Mathematische Physik

This book presents the iterative beauty of fractals and fractal functions graphically with the aid of MATLAB programming. The fractal images generated using the MATLAB codes provide visual delight and highly encourage the fractal lovers for creative thinking. The book compiles five cutting-edge research chapters, each with state-of-the art fractal illustrations. It starts with the fundamental theory for the construction of fractal sets via the deterministic iteration algorithm. Incorporating the theoretical base, fractal illustrations of elementary fractal sets are provided with the explicit MATLAB code. The book gives examples of MATLAB codes to present the fractal surfaces.This book is contributed to all the research beginners as well as the professionals on the field of fractal analysis. As it covers basic fractals like Sierpinski triangle to advanced fractal functions with explicit MATLAB code, the presented fractal illustrations hopefully benefit even the non-field readers. The book is a useful course to all the research beginners on the fractal and fractal-related fields.

This book is developed primarily from the author's 20 years of teaching the course at his own university. It addresses both theory and applications, interweaving application with theory throughout the text. The author links ordinary differential equations with advanced mathematical topics such as differential geometry, Lie group theory, analysis in infinite-dimensional spaces and even abstract algebra. The revised edition includes considerable new material; the impressive array of exercises has been more than doubled in size and enhanced in scope.

The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum fi eld theory. It offers an introduction to calculations with Wilson lines, and shows the recent development of the subject in different important areas of research within the historical context.

"Bridging Quantum and Classical: A Path Integral Journey" delves into the fascinating concept of Feynman Path Integrals. Unlike the strange ideas often associated with quantum mechanics, path integrals offer an intuitive bridge between the familiar world of classical mechanics and the bizarre realm of the quantum. This book explains how particles, unlike billiard balls on a table, explore every possible path between two points, with some paths influencing the outcome more than others. Through this path integral approach, you'll gain a deeper understanding of the quantum world and its connection to our everyday reality.

HC gerader Rücken kaschiert

This book provides an up-to-date account of current research in quantum information theory, at the intersection of theoretical computer science, quantum physics, and mathematics. The book confronts many unprecedented theoretical challenges generated by infinite dimensionality and memory effects in quantum communication. The book will also equip readers with all the required mathematical tools to understand these essential questions.

This book highlights the fundamental physics of orbit theory, dynamical models, methods of orbit determination, design, measurement, adjustment, and complete calculations for the position, tracking, and prediction of satellites and deep spacecraft. It emphasizes specific methods, related mathematical calculations, and worked examples and exercises. Therefore, technicians and engineers in the aerospace industry can directly apply them to their practical work. Dedicated to undergraduate students and graduate students, researchers, and professionals in astronomy, physics, space science, and related aerospace industries, the book is an integrated work based on the accumulated knowledge in satellite orbit dynamics and the author's more than five decades of personal research and teaching experience in astronomy and aerospace dynamics.

This book deals with theoretical mechanics. Newton published the "Philosophiæ Naturalis Principia Mathematica" in 1687. In it, he sets out the basic principles of physics that are required to understand the motion of the planets, their moons, and the comets in the solar system. It includes the gravitational (inverse square) law, the inertial principle, and the basic elements of mechanics. Since its publication, a large number of refinements and reformulations have been introduced, thereby adding enormous insight into the structure of mechanics, which is commonly known as "classical mechanics". All these have in common that by taking a suitable limit, Newton's original principles re-appear. Thus, physicists and mathematicians who work on the subject always have a notion that if their theories do not return to Newton's foundations, then there is something wrong. Newton himself acknowledged that 'if I have seen further (than others), it is by standing on the shoulders of giants'. One of these giants was undoubtedly Galileo who died in the year Newton was born. So, Newton himself adhered to the 'classical limit'.

This book undertakes an extensive exploration of manganese-based compounds, such as T¿¿¿SrxMnO¿ (T = La, Pr; x = 0.35, 0.25) using density functional theory and Monte Carlo simulations with a focus on understanding their electronic, magnetic, and magnetocaloric properties. Bä¿¿SrxFeO¿ (x = 0, 0.2) is also studied via different approximations, offering a comparative perspective. In addition, the book looks at the influence of magnetism using Monte Carlo simulations, revealing crucial parameters and examining the GdCrO¿ system through DFT and Monte Carlo simulation, shedding light on recent experimental observations. Additionally, Monte Carlo studies investigate magnetic and magnetocaloric features of Sr¿FeMoO¿, LäSrMn¿O¿ bilayer manganite, perovskite ferromagnetic thin films' surface effects, and SmFe¿¿¿MnxO¿ perovskite. In essence, this book significantly advances our comprehension of magnetic and magnetocaloric phenomena across diverse materials and is well-suited for both experimentalists and computational researchers working in this field.

This work presents some essential techniques that constitute the modern strategy for computing scattering amplitudes. It begins with an introductory chapter to fill the gap between a standard QFT course and the latest developments in the field. The author then tackles the main bottleneck: the computation of the loop Feynman integrals. The most efficient technique for their computation is the method of the differential equations. This is discussed in detail, with a particular focus on the mathematical aspects involved in the derivation of the differential equations and their solution. Ample space is devoted to the special functions arising from the differential equations, to their analytic properties, and to the mathematical techniques which allow us to handle them systematically. The thesis also addresses the application of these techniques to a cutting-edge problem of importance for the physics programme of the Large Hadron Collider: five-particle amplitudes at two-looporder. It presents the first analytic results for complete two-loop five-particle amplitudes, in supersymmetric theories and QCD. The techniques discussed here open the door to precision phenomenology for processes of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.

This book is based on the analysis of canonical commutation relations (CCRs) and their possible deformations. In light of the recent interest on PT-quantum mechanics, the author presents a special deformed version of the CCRs, and discusses the consequences of this deformation both from a mathematical side, and for its possible applications to physics. These include the analysis of several non self-adjoint Hamiltonians, a novel view to the position and momentum operators, and a general approach to compute path integrals and transition probabilities using the so-called bi-coherent states. The book is meant for researchers and is also suited for advanced students. It can be used as a gentle introduction to some delicate aspects in functional analysis and in quantum mechanics for non self-adjoint observables.

This book highlights the mathematical models and solutions of the generalized dynamics of soft-matter quasicrystals (SMQ) and introduces possible applications of the theory and methods. Based on the theory of quasiperiodic symmetry and symmetry breaking, the book treats the dynamics of individual quasicrystal systems by reducing them to nonlinear partial differential equations and then provides methods for solving the initial-boundary value problems in these equations. The solutions obtained demonstrate the distribution, deformation and motion of SMQ and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. The reader benefits from a detailed comparison of the mathematical solutions for both solid and soft-matter quasicrystals, gaining a deeper understanding of the universal properties of SMQ. The second edition covers the latest research progress on quasicrystals in topics such as thermodynamic stability, three-dimensional problems and solutions, rupture theory, and the photonic band-gap and its applications. These novel chapters make the book an even more useful and comprehensive reference guide for researchers in condensed matter physics, chemistry and materials sciences.

A brief description of Cosmology.- Topological Defects.- Supercomputing with Graphics Processing Units.- Calibration of Extended VOS models.- Strings in U(1)_L x U(1)_L simulations.- A New Generation of String Simulations.

This open access book offers a concise overview of how data from large scale experiments are analyzed and how technological tools are used in practice, as in the search for new elementary particles. It focuses on interconnects between physics and detector technology in experimental particle physics, and includes descriptions of mathematical approaches. Readers find all the important steps in analysis, including reconstruction of the momentum and energy of particles from detector information, particle identification, and also the general concept of simulating particle production from collisions and detector responses. As the scale of scientific experiments becomes larger and data-intensive science emerges, the techniques used in the data analysis become ever more complicated, making it difficult for beginners to grasp the overall picture. The book provides an explanation of the idea and concepts behind the methods, helping readers understand journal articles on high energy physics. This book is engaging as it does not overemphasize mathematical formalism and it gives a lively example of how such methods have been applied to the Higgs particle discovery in the Large Hadron Collider (LHC) experiments, which led to Englert and Higgs being awarded the Nobel Prize in Physics for 2013.Graduate students and young researchers can easily obtain the required knowledge on how to start data analyses from these notes, without having to spend time in consulting many experts or digesting huge amounts of literature.

This book compactly provides the fundamentals of experimental physics for students of the natural sciences who are taking physics as a minor or major subject. Interspersed throughout the main text are numerous exercises with pre-calculated solutions, and the most important formulas are listed again at the end of each chapter. This book enables readers to gain an overview of the individual areas and is thus ideally suited to accompany lectures during studies as well as for exam preparation.The textbook originated from a lecture on "Experimental Physics for Natural Scientists" at the University of Tübingen and is intended for all students in subjects such as biochemistry, bioinformatics, biology, chemistry, computer science, mathematics, pharmacy, geoecology, and earth sciences.The first part of the book deals with Newtonian mechanics including continuum mechanics and oscillations and waves. The second part deals with the basic concepts of thermodynamics with emphasis onthe statistical explanations. The third part covers electromagnetic phenomena, especially electrostatics and magnetostatics, electrodynamics, and an introduction to electronic components and circuits. Optics with its subfields, ray optics, wave optics, and quantum optics, is presented in the fourth part. In the fifth and last part of the book, the reader is given an overview of the basic principles of quantum mechanics, including atomic and nuclear physics. For this second edition, the content has been improved and supplemented in many places, including a new section on heat transport and phase transitions, as well as an outlook into alternative interpretations of quantum mechanics.

Will artificial intelligence make scientific formulae redundant by eventually solving all current and future physical problems? The authors of this book would argue that there is still a vital role for humans to play in making sense of the laws of nature. To derive a formula one follows a series of steps, only the last of which is to check that the result is correct. The book is about unravelling this machinery.Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject: familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Learners could lose motivation, not seeing the wood for the trees.This two-volume book How to Derive a Formula is an attempt to engage learners by presenting mathematical methods in as simple terms as possible, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigour, it teaches students from scratch using pertinent examples, many taken from across the physical sciences to demonstrate the application of the methods taught.This book draws on humour and historical facts to provide an interesting new perspective on what a mathematics textbook could be. The two volumes are presented as an ascent to Everest. Volume 1 covered the necessary basics, taking readers from Base Camp to Camps 1 and 2. This volume moves readers from Camp 2 up to Camps 3 and 4, tackling more advanced methods for deriving formulae. Inevitably, Volume 2 requires readers to tackle more challenging terrain than was experienced in Volume 1 and so is targeted at more advanced students.

This book describes the computational methods most frequently used to deal with the interaction of charged particles, notably electrons, with condensed matter. Both elastic and inelastic scattering phenomena are discussed, and methods for calculating the relevant cross sections are explained in a rigorous but simple way. It provides readers with all the information they need in order to write their own Monte Carlo code and to simulate the transport of fast particles in condensed matter. Many numerical and experimental examples are presented throughout the book.The updated and extended fourth edition features ab initio methods for calculating dielectric function and energy loss function. Non-relativistic partial wave expansion method for calculating the differential elastic scattering cross section is also included in this new edition. It represents a very useful introduction to the relativistic partial wave expansion method, i.e., to the Mott theory, already discussed inthe previous editions of this book. Further details about the effects of spin-polarization on the differential elastic scattering cross section are included in this new edition. The multiple reflection method is extended to the general case of a system composed of a set of layers of different materials and thicknesses. Analytical expressions are provided for calculating the backscattering coefficient of multilayers. New results are presented, notably about Monte Carlo simulations of reflection electron energy loss spectra and of the radial dose deposited along the track of ions impinging on materials.

In the present era, many methods for modeling and qualitative analysis of various kinds of mathematical and wireless systems are available. These analyzing methods show how to use predictive computational models to acquire and analyze knowledge about these systems. The book covers real-life examples of continuous computational scenarios. This book aims to capture new developments in the mathematical modeling of systems, as well as the performance computation of wireless networks. For more details, please visit https://centralwestpublishing.com

Distant galaxies, dark matter, black holes - elusive, incomprehensible and inhospitable - these are the building blocks of modern physics. But where do we fit in this picture?'A delightful account of one of the deepest and most fascinating explorations going on today.' CARLO ROVELLI, AUTHOR OF WHITE HOLESFor centuries, we have separated mind from matter. While physicists have pursued a theory of 'everything' with single-minded purpose, the matter of the mind, of human consciousness, has been conveniently sidestepped and ignored - consigned to priests, philosophers and poets.With the ambition of Stephen Hawking, Carlo Rovelli and Brian Cox, Putting Ourselves Back in the Equation sets out a bold new vision for theoretical physics, unrestricted by sleek equations and neat formulations. Combining cutting-edge neuroscience with the latest in quantum mechanics, acclaimed writer Musser offers a new interpretation of human consciousness. From bizarre cognitive phenomena, like lucid dreaming and self-taught synaesthesia, to the latest technological developments in AI, Musser asks: what can physics teach us about what it means to be human?***'The renowned science writer George Musser has taken on one of our time's greatest issues: AI, how it works, and what makes it so powerful. This masterfully written book shows a surprising connection with theoretical physics.' MAX TEGMARK, AUTHOR OF LIFE 3.0'Musser is to be applauded for tackling both consciousness and the quantum realm... He joins a distinguished list of thinkers... Musser's book is readable and enthusiastic, packed with first-person anecdotes.' TLS'In this captivating book, George Musser takes us on a fascinating tour of the modern, surprising connections scientists discover between the cosmos and our inner world of consciousness.' MARIO LIVIO, AUTHOR OF THE GOLDEN RATIO

This book includes contributions about mathematics, physics, philosophy of science, economics and finance and resulted from the Summer School "Complexity and Emergence: Ideas, Methods, with a Special Attention to Economics and Finance" held in Lake Como School of Advanced Studies, on 22-27 July 2018.The aim of the book is to provide useful instruments from the theory of complex systems, both on the theoretical level and the methodological ones, profiting from knowledge and insights from leading experts of different communities. It moves from the volume editors' conviction that to achieve progress in understanding socio-economical as well as ecological problems of our complex word such preparation is needed, together with a critical reconsideration of our basic scientific and economical approach.The potential readers are primarily master and doctorate students of mathematics, information sciences, theoretical physics and economics, as well as research workers in those areas, who want to enlarge their spectrum of knowledge towards the area of complexity and emergence. Since ideas and methods of the theory of complex systems also apply to other areas (from engineering and architecture to biology and medicine, e.g.), students and research workers from those areas will also profit from this book.

The "holy grail" of physics is quantum gravity, often called the theory of everything. But any scientific theory will be incomplete without the God of the Bible. Physicists claim the cosmos began with a big bang created from nothing. But the word nothing is meaningless in physics. Furthermore, the big bang is an impenetrable barrier to whatever preceded it. In addition, a finite cosmos cannot contain within itself an explanation for its own existence. To claim we are here by accident explains nothing and leads to a logical dead end.The cause of the universe is information in the form of mathematical laws left behind for science to discover. The fundamental properties of these laws have the same attributes as the Supreme Lawgiver of Genesis. An intelligible cosmos is unmistakable evidence the Creator is an Intelligent Mind. The Creator's Voice is a valid scientific theory confirming the truth of Genesis; God spoke the laws creating the universe out of nothing, creatio ex nihilo. The foundation of the universe is ethereal cosmic waves which interact according to the laws to create and sustain the illusion of reality we experience. Space, time, energy and matter are made from quantum information; nothing else is needed. By a process of elimination, God is the only possible explanation for everything we know.The human mind is evidence consciousness is endemic to the cosmos. Cosmic waves interact with the human mind in mysterious ways. The cosmos relates to humans more like a great Mind than a mindless machine. The god-like nature of the human mind is evidence; we are made imago Dei. Even if God is included in a scientific theory, it means little unless it can be shown God is a real Being, alive, present in the world and relevant to our lives.

The idea for this text emerged over several years as the authors participated in research projects related to analysis of data from NASA's RHESSI Small Explorer mission. The data produced over the operational lifetime of this mission inspired many investigations related to a specific science question: the when, where, and how of electron acceleration during solar flares in the stressed magnetic environment of the active Sun.A vital key to unlocking this science problem is the ability to produce high-quality images of hard X-rays produced by bremsstrahlung radiation from electrons accelerated during a solar flare. The only practical way to do this within the technological and budgetary limitations of the RHESSI era was to opt for indirect modalities in which imaging information is encoded as a set of two-dimensional spatial Fourier components. Radio astronomers had employed Fourier imaging for many years. However, differentlythan for radio astronomy, X-ray images produced by RHESSI had to be constructed from a very limited number of sparsely distributed and very noisy Fourier components. Further, Fourier imaging is hardly intuitive, and extensive validation of the methods was necessary to ensure that they produced images with sufficient accuracy and fidelity for scientific applications.This book summarizes the results of this development of imaging techniques specifically designed for this form of data. It covers a set of published works that span over two decades, during which various imaging methods were introduced, validated, and applied to observations. Also considering that a new Fourier-based telescope, STIX, is now entering its nominal phase on-board the ESA Solar Orbiter, it became more and more apparent to the authors that it would be a good idea to put together a compendium of these imaging methods and their applications. Hence the book you are now reading.

This book bridges the huge gap between popular science and mathematical treatments of Einstein's theories. It explains special and general relativity, gravity, black holes, and gravitational waves, also presenting current ideas about dark matter and dark energy. The explanations are entirely non-mathematical, using many color pictures and clear concepts. In this way, the reader is led to a much deeper understanding than any popular science book can provide. The author has written this book for everyone who wants to go beyond superficial descriptions of relativity's remarkable phenomena, but is not equipped to read the professional literature and complicated math behind the theory. By providing a complete description in terms of concepts and pictures, the book answers many questions about why the theory works as it does. For example, it explains why and how momentum and pressure are related to gravity; why and how mass causes spacetime to curve and how curvature tells objects how to move; it also reveals the origin of the ring seen around the first ever image of a black hole. Not least, the reader will learn in detail how gravitational waves are produced and measured.Since their conception, the theories of relativity have appealed to the public's imagination. Thanks to this book, readers now have the opportunity to convert their fascination with the topic to a deep understanding.