Perturbation Theory: Mathematics, Methods and Applications

ISBN-13: 9781071626207 / Angielski / Twarda / 2022 / 596 str.

Giuseppe Gaeta

Opis

This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

Spis treści

Diagrammatic Methods in Classical Perturbation Theory

Hamiltonian Perturbation Theory (and Transition to Chaos)

Kolmogorov-Arnold-Moser (KAM) Theory for Finite and Infinite Dimensional Systems

n-Body Problem and Choreographies

Nekhoroshev Theory

Symmetry and Perturbation Theory in Non-linear Dynamics

Normal Forms in Perturbation Theory

Perturbation Analysis of Parametric Resonance

Perturbation of Equilibria in the Mathematical Theory of Evolution

Perturbation of Systems with Nilpotent Real Part

Perturbation Theory

Perturbation Theory in Celestial Mechanics

Introduction to Perturbation Theory

Perturbation Theory and Molecular Dynamics

Perturbation Theory for Non-smooth Systems

Perturbation Theory for PDEs

Perturbation Theory in Quantum Mechanics

Semiclassical Perturbation Theory

Convergence of Perturbative Expansions

Quantum Bifurcations

Perturbation of superintegrable systems

Computational methods in perturbation theory

Perturbation Theory for Water Waves

Perturbation Theory and the Method of Detuning

Periodic Rogue Waves and Perturbation Theory

Convergent perturbative expansion in Condensed Matter and Quantum Field Theory

Quantum Adiabatic Theorem

Exact and perturbation methods in the dynamics of legged locomotion

Correlation corrections as a perturbation to the quasi-free approximation in many-body quantum systems

O autorze

G. Gaeta studied Theoretical Physics in Roma and New York; he had postdoctoral positions in Montreal, Paris, Madrid, and Utrecht and was Reader in Nonlinear Systems in Loughborough, UK, before landing in Milano, Italy, where he is now Professor of Mathematical Physics. His main fields of research are Mathematical Physics – in particular Nonlinear Systems, Perturbation Theory, and Symmetry – and Mathematical Biology. He is the author of over 150 research papers and 3 research monographs, together with a textbook in introductory Mathematical Biology. He is also the main organizer of the SPT (Symmetry and Perturbation Theory) series of conferences, which started in 1996, and the Director of the virtual Research Institute SMRI.