Matematisk fysik

This book celebrates the life and work of the late Giovanni Morchio (1944¿2021). It features scientific and anecdotal contributions written by his former colleagues, co-authors, and students, as well as senior scientists who were active witnesses to the dramatic advances in physics and in mathematics that took place during his 50-year-long career. The volume begins with a biographical introduction, detailing Giovanni Morchiös life and his role as a physicist, mathematician, teacher, and scientist. The core of the book covers a vast spectrum of ideas, reflecting Dr Morchiös scientific interests. Each chapter develops a specific topic of modern research, ranging from quantum mechanics and quantum field theory to additional themes such as the connection between general relativity and Newtonian gravitation. Every contribution provides a historical retrospective, a survey of advances, an outlook of future perspectives and challenges, and an updated bibliography. The last part collects the authors¿ recollections of their professional and personal interactions with Dr Morchio, in recognition of his deep achievements, his exceptional pedagogical qualities, and his praiseworthy social and pro bono commitment. Authored by physicists of international calibre covering a broad range of subjects, the book will be a valuable reference for researchers and students of theoretical and mathematical physics.

This volume celebrates the 100th birthday of Professor Chen-Ning Frank Yang (Nobel 1957), one of the giants of modern science and a living legend. Starting with reminiscences of Yang's time at the research centre for theoretical physics at Stonybrook (now named C. N. Yang Institute) by his successor Peter van Nieuwenhuizen, the book is a collection of articles by world-renowned mathematicians and theoretical physicists. This emphasizes the Dialogue Between Physics and Mathematics that has been a central theme of Professor Yang's contributions to contemporary science. Fittingly, the contributions to this volume range from experimental physics to pure mathematics, via mathematical physics. On the physics side, the contributions are from Sir Anthony Leggett (Nobel 2003), Jian-Wei Pan (Willis E. Lamb Award 2018), Alexander Polyakov (Breakthrough Prize 2013), Gerard 't Hooft (Nobel 1999), Frank Wilczek (Nobel 2004), Qikun Xue (Fritz London Prize 2020), and Zhongxian Zhao (Bernd T. Matthias Prize 2015), covering an array of topics from superconductivity to the foundations of quantum mechanics. In mathematical physics there are contributions by Sir Roger Penrose (Nobel 2022) and Edward Witten (Fields Medal 1990) on quantum twistors and quantum field theory, respectively. On the mathematics side, the contributions by Vladimir Drinfeld (Fields Medal 1990), Louis Kauffman (Wiener Gold Medal 2014), and Yuri Manin (Cantor Medal 2002) offer novel ideas from knot theory to arithmetic geometry.Inspired by the original ideas of C. N. Yang, this unique collection of papers b masters of physics and mathematics provides, at the highest level, contemporary research directions for graduate students and experts alike.

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.

Light signals in optical waveguides can be used to transmit very large amounts of data quickly and largely without interference. In the industrial and infrastructural sectors, e.g. in the automotive and aerospace industries, the demand to further exploit this potential is therefore increasing. Which technologies can be used to effectively integrate systems that transmit data by means of light into existing components? This is a central question for current research. So far, there have been some technical limitations in this regard. For example, it is difficult to couple the signal of an optical waveguide to other optical waveguides without interruption. There is also a lack of suitable fabrication technologies for three-dimensional waveguides, as well as design and simulation environments for 3D opto-MID. This book addresses these and other challenges.

Despite successes of modern physics, the existence of dark energy and matter is indicative that conventional mechanical accounting is lacking. The most basic of all mechanical principles is Newton's second law, and conventionally, energy is just energy whether particle or wave energy. In this monograph, Louis de Broglie's idea of simultaneous existence of both particle and associated wave is developed, with a novel proposal to account for mass and energy through a combined particle-wave theory. Newton's second law of motion is replaced by a fully Lorentz invariant reformulation inclusive of both particles and waves.  The model springs from continuum mechanics and forms a natural extension of special relativistic mechanics. It involves the notion of "e;force in the direction of time"e; and every particle has both particle and wave energies, arising as characteristics of space and time respectively. Dark matter and energy then emerge as special or privileged states occurring for alignments of spatial forces with the force in the direction of time. Dark matter is essentially a backward wave and dark energy a forward wave, both propagating at the speed of light.  The model includes special relativistic mechanics and Schrodinger's quantum mechanics, and the major achievements of mechanics and quantum physics.  Our ideas of particles and waves are not yet properly formulated, and are bound up with the speed of light as an extreme limit and particle-wave demarcation. Sub-luminal particles have an associated superluminal wave, so if sub-luminal waves have an associated superluminal particle, then there emerges the prospect for faster than light travel with all the implications for future humanity. Carefully structured over special relativity and quantum mechanics, Mathematics of Particle-Wave Mechanical Systems is not a completed story, but perhaps the first mechanical model within which such exalted notions might be realistically and soberly examined. If ultimately the distant universe become accessible, this will necessitate thinking differently about particles, waves and the role imposed by the speed of light. The text constitutes a single proposal in that direction and a depository for mathematically related results.  It will appeal to researchers and students of mathematical physics, applied mathematics and engineering mechanics. 

This book reports on innovative research in solid and fluid mechanics, and thermal engineering, giving a special emphasis on methods, modeling, and simulation tools for analyzing material behavior and energy systems. It gathers the best papers presented at 15th International Moroccan Congress of Mechanics "Congrès de Mécanique", CMM 2022, held on May 24-27, 2022, in Casablanca, Morocco, and organized by the Moroccan Society of Mechanics (SMSM) and the Faculty of Science Ain Chock of the University of Hassan II, Casablanca, Morocco. With a good balance of theory and practice, the book offers a timely snapshot of current advances in mechanics, and a source of inspiration for future research and international collaborations.

This wide-ranging book introduces information as a key concept not only in physics, from quantum mechanics to thermodynamics, but also in the neighboring sciences and in the humanities. The central part analyzes dynamical processes as manifestations of information flows between microscopic and macroscopic scales and between systems and their environment. Quantum mechanics is interpreted as a reconstruction of mechanics based on fundamental limitations of information processing on the smallest scales. These become particularly manifest in quantum chaos and in quantum computing. Covering subjects such as causality, prediction, undecidability, chaos, and quantum randomness, the book also provides an information-theoretical view of predictability. More than 180 illustrations visualize the concepts and arguments. The book takes inspiration from the author's graduate-level topical lecture but is also well suited for undergraduate studies and is a valuable resource for researchers and professionals.

The book explores cost-effective and efficient supply chain management to achieve resilience in the post-COVID environment. Qualitative, quantitative, case studies, and systematic literature reviews are made in the book. The book follows a didactic approach through which it informs global researchers and practitioners to deal with the most significant insights on future supply chains with a more in-depth analysis of post-COVID opportunities and challenges. In particular, this book provides an in-depth assessment of disruptive supply chain management in certain industrial contexts and explores various Industry 4.0 and Industry 5.0 technologies to achieve resilience.The book is used as a supplemental textbook for study within university level programs, at late undergraduate and graduate levels, in faculties of business and management, engineering systems, information systems, education, and computing.

This textbook provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments. Readers will be introduced to a variety of methods that reflect current trends in research, including the Bergman kernel approach for solving boundary value and spectral problems for PDEs with variable coefficients. With its careful treatment of the fundamentals as well as coverage of topics not often encountered in textbooks, this will be an ideal text for both introductory and more specialized courses.The first five chapters present standard material, including the classification of PDEs, an introduction to boundary value and initial value problems, and an introduction to the Fourier method of separation of variables. More advanced material and specialized treatments follow, including practical methods for solving direct and inverse Sturm-Liouville problems; the theory of parabolic equations, harmonic functions, potential theory, integral equations and the method of non-orthogonal series.Methods of Mathematical Physics is ideal for undergraduate students and can serve as a textbook for a regular course in equations of mathematical physics as well as for more advanced courses on selected topics.

In einer umfassenden Darstellung entwickeln und vertiefen die vier Bände dieses Lehrbuchs das Gebäude der nichtrelativistischen Quantenmechanik, weshalb sie auch bestens als Nachschlagewerk geeignet sind.Der vierte Band beginnt mit einem ausführlichen Kapitel zur nichtrelativistischen Quantenelektrodynamik (QED), traditionell als "Quantentheorie der Strahlung" bezeichnet, und leitet dann über in die relativistische Quantentheorie. Eine sorgfältige Behandlung der Möglichkeiten und Grenzen einer relativistischen Quantenmechanik sowie eine gründliche Untersuchung von Symmetrien in der relativistischen Quantentheorie schließen das Lehrbuch ab.Besonderheiten:Auch komplizierte Zusammenhänge werden illustrativ und klar erklärt. Zahlreiche mathematische Einschübe erläutern allgemeine mathematische Zusammenhänge. Besondere Highlights des Buches sind eine ausführliche Diskussionder Lamb-Verschiebung und des Casimir-Effekts, einschließlich der in diesem Zusammenhang offenbar werdenden Problematik der Renormierung, sowie die Analyse der Einteilchen-Interpretation in der relativistischen Quantenmechanik und die Betrachtung von Gruppenkontraktionen im Übergang von relativistischen zu nichtrelativistischen Symmetriegruppen und ihrer Darstellungen.Inhalt1. Quantisierung des elektromagnetischen Feldes - 2. Relativistische Quantenmechanik - 3. Symmetrien in der Quantenmechanik IIZielgruppe:Das Buch richtet sich sowohl an Bachelor- als auch an Masterstudierende sowie ihre Lehrenden. Aufgrund seines mehrbändigen Charakters, der breiten Themenvielfalt und Bezügen zu wissenschaftlichen Originalarbeiten allerdings ein Muss für jedes Bücherregal einer in der Physik tätigen Person.Vorkenntnisse:Vorausgesetzt werden Kenntnisse der Theoretischen Mechanik, der Elektrodynamik und der Speziellen Relativitätstheorie, sowie der Analysis, der linearen Algebra und der Funktionentheorie.

This book provides a comprehensive yet informal introduction to differentiating and integrating real functions with one variable. It also covers basic first-order differential equations and introduces higher-dimensional differentiation and integration. The focus is on significant theoretical proofs, accompanied by illustrative examples for clarity. A comprehensive bibliography aids deeper understanding. The concept of a function's differential is a central theme, relating to the "differential" within integrals. The discussion of indefinite integrals (collections of antiderivatives) precedes definite integrals, naturally connecting the two. The Appendix offers essential math formulas, exercise properties, and an in-depth exploration of continuity and differentiability. Select exercise solutions are provided. This book suits short introductory math courses for novice physics/engineering students. It equips them with vital differentialand integral calculus tools for real-world applications. It is also useful for first-year undergraduates, reinforcing advanced calculus foundations for better Physics comprehension.

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.

This textbook gradually introduces the reader to several topics related to black hole physics with a didactic approach. It starts with the most basic black hole solution, the Schwarzschild metric, and discusses the basic classical properties of black hole solutions as seen by different probes. Then it reviews various theorems about black hole properties as solutions to Einstein gravity coupled to matter fields, conserved charges associated with black holes, and laws of black hole thermodynamics. Next, it elucidates semiclassical and quantum aspects of black holes, which are relevant in ongoing and future research. The book is enriched with many exercises and solutions to assist in the learning.The textbook is designed for physics graduate students who want to start their research career in the field of black holes; postdocs who recently changed their research focus towards black holes and want to get up-to-date on recent and current research topics; advanced researchers intending to teach (or learn) basic and advanced aspects of black hole physics and the associated mathematical tools. Besides general relativity, the reader needs to be familiar with standard undergraduate physics, like thermodynamics, quantum mechanics, and statistical mechanics. Moreover, familiarity with basic quantum field theory in Minkowski space is assumed. The book covers the rest of the needed background material in the main text or the appendices.

Dieses Lehrbuch behandelt präzise und ausführlich die klassische Elektrodynamik, wie sie für das Physik-Studium erforderlich ist. Es beginnt mit einer detaillierten Beschreibung der Maxwell-Gleichungen, so dass die Grundlagen für die verschiedenen Anwendungsgebiete geschaffen sind: Elektro- und Magnetostatik im Vakuum und in Materie und die Strahlung elektromagnetischer Wellen. Gerade der dynamischen Theorie der Röntgenstrahlung und der speziellen Relativitätstheorie wird dabei ein längerer Abschnitt eingeräumt. Zudem schlägt das Werk in vielen Bereichen eine Brücke zu den entsprechenden Fragestellungen der Festkörperphysik.Die Herleitung einiger Formeln sowie weitere Fragestellungen finden sich am Ende eines jeden Kapitels in den Übungsaufgaben. Im Anhang findet sich eine umfangreiche Zusammenfassung der notwendigen mathematischen Grundlagen. In der vorliegenden vierten Auflage ist die Quantisierung des elektromagnetischen Feldes hinzugekommen.Aus dem InhaltDie Maxwell'schen Feldgleichungen ¿ Ruhende elektrische Ladungen und die Verteilung der Elektrizität auf Leitern ¿ Randwertprobleme in der Elektrostatik ¿ Magnetostatik im Vakuum ¿ Elektromagnetische Vorgänge in Materie ¿ Elektrostatik in Materie ¿ Magnetostatik in Materie ¿ Felder von bewegten Ladungen ¿ Quasistationäre Ströme ¿ Elektromagnetische Wellen ¿ Röntgenstreuung ¿ Spezielle Relativitätstheorie ¿ Kovariante Elektrodynamik ¿ Relativistische Mechanik

This new edition has been thoroughly revised, expanded and contain some updates function of the novel results and shift of scientific interest in the topics. The book has a Foreword by Jerry L. Bona and Hongqiu Chen. The book is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems.The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given.The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics.This book is intended for graduate students and researchers in mathematics, physics and engineering.

This book is a different approach to teaching the foundations of mathematical analysis and of computation. The main idea is to delay the use of "formal definitions", which are definitions that nobody can understand without working with them. The approach of this book is to employ the history of mathematics to first develop fundamental concepts of mathematical analysis and the theory of computation and to only introduce formal definitions after the concepts are understood by the students.The historical order clarifies what analysis is really about and also why the theory of computation came about. The book provides students with a broader background involving for instance glimpses of cardinal arithmetic, predicate logic background, as well as the importance of a sound theory of the infinitesimal (which is in essence the foundations of mathematics and computation).There is a wealth of exercises and numerous graphical illustrations which give an experienced instructor lots of possibilities to select a stimulating course with a broader background. Even for just browsing by general readers, this book presents stories, insights and mathematical theories, covering a window of ancient times to the present.The book is self explanatory and self sufficient, so any staff member in the departments of mathematics or computer science can teach this course.This book will give the students the right techniques and skills to work with mathematical analysis and the theory of computation and to go on further to study more advanced courses on the subject.

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

"Experts Plebaânski and Krasiânski provide a thorough introduction to the tools of general relativity and relativistic cosmology, guiding advanced students through complete derivations of the results. Starting with a short course on differential geometry, the main text describes relativity as a physical theory"--

Based on Jost function theory this book presents an approach useful for different types of quantum mechanical problems. These include the description of scattering, bound, and resonant states, in a unified way. The reader finds here all that is known about Jost functions as well as what is needed to fill the gap between the pure mathematical theory and numerical calculations. Some of the topics covered are: quantum resonances, Regge poles, multichannel scattering, Coulomb interaction, Riemann surfaces, multichannel analog of the effective range theory, one- and two-dimensional problems, many-body problems within the hyperspherical approach, just to mention few of them. These topics are relevant in the fields of quantum few-body theory, nuclear reactions, atomic collisions, and low-dimensional semiconductor nanostructures. In light of this, the book is meant for students, who study quantum mechanics, scattering theory, or nuclear reactions at the advanced level as well as for post-graduate students and researchers in the fields of nuclear and atomic physics. Many of the arguments that are traditional for textbooks on quantum mechanics and scattering theory, are covered here in a different way, using the Jost functions. This gives the reader a new insight into the subject, revealing new features of various mathematical objects and quantum phenomena.

Interaction of Disturbances in Shear Flows aims to provide a comprehensive, in-depth overview of the current state of knowledge on the subject. Authored by a recognized expert with decades of experience and many software patents to his credit, the volume covers advances in computational fluid dynamics to showcase innovative ways to apply physical measurements and visualization patterns to solve various aero- and hydrodynamic problems. It also delves into analytical methodologies to compare and contrast with the theoretical models most commonly used in the field. Additionally, it demonstrates the significance of comprehending and managing disturbances in shear flows, discussing practical applications of the research to optimize the design of aircraft, automotive vehicles, and marine vessels, with a strong emphasis on enhancing aero- and hydrodynamic efficiency, fuel economy, and the reduction of harmful emissions. Academia and industry readers alike will find this a useful resource to equip themselves with the tools needed to understand and address practical engineering challenges encountered in their studies or work.

This book provides the rigorous mathematical foundations of Quantum Physics, from the operational meaning of the measuring process to the most recent theories for the quantum scale of space-time geometry. Topics like relativistic invariance, quantum systems with finite and infinitely many degrees of freedom, second quantisation, scattering theory, are all presented through the formalism of Operator Algebras for a precise mathematical justification.The book is targeted to graduate students and researchers in the area of theoretical/mathematical physics who want to learn about the mathematical foundations of quantum physics, as well as the mathematics students and researchers in the area of operator algebras/functional analysis who want to dive into some of the applications of the theory to physics. 

In addition to expanding and clarifying a number of sections of the first edition, it generalizes the analysis that eliminates the noncausal pre-acceleration so that it applies to removing any pre-deceleration as well. It also introduces a robust power series solution to the equation of motion that produces an extremely accurate solution to problems such as the motion of electrons in uniform magnetic fields.

This book offers a primer on the fundamentals and applications of the Geroch-Held-Penrose (GHP) calculus, a powerful formalism designed for spacetimes that occur frequently in the teaching of General Relativity. Specifically, the book shows in detail the power of the calculus when dealing with spherically symmetric spacetimes. After introducing the basics, a new look at all the classical spherically symmetric black hole solutions is given within the GHP formalism. This is then employed to give new insights into the Tolman-Oppenheimer-Volkoff equations for stellar structure, including a derivation of new exact anisotropic fluid solutions. Finally, a re-writing of some essential features of black hole thermodynamics within the GHP formalism is performed. The book is based on the authors' lecture notes, used in their undergraduate and graduate lectures and while supervising their upper undergraduate and graduate students. To fully benefit from this concise primer, readers only need an undergraduate background in general relativity.

This book introduces the basic concept of a dissipative soliton, before going to explore recent theoretical and experimental results for various classes of dissipative optical solitons, high-energy dissipative solitons and their applications, and mode-locked fiber lasers.A soliton is a concept which describes various physical phenomena ranging from solitary waves forming on water to ultrashort optical pulses propagating in an optical fiber. While solitons are usually attributed to integrability, in recent years the notion of a soliton has been extended to various systems which are not necessarily integrable.  Until now, the main emphasis has been given to well-known conservative soliton systems, but new avenues of inquiry were opened when physicists realized that solitary waves did indeed exist in a wide range of non-integrable and non-conservative systems leading to the concept of so-called dissipative optical solitons.Dissipative optical solitons have many unique properties which differ from those of their conservative counterparts. For example, except for very few cases, they form zero-parameter families and their properties are completely determined by the external parameters of the optical system. They can exist indefinitely in time, as long as these parameters stay constant. These features of dissipative solitons are highly desirable for several applications, such as in-line regeneration of optical data streams and generation of stable trains of laser pulses by mode-locked cavities.