Download or read book Introduction to Isospectrality written by Alberto Arabia and published by Springer Nature. This book was released on 2022-09-13 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Can one hear the shape of a drum?" This striking question, made famous by Mark Kac, conceals a precise mathematical problem, whose study led to sophisticated mathematics. This textbook presents the theory underlying the problem, for the first time in a form accessible to students. Specifically, this book provides a detailed presentation of Sunada's method and the construction of non-isometric yet isospectral drum membranes, as first discovered by Gordon–Webb–Wolpert. The book begins with an introductory chapter on Spectral Geometry, emphasizing isospectrality and providing a panoramic view (without proofs) of the Sunada–Bérard–Buser strategy. The rest of the book consists of three chapters. Chapter 2 gives an elementary treatment of flat surfaces and describes Buser's combinatorial method to construct a flat surface with a given group of isometries (a Buser surface). Chapter 3 proves the main isospectrality theorems and describes the transplantation technique on Buser surfaces. Chapter 4 builds Gordon–Webb–Wolpert domains from Buser surfaces and establishes their isospectrality. Richly illustrated and supported by four substantial appendices, this book is suitable for lecture courses to students having completed introductory graduate courses in algebra, analysis, differential geometry and topology. It also offers researchers an elegant, self-contained reference on the topic of isospectrality.
Download or read book Twisted Isospectrality Homological Wideness and Isometry written by Gunther Cornelissen and published by Springer Nature. This book was released on 2023-05-10 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics. This book focusses on the case of compact Riemannian manifolds, and, in particular, the question whether one can find finitely many natural operators that determine whether two such manifolds are isometric (coverings). The methods outlined in the book fit into the tradition of the famous work of Sunada on the construction of isospectral, non-isometric manifolds, and thus do not focus on analytic techniques, but rather on algebraic methods: in particular, the analogy with constructions in number theory, methods from representation theory, and from algebraic topology. The main goal of the book is to present the construction of finitely many “twisted” Laplace operators whose spectrum determines covering equivalence of two Riemannian manifolds. The book has a leisure pace and presents details and examples that are hard to find in the literature, concerning: fiber products of manifolds and orbifolds, the distinction between the spectrum and the spectral zeta function for general operators, strong isospectrality, twisted Laplacians, the action of isometry groups on homology groups, monomial structures on group representations, geometric and group-theoretical realisation of coverings with wreath products as covering groups, and “class field theory” for manifolds. The book contains a wealth of worked examples and open problems. After perusing the book, the reader will have a comfortable working knowledge of the algebraic approach to isospectrality. This is an open access book.
Download or read book Supersymmetric Quantum Mechanics written by Asim Gangopadhyaya and published by World Scientific. This book was released on 2011 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first such text which will be directed to undergraduates. Our approach is to provide a self-contained exposition, which begins with a review of the relevant introductory quantum mechanics, then segues into SUSYQM. We concentrate on the essentials, both in the chapters developing the architecture, and in the later chapters of applications. While the text is designed to be accessible to undergraduate students, it should also be useful to graduate students and to researchers in the field. The text contains a large selection of examples and problems that illustrate the ideas and their applications. It is richly illustrated with figures that we have designed and produced. We have selected an attractive and relevant list of topics.
Download or read book New Developments in Lie Theory and Geometry written by Carolyn Gordon and published by American Mathematical Soc.. This book was released on 2009 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the Sixth Workshop on Lie Theory and Geometry, held in the province of Cordoba, Argentina in November 2007. The representation theory and structure theory of Lie groups play a pervasive role throughout mathematics and physics. Lie groups are tightly intertwined with geometry and each stimulates developments in the other. The aim of this volume is to bring to a larger audience the mutually beneficial interaction between Lie theorists and geometers that animated the workshop. Two prominent themes of the representation theoretic articles are Gelfand pairs and the representation theory of real reductive Lie groups. Among the more geometric articles are an exposition of major recent developments on noncompact homogeneous Einstein manifolds and aspects of inverse spectral geometry presented in settings accessible to readers new to the area.
Download or read book Mathematical Congress of the Americas written by Jimmy Petean and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the First Mathematical Congress of the Americas, held from August 5-9, 2013, in Guanajuato, México. With the participation of close to 1,000 researchers from more than 40 countries, the meeting set a benchmark for mathematics in the two continents. The papers, written by some of the plenary and invited speakers, as well as winners of MCA awards, cover new developments in classic topics such as Hopf fibrations, minimal surfaces, and Markov processes, and provide recent insights on combinatorics and geometry, isospectral spherical space forms, homogenization on manifolds, and Lagrangian cobordism, as well as applications to physics and biology.
Download or read book Introduction to Quantum Graphs written by Gregory Berkolaiko and published by American Mathematical Soc.. This book was released on 2013 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.
Download or read book Supersymmetric Quantum Mechanics written by Asim Gangopadhyaya and published by World Scientific Publishing Company. This book was released on 2017-10-17 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have written this book in order to provide a single compact source for undergraduate and graduate students, as well as for professional physicists who want to understand the essentials of supersymmetric quantum mechanics. It is an outgrowth of a seminar course taught to physics and mathematics juniors and seniors at Loyola University Chicago, and of our own research over a quarter of a century.
Download or read book Non Linear Dynamics and Fundamental Interactions written by Faqir Khanna and published by Springer Science & Business Media. This book was released on 2006-06-26 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the NATO Advanced Research Institute on "Non-Linear Dynamics and Fundamental Interactions" held in Tashkent, Uzbekistan, from Oct.10-16,2004. The main objective of the Workshop was to bring together people working in areas of Fundamental physics relating to Quantum Field Theory, Finite Temperature Field theory and their applications to problems in particle physics, phase transitions and overlap regions with the areas of Quantum Chaos. The other important area is related to aspects of Non-Linear Dynamics which has been considered with the topic of chaology. The applications of such techniques are to mesoscopic systems, nanostructures, quantum information, particle physics and cosmology. All this forms a very rich area to review critically and then find aspects that still need careful consideration with possible new developments to find appropriate solutions. There were 29 one-hour talks and a total of seven half-hour talks, mostly by the students. In addition two round table discussions were organised to bring the important topics that still need careful consideration. One was devoted to questions and unsolved problems in Chaos, in particular Quantum Chaos. The other round table discussion considered the outstanding problems in Fundamental Interactions. There were extensive discussions during the two hours devoted to each area. Applications and development of new and diverse techniques was the real focus of these discussions. The conference was ably organised by the local committee consisting of D.U.
Download or read book Spectral Analysis in Geometry and Number Theory written by Motoko Kotani and published by American Mathematical Soc.. This book was released on 2009 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of an international conference in honor of Toshikazu Sunada on the occasion of his sixtieth birthday. The conference took place at Nagoya University, Japan, in 2007. Sunada's research covers a wide spectrum of spectral analysis, including interactions among geometry, number theory, dynamical systems, probability theory and mathematical physics. Readers will find papers on trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. This volume also contains an article that presents an overview of Sunada's work in mathematics up to the age of sixty.
Download or read book Analysis on Graphs and Its Applications written by Pavel Exner and published by American Mathematical Soc.. This book was released on 2008 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.
Download or read book Proceedings of the 10th International Operational Modal Analysis Conference written by Carlo Rainieri and published by Springer Nature. This book was released on 2024 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the latest advances and innovations in the field of operational modal analysis and structural health monitoring, as presented at the 10th International Operational Modal Analysis Conference (IOMAC), held in Naples, Italy on May 22-24, 2024. The contributions cover a diverse range of topics, including AI for data interpretation, automatic modal parameter estimation, Digital Twin, modal testing methods, instrumentation and case studies, model correlation and updating, modal-based SHM, modal mass estimation. Selected by means of a rigorous peer-review process, they will spur novel research directions and foster future multidisciplinary collaborations.
Download or read book ICM 90 Satellite Conference Proceedings written by Satoru Igari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a Conference held in Sendai, Japan, August 14-18, 1990
Download or read book Top Down Design of Disordered Photonic Structures written by Sunkyu Yu and published by Springer Nature. This book was released on 2019-09-03 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces recent advances in the deterministic design of photonic structures, which overcome the current limitation in conventional disordered materials. It develops new concepts for disordered photonics inspired by notions in quantum mechanics, solid-state physics, mathematics and network theory, such as isospectrality, supersymmetry, graph network, small-world, de Broglie-Bohm theory, and parity-time symmetry. The multidisciplinary approach based on the core concepts of isospectrality (Chapter 2) and metadisorder (Chapter 3) offers a new perspective on the design methodology in photonics and in general disordered structures toward top-down designs of future photonic applications: perfect bandgap with strong modal localization, switching of random waves for binary and fuzzy logics, photonic analogy of graph networks, interdimensional signal transport, robust wave functions in disordered structures, and a novel method of energy storage and phase trapping based on Bohmian photonics. This book will provide new design criteria for physicists and engineers in photonics, and inspirations for researchers in other fields.
Download or read book Large Coulomb Systems written by Jan Derezinski and published by Springer Science & Business Media. This book was released on 2006-05-08 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically consistent formulation of relativistic quantum electrodynamics (QED) has still to be found. Nevertheless, there are several simplified effective models that successfully describe many body quantum systems and the interaction of radiation with matter. Large Coulomb Systems explores a selection of mathematical topics inspired by QED. It comprises selected, expanded and edited lectures given by international experts at a topical summer school.
Download or read book Space Time Matter written by Jochen Brüning and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-09 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Download or read book Twisted Isospectrality Homological Wideness and Isometry written by Gunther Cornelissen and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter. 1. Introduction -- Part I: Leitfaden -- Chapter. 2. Manifold and orbifold constructions -- Chapter. 3. Spectra, group representations and twisted Laplacians -- Chapter. 4. Detecting representation isomorphism through twisted spectra -- Chapter. 5. Representations with a unique monomial structure -- Chapter. 6. Construction of suitable covers and proof of the main theorem -- Chapter. 7. Geometric construction of the covering manifold -- Chapter. 8. Homological wideness -- Chapter. 9. Examples of homologically wide actions -- Chapter. 10. Homological wideness, “class field theory” for covers, and a number theoretical analogue -- Chapter. 11. Examples concerning the main result -- Chapter. 12. Length spectrum -- References -- Index.
