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Master Sciences de la matière, Ecole d'ingénieurs Les principes variationnels sont présents dans tous les domaines de la physique. Le manuel se focalise principalement sur la mécanique analytique de Lagrange et d’Hamilton, et donne des aperçus sur plusieurs de ses extensions. Les principes variationnels sont présents dans tous les domaines de la physique.Rédigé à l’attention des étudiants en Masters Sciences de la matière et en écoles d’ingénieurs, ce manuel se focalise principalement sur la mécanique analytique de Lagrange et d’Hamilton, essentielle à la culture de tout physicien, et donne des aperçus sur plusieurs de ses extensions. Il est complété par des démonstrations ainsi que de nombreux exercices corrigés.
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Analytical mechanics is much more than an efficient tool for the solution of dynamical problems encountered in physics and engineering. There is hardly a branch of the mathematical sciences in which abstract rigorous speculation and experimental evidence go together so beautifully and support each other so perfectly. Professor Lanczos's book is not a textbook on advances mechanics. Its purpose is to formulate and explain these fundamental concepts of this exact science which started with the work of Galileo and led to the achievements of modern relativity theory and quantum theory. "There is a tremendous treasure of philosophical meaning behind the great theories of Euler and Lagrange, and of Hamilton and Jacobi, which is complete smothered in a purely formalistic treatment," writes the author, "although it cannot fail to be a source of the greatest intellectual enjoyment to every mathematically minded person." To give the student a chance to discover for himself the hidden beauty of these theories was one of the foremost intentions of the author. He has led the reader through the entire historical development, included problems to familiarize the student with the new concepts and illustrate the general principles involved. For the most part, however, the author's aim is not to teach the solving of problems but rather to help the reader gain insight into the structure and significance of classical mechanics. The second edition adds a new chapter, "Relativistic Mechanics."
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Mathematical physics. --- Variational principles. --- Variational principles --- Mathematical physics
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Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to state-of-the-art quantum Monte Carlo techniques relevant for applications in correlated systems. Providing a clear overview of variational wave functions, and featuring a detailed presentation of stochastic samplings including Markov chains and Langevin dynamics, which are developed into a discussion of Monte Carlo methods. The variational technique is described, from foundations to a detailed description of its algorithms. Further topics discussed include optimisation techniques, real-time dynamics and projection methods, including Green's function, reptation and auxiliary-field Monte Carlo, from basic definitions to advanced algorithms for efficient codes, and the book concludes with recent developments on the continuum space. Quantum Monte Carlo Approaches for Correlated Systems provides an extensive reference for students and researchers working in condensed matter theory or those interested in advanced numerical methods for electronic simulation.
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