser and a detector.- A laser and a beam splitter.- A Mach-Zehnder interferometer.- The breakdown of classical concepts.
Chapter 2: Photons and Interference.- Photon paths and superpositions.- The beam splitter as a matrix.- The phase in an interferometer.- How to calculate probabilities.- Gravitational wave detection.
Chapter 3: Electrons with Spin.- The Stern-Gerlach experiment.- The spin observable.- The Bloch sphere.- The uncertainty principle.- Magnetic resonance imaging.
Chapter 4: Atoms and Energy.- The energy spectrum of atoms.- Changes over time.- The Hamiltonian.- Interactions.- Atomic clocks.
Chapter 5: Operators.- Eigenvalue problems.- Observables.- Evolution.- The commutator.- Projectors.
Chapter 6: Entanglement.- The state of two electrons.- Entanglement.- Quantum teleportation.- Quantum computers.
Chapter 7: Decoherence.- Classical and quantum uncertainty.- The density matrix.- Interactions with the environment.- Entropy and Landauer's principle.
Chapter 8: The Motion of Particles.- A particle in a box.- The momentum of a particle.- The energy of a particle.- The scanning tunneling microscope.- Chemistry.
Chapter 9: Uncertainty Relations.- Quantum uncertainty revisited.- Position-momentum uncertainty.- The energy-time uncertainty relation.- The quantum mechanical pendulum.- Precision measurements.
Chapter 10: The Nature of Reality.- The emergent classical world.- The quantum state revisited.- Nonlocality.- Contextuality.- A compendium of interpretations.
Format: Paperback / softback, 300 pages, height x width: 240x168 mm,
16 Illustrations, black and white; XIV, 300 p. 16 illus.
Series: Frontiers in Mathematics
Pub. Date: 18-Dec-2022
ISBN-13: 9783031164965
This monograph thoroughly explores the development of the theory of varieties of semigroups and of two related algebras: involution semigroups and monoids. Through this in-depth analysis, readers will attain a deeper understanding of the differences between these three types of varieties, which may otherwise seem counterintuitive. New results with detailed proofs are also presented that answer previously unsolved fundamental problems. Featuring both a comprehensive overview as well as highlighting the author's own significant contributions to the area, this book will help establish this subfield as a matter of timely interest. Advances in the Theory of Varieties of Semigroups will appeal to researchers in universal algebra and will be particularly valuable for specialists in semigroups.
Historical overview and main results.- Preliminaries. Part I - Semigroups.- Aperiodic Rees-Suschkewitsch varieties.- A problem of Pollak and Volkov on hereditarily finitely based identities.- Sufficient conditions for the non-finite basis property.- Semigroups without irredundant identity bases.- Part II - Involution Semigroups.- Involution semigroups with infinite irredundant identity bases.- Finitely based involution semigroups with non-finitely based reducts.- Counterintuitive examples of involution semigroups.- Equational theories of twisted involution semigroups.- Part III - Monoids.- Hereditarily finitely based varieties of monoids.- Varieties of aperiodic monoids with central idempotents.- Certain Cross varieties of aperiodic monoids with commuting idempotents.- Counterintuitive examples of monoids.
Format: Hardback, 330 pages, height x width: 235x155 mm, 10 Tables, color; 7 Illustrations,
color; 16 Illustrations, black and white; XVIII, 330 p. 23 illus., 7 illus. in color.
Pub. Date: 06-Dec-2022
ISBN-13: 9783031139901
This book is devoted to the construction of space group representations, their tabulation, and illustration of their use. Representation theory of space groups has a wide range of applications in modern physics and chemistry, including studies of electron and phonon spectra, structural and magnetic phase transitions, spectroscopy, neutron scattering, and superconductivity. The book presents a clear and practical method of deducing the matrices of all irreducible representations, including double-valued, and tabulates the matrices of irreducible projective representations for all 32 crystallographic point groups. One obtains the irreducible representations of all 230 space groups by multiplying the matrices presented in these compact and convenient to use tables by easily computed factors. A number of applications to the electronic band structure calculations are illustrated through real-life examples of different crystal structures. The book's content is accessible to both graduate and advanced undergraduate students with elementary knowledge of group theory and is useful to a wide range of experimentalists and theorists in materials and solid-state physics.
Scope and Overview.- Mathematical Preliminaries.- Induced Representations.- Projective Representations.- Representations of the Space Groups.- Tables.- Group Theory and Quantum Mechanics.
Format: Hardback, 623 pages, height x width: 235x155 mm, 1 Tables, color; 1 Illustrations,
color; 1 Illustrations, black and white; XVIII, 623 p. 2 illus., 1 illus. in color
Pub. Date: 14-Dec-2022
ISBN-13: 9783031144585
This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.
Partial Sums of Vilenkin-Fourier Series in Lebesgue Spaces.- Martingales and Almost Everywhere Convergence of Partial sums of Vilenkin-Fourier Series.- Vilenkin-Fejer means and an Approximate Identity in Lebesgue Spaces.- Norlund and T Means of Vilenkin-Fourier series in Lebesgue Spaces.- Theory of Martingale Hardy Spaces.- Vilenkin-Fourier Coefficients and Partial Sums in Martingale Hardy Spaces.- Vilenkin-Fejer Means in Martingale Hardy Spaces.- Norlund and T Means of Vilenkin-Fourier Series in Martingale Hardy Spaces.- Convergence of Vilenkin-Fourier Series in Variable Martingale Hardy Spaces.- Appendix: Dyadic Group and Walsh and Kaczmarz Systems.
Format: Hardback, 310 pages, height x width: 235x155 mm, 61 Illustrations,
color; 22 Illustrations, black and white; X, 310 p. 83 illus., 61 illus. in color.
Series: Contributions to Statistics
Pub. Date: 04-Dec-2022
ISBN-13: 9783031141966
This book presents a selection of peer-reviewed contributions on the latest developments in time series analysis and forecasting, presented at the 7th International Conference on Time Series and Forecasting, ITISE 2021, held in Gran Canaria, Spain, July 19-21, 2021. It is divided into four parts. The first part addresses general modern methods and theoretical aspects of time series analysis and forecasting, while the remaining three parts focus on forecasting methods in econometrics, time series forecasting and prediction, and numerous other real-world applications. Covering a broad range of topics, the book will give readers a modern perspective on the subject. The ITISE conference series provides a forum for scientists, engineers, educators and students to discuss the latest advances and implementations in the foundations, theory, models and applications of time series analysis and forecasting. It focuses on interdisciplinary research encompassing computer science, mathematics, statistics and econometrics.
Preface.- Part 1 Theoretical Aspects of Time Series.- Part 2 Econometrics and Forecasting.- Part 3 Time Series Prediction Applications.- Part 4 Advanced Applications in Time Series Analysis.
Format: Paperback / softback, 140 pages, height x width: 235x155 mm, X, 140 p.,
Series: Lecture Notes in Mathematics 2322
Pub. Date: 09-Jan-2023
ISBN-13: 9783031177811
This book is essentially a survey of results on the Fuglede-Putnam theorem and its generalizations in a wide variety of directions. Presenting a broad overview of the results obtained in the field since the early 1950s, this is the first monograph to be dedicated to this powerful tool and its variants. Starting from historical notes and classical versions with their different proofs, the book then explores asymptotic versions, generalizations to non-normal operators, generalizations to unbounded operators, counterexamples, applications, intertwining relations, and conjectures. A rich collection of applications is included. Aimed at postgraduate students as well as researchers interested in operator theory, this book could also be taught as a specialized course.
Preliminaries.- Classical versions and some historical notes.- Generalizations to nonnormal operators. - Asymptotic versions.- Generalizations of the Fuglede-Putnam theorem to Banach spaces.- Generalizations to unbounded operators.- Some applications.- Some other intertwining relations.
Format: Hardback, 282 pages, height x width: 235x155 mm,
25 Illustrations, black and white; X, 282 p. 25 illus.
Series: Springer Monographs in Mathematics
Pub. Date: 21-Dec-2022
ISBN-13: 9783031183065
This book provides a comprehensive introduction to the Calculus of Variations and its use in modelling mechanics and physics problems. Presenting a geometric approach to the subject, it progressively guides the reader through this very active branch of mathematics, accompanying key statements with a huge variety of exercises, some of them solved. Stressing the need to overcome limitations of the initial point of view, and emphasising the interconnectivity of various branches of mathematics (algebra, analysis and geometry), the book includes some advanced material to challenge the most motivated students. Systematic, short historical notes provide details on the subject's odyssey, and how new tools have been developed over the last two centuries. This English translation updates a set of notes for a course first given at the Ecole polytechnique in 1987. It will be accessible to graduate students and advanced undergraduates.
Part I The Analytic Setting.- A First Generalisation of the Notion of Space: Spaces of Infinite Dimension.- Banach Spaces and Hilbert Spaces.- Linearisation and Local Inversion of Differentiable Maps.- Part II The Geometric Setting.- Some Applications of Differential Calculus.- New Generalisation of the Notion of a Space: Configuration Spaces.- Tangent Vectors and Vector Fields on Configuration Spaces.- Regular Points and Critical Points of Numerical Functions.- Part III The Calculus of Variations.- Configuration Spaces of Geometric Objects.- The Euler-Lagrange Equations.- The Hamiltonian Viewpoint.- Symmetries and Conversation Laws.- Appendix: Basic Elements of Topology.- References.- Notation Index.- Subject Index.
Format: Hardback, 440 pages, height x width: 235x155 mm, 3 Tables, color; 4 Illustrations, color; X, 440 p. 4 illus. in color.
Series: Trends in Mathematics
Pub. Date: 25-Jan-2023
ISBN-13: 9783031200205
This book collects selected peer reviewed papers on the topics of Nonlinear Analysis, Functional Analysis, (Korovkin-Type) Approximation Theory, and Partial Differential Equations. The aim of the volume is, in fact, to promote the connection among those different fields in Mathematical Analysis. The book celebrates Francesco Altomare, on the occasion of his 70th anniversary.
On Wachnicki's generalization of the Gauss-Weierstrass integral.- Generalized subharmonic and weakly convex functions.- A strong variant of Weyl's theorem under functional calculus and perturbations.- Multiplication and convolution topological algebras in spaces of !-ultradifferentiable functions of Beurling type.- Higher Order Elliptic Equations in Generalized Morrey Spaces.- Norm and essential norm of composition operators mapping into weighted Banach spaces of harmonic mappings.- Generalized Gaussian estimates for elliptic operators with unbounded coefficients on domains.- An existence result for perturbed (p,q)--quasilinear elliptic problems.- Weighted composition operators on weighted spaces of Banach valued analytic functions.- Existence of positive solutions of nonlinear second order Dirichlet problems perturbed by integral boundary conditions.- A degenerate operator in non divergence form.- Korovkin approximation of set-valued integrable functions.- Convergence of a class of generalized sampling Kantorovich operators perturbed by multiplicative noise.- A modification of Bernstein-Durrmeyer operators with Jacobi weights on the unit interval.- On a particular scaling for the prototype anisotropic p-Laplacian.- A deformation theory in augmented spaces and concentration results for NLS equations around local maxima.- Some Geometric Observations on Heat Kernels of Markov Semigroups with Non-local Generators.- On a class of nonautonomous problems extending the Black-Scholes equation.- On oscillatory behavior of Third order half-linear difference equations.- Existence of bounded solutions for a weighted.- Elliptic and Parabolic problems for a Bessel-type operator.- Anisotropic (1)p; q-Equations with Convex and Negative Concave Terms.- Implicit Coupled k-Generalized -Hilfer Fractional Differential Systems with Terminal Conditions in Banach spaces.