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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.

Principes variationnels. --- Variational principles

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Mechanics, Analytic. --- Variational principles.

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Mathematical physics. --- Variational principles. --- Variational principles --- Mathematical physics

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Differential equations, Partial. --- Variational principles.

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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.

Monte Carlo method. --- Variational principles.