Format: Paperback / softback, 305 pages, height x width: 235x155 mm, weight: 492 g, 21 Illustrations, color;
6 Illustrations, black and white; XIV, 305 p. 27 illus., 21 illus. in color., 1 Paperback / softback
Series: Fundamental Theories of Physics 204
Pub. Date: 16-Mar-2023
ISBN-13: 9783030887834
Quantum theory is at the foundation of the physical description of our world. One of the people who contributed significantly to our conceptual understanding of this theory was Heinz-Dieter Zeh (1932-2018). He was the pioneer of the process of decoherence, through which the classical appearance of our world can be understood. This volume presents a collection of essays dedicated to his memory, written by distinguished scientists and scholars. They cover all aspects of the interpretation of quantum theory in general and the quantum-to-classical transition in particular. This volume provides illuminating reading to anyone seeking a deep understanding of quantum theory and its relevance to the foundations of physics.
Format: Paperback / softback, 838 pages, height x width: 235x155 mm, weight: 1288 g,
10 Illustrations, black and white; XVIII, 838 p. 10 illus., 1 Paperback / softback
Series: Fundamental Theories of Physics 205
Pub. Date: 08-Apr-2023
ISBN-13: 9783030895914
This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.
Introduction.- Spacetime.- Galileian metric field.- Galileian
gravitational field.- Galileian electromagnetic field.- Joined spacetime
connection.- Classical dynamics.- Sources of gravitational and
electromagnetic fields.- Fundamental fields of phase space.- Geometric
structures of phase space.- Hamiltonian formalism.- Lie algebra of special
phase functions.- Classical symmetries.- Quantum bundle.- Galileian upper
quantum connection.- Quantum differentials.- Quantum dynamics.-
Hydrodynamical picture of QM.- Quantum symmetries.- Quantum differential
operators.- Quantum currents and expectation forms.- Sectional quantum
bundle.- Feynman path integral.- Conclusions and further developments.-
Examples.
Format: Paperback / softback, 486 pages, height x width: 235x155 mm, weight: 765 g, 9 Illustrations, color;
12 Illustrations, black and white; XVII, 486 p. 21 illus., 9 illus. in color., 1 Paperback / softback
Series: Fundamental Theories of Physics 206
Pub. Date: 04-Apr-2023
ISBN-13: 9789811681912
This book presents a comprehensive account of the renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view.
It extract long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature.
The book begins with the basic notion of the RG theory, including its connection with the separation of scales. Then it formulates the RG method as a construction method of envelopes of the naive perturbative solutions containing secular terms, and then demonstrates the formulation in various types of evolution equations. Lastly, it describes successful physical examples, such as stochastic and transport phenomena including second-order relativistic as well as nonrelativistic fluid dynamics with causality and transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times.
Requiring only an undergraduate-level understanding of physics and mathematics, the book clearly describes the notions and mathematical techniques with a wealth of examples. It is a unique and can be enlightening resource for readers who feel mystified by renormalization theory in quantum field theory.
PART I Introduction to Renormalization Group (RG) Method
1 Introduction: Notion of Effective Theories in Physical Sciences
2 Divergence and Secular Term in the Perturbation Series of Ordinary
Differential Equations
3 Traditional Resummation Methods
3.1 Reductive Perturbation Theory
3.2 Lindstedt's Method
3.3 Krylov-Bogoliubov-Mitropolsky's Method for Nonlinear
Oscillators
4 Elementary Introduction of the RG method in Terms of the Notion of
Envelopes
4.1 Notion of Envelopes of Family of Curves Adapted for a
Geometrical Formulation of the RG Method
4.2 Elementary Examples: Damped Oscillator and Boundary-Layer
Problem
5 General Formulation and Foundation of the RG Method:
Ei-Fujii-Kunihiro
Formulation and Relation to Kuramoto's reduction scheme
6 Relation to the RG Theory in Quantum Field Theory
7 Resummation of the Perturbation Series in Quantum Methods
PART II Extraction of Slow Dynamics Described by Differential and
Difference Equations
8 Illustrative Examples
8.1 Rayleigh/Van der Pol equation and jumping phenomena
8.2 Lotka-Volterra Equation
8.3 Lorents Model
9 Slow Dynamics Around Critical Point in Bifurcation Phenomena
10 Dynamical Reduction of A Generic Non-linear Evolution Equation with
Semi-simple Linear Operator11 A Generic Case when the Linear Operator
Has a Jordan-cell Structure
12 Dynamical Reduction of Difference Equations (Maps)
13 Slow Dynamics in Some Partial Differential Equations
13.1 Dissipative One-Dimensional Hyperbolic Equation
13.2 Swift-Hohenberg Equation
13.3 Damped Kuramoto-Shivashinsky Equation
13.4 Diffusion in Porus Medium --- Barrenblatt Equation
14 Appendix: Some Mathematical Formulae
PART III Application to Extracting Slow Dynamics of Non-equilibrium
Phenomena
15 Dynamical Reduction of Kinetic Equations
15.1 Derivation of Boltzmann Equation from Liouville Equation
15.2 Derivation of the Fokker-Planck (FP) Equation from Langevin
Equation
15.3 Adiabatic Elimination of Fast Variables in FP Equation: Derivation
of Generalized Kramers Equations
16 Relativistic First-Order Fluid Dynamic Equation
17 Doublet Scheme and its Applications
17.1 General Formulation
17.2 Lorentz Model Revisited
18 Relativistic Causal Fluid dynamic Equation
19 Numerical Analysis of Transport Coefficients and Relaxation Times
20 Reactive-Multi-component Systems
21 Non-relativistic Case and Application to Cold Atoms
PART IV Summary and Future Prospect
22 Summary and Future Prospects
Format: Hardback, 632 pages, height x width: 235x155 mm, 10 Tables, color; 4 Illustrations,
color; 15 Illustrations, black and white; XIV, 632 p. 19 illus., 4 illus. in color., 1 Hardback
Series: Theoretical and Mathematical Physics
Pub. Date: 27-Aug-2023
ISBN-13: 9783031342479
Goodreads reviews
This second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts:
Part One: Classical Dynamical Systems
Format: Hardback, 626 pages, height x width: 235x155 mm, 12 Illustrations, color;
6 Illustrations, black and white; X, 626 p. 18 illus., 12 illus. in color., 1 Hardback
Pub. Date: 30-Aug-2023
ISBN-13: 9783031319242
This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research.
This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex.
1 Le Dung Trang and Bernard Teissier, Limits of tangents, Whitney
stratifications and a Plucker type formula.- 2 Anne Fruhbis-Kruger and
Matthias Zach, Determinantal singularities.- 3 Shihoko Ishii, Singularities,
the space of arcs and applications to birational geometry.- 4 Hussein
Mourtada, Jet schemes and their applications in singularities, toric
resolutions and integer partitions.- 5 Wolfgang Ebeling and Sabir M.
Gusein-Zade, Indices of vector fields and 1-forms.- 6 Shoji Yokura, Motivic
Hirzebruch class and related topics.- 7 Guillaume Valette, Regular vectors
and bi-Lipschitz trivial stratifications in o-minimal structures.- 8 Lev
Birbrair and Andrei Gabrielov, Lipschitz Geometry of Real Semialgebraic
Surfaces.- 9 Alexandre Fernandes and Jose Edson Sampaio, Bi-Lipschitz
invariance of the multiplicity.- 10 Lorenzo Fantini and Anne Pichon, On
Lipschitz Normally Embedded singularities.- 11 Ana Bravo and Santiago
Encinas, Hilbert-Samuel multiplicity and finite projections.- 12 Francisco J.
Castro-Jimenez, David Mond and Luis Narvaez-Macarro, Logarithmic Comparison
Theorems.
Format: Hardback, 392 pages, height x width: 235x155 mm, 9 Illustrations, color; 121 Illustrations,
black and white; VIII, 392 p. 130 illus., 9 illus. in color. With online files/update., 1 Hardback
Pub. Date: 06-Sep-2023
This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs). Beginning with IVPs involving Ordinary Differential Equations (ODEs) and progressing to problems with Partial Differential Equations (PDEs) in 1+1 and 3+1 dimensions, it provides readers with a clear and systematic progression from simple to complex concepts.
The numerical methods selected in this textbook can solve a considerable variety of problems and the applications presented cover a wide range of topics, including population dynamics, chaos, celestial mechanics, geophysics, astrophysics, and more. Each chapter contains a variety of solved problems and exercises, with code included. These examples are designed to motivate and inspire readers to delve deeper into the state-of-the-art problems in their own fields. The code is written in Fortran 90, in a library-free style, making them easy to program and efficient to run. The appendix also includes the same code in C++, making the book accessible to a variety of programming backgrounds.
At the end of each chapter, there are brief descriptions of how the methods could be improved, along with one or two projects that can be developed with the methods and codes described. These projects are highly engaging, from synchronization of chaos and message encryption to gravitational waves emitted by a binary system and non-linear absorption of a scalar field. With its clear explanations, hands-on approach, and practical examples, this textbook is an essential resource for advanced undergraduate and graduate students who want to the learn how to use numerical methods to tackle challenging problems.
Chapter1. Introduction.
Chapter2. Ordinary Differential Equations.-
Chapter3. Simple Methods for Initial Value Problems Involving PDEs.-
Chapter4. Method of Lines for Initial Value Problems Involving PDEs.-
Chapter5. Finite Volume Methods.
Chapter6. Initial Value Problems in 3+1 and
2+1 dimensions.
Chapter7. Appendix A: Stability of Evolution Schemes.-
Chapter8. Appendix B: Codes.