| Titre : | Statistical Mechanics: Theory and Molecular Simulation |
| Auteurs : | Tuckerman Mark E, Auteur |
| Type de document : | Monographie imprimée |
| Mention d'édition : | Second Edition |
| Editeur : | Oxford University Press, 2023 |
| ISBN/ISSN/EAN : | 978-0-19-882556-2 |
| Format : | 1VOL.(48p) / ill.couv.ill.en coul / 24Cm |
| Langues: | Anglais |
| Langues originales: | Anglais |
| Index. décimale : | 53013 |
| Résumé : | Scientists are increasingly finding themselves engaged in research problems that cross the traditional disciplinary lines of physics, chemistry, biology, materials science, and engineering. Because of its broad scope, statistical mechanics is an essential tool for students and more experienced researchers planning to become active in such an interdisciplinary research environment. Powerful computational methods that are based in statistical mechanics allow complex systems to be studied at an unprecedented level of detail.This book synthesizes the underlying theory of statistical mechanics with the computational techniques and algorithms used to solve real-world problems and provides readers with a solid foundation in topics that reflect the modern landscape of statistical mechanics.Topics covered include detailed reviews of classical and quantum mechanics, in-depth discussions of the equilibrium ensembles and the use of molecular dynamics and Monte Carlo to sample classical and quantum ensemble distributions, Feynman path integrals, classical and quantum linear-response theory, nonequilibrium molecular dynamics, the Langevin and generalized Langevin equations, critical phenomena, techniques for free energy calculations, machine learning models, and the use of these models in statistical mechanics applications. The book is structured such that the theoretical underpinnings of each topic are covered side by side with computational methods used for practical implementation of the theoretical concepts. |
| Sommaire : |
Cover
Titlepage Copyright Dedication Preface Contents 1 Classical mechanics 1.1 Introduction 1.2 Newton’s laws of motion 1.3 Phase space: visualizing classical motion 1.4 Lagrangian formulation of classical mechanics: A general framework for Newton’s laws 1.5 Legendre transforms 1.6 Generalized momenta and the Hamiltonian formulation of classical mechanics 1.7 A simple classical polymer model 1.8 The action integral 1.9 Lagrangian mechanics and systems with constraints 1.10 Gauss’s principle of least constraint 1.11 Rigid body motion: Euler angles and quaternions 1.12 Non-Hamiltonian systems 1.13 Problems 2 Theoretical foundations of classical statistical mechanics 2.1 Overview 2.2 The laws of thermodynamics 2.3 The ensemble concept 2.4 Phase-space volumes and Liouville’s theorem 2.5 The ensemble distribution function and the Liouville equation 2.6 Equilibrium solutions of the Liouville equation 2.7 Problems 3 The microcanonical ensemble and introduction to molecular dynamics 3.1 Brief overview 3.2 Basic thermodynamics, Boltzmann’s relation, and the partition function of the microcanonical ensemble 3.3 The classical virial theorem 3.4 Conditions for thermal equilibrium 3.5 The free particle and the ideal gas 3.6 The harmonic oscillator and harmonic baths 3.7 Introduction to molecular dynamics 3.8 Integrating the equations of motion: Finite difference methods 3.9 Systems subject to holonomic constraints 3.10 The classical time evolution operator and numerical integrators 3.11 Multiple time-scale integration 3.12 Symplectic integration for quaternions 3.13 Exactly conserved time-step dependent Hamiltonians 3.14 Illustrative examples of molecular dynamics calculations 3.15 Problems 4 The canonical ensemble 4.1 Introduction: A different set of experimental conditions 4.2 Thermodynamics of the canonical ensemble 4.3 The canonical phase-space distribution and partition function 4.4 Canonical ensemble via entropy maximization 4.5 Energy fluctuations in the canonical ensemble 4.6 Simple examples in the canonical ensemble 4.7 Structure and thermodynamics in real gases and liquids from spatial distribution functions 4.8 Perturbation theory and the van der Waals equation 4.9 Molecular dynamics in the canonical ensemble: Hamiltonian formulation in an extended phase space 4.10 Classical non-Hamiltonian statistical mechanics 4.11 Nos´e-Hoover chains 4.12 Integrating the Nos´e-Hoover chain equations 4.13 The isokinetic ensemble: A variant of the canonical ensemble 4.14 Isokinetic Nos´e-Hoover chains: Achieving very large time steps 4.15 Applying canonical molecular dynamics: Liquid structure 4.16 Problems 5 The isobaric ensembles 5.1 Why constant pressure? 5.2 Thermodynamics of isobaric ensembles 5.3 Isobaric phase-space distributions and partition functions 5.4 Isothermal-isobaric ensemble via entropy maximization 5.5 Pressure and work virial theorems 5.6 An ideal gas in the isothermal-isobaric ensemble 5.7 Extending the isothermal-isobaric ensemble: Anisotropic cell fluctuations 5.8 Derivation of the pressure tensor estimator from the canonical partition function 5.9 Molecular dynamics in the isoenthalpic-isobaric ensemble 5.10 Molecular dynamics in the isothermal-isobaric ensemble I: Isotropic volume fluctuations 5.11 Molecular dynamics in the isothermal-isobaric ensemble II: Anisotropic cell fluctuations 5.12 Atomic and molecular virials 5.13 Integrating the Martyna-Tobias-Klein equations of motion 5.14 The isothermal-isobaric ensemble with constraints: The ROLL algorithm 5.15 Problems 6 The grand canonical ensemble 6.1 Introduction: The need for yet another ensemble 6.2 Euler’s theorem 6.3 Thermodynamics of the grand canonical ensemble 6.4 Grand canonical phase space and the partition function 6.5 Grand canonical ensemble via entropy maximization 6.6 Illustration of the grand canonical ensemble: The ideal gas 6.7 Particle number fluctuations in the grand canonical ensemble 6.8 Potential distribution theorem 6.9 Molecular dynamics in the grand canonical ensemble 6.10 Problems 7 Monte Carlo 7.1 Introduction to the Monte Carlo method 7.2 The Central Limit theorem 7.3 Sampling distributions 7.4 Hybrid Monte Carlo 7.5 Replica exchange Monte Carlo 7.6 Wang-Landau sampling 7.7 Transition path sampling and the transition path ensemble 7.8 Problems 8 Free-energy calculations 8.1 Free-energy perturbation theory 8.2 Adiabatic switching and thermodynamic integration 8.3 Adiabatic free-energy dynamics 8.4 Jarzynski’s equality and nonequilibrium methods 8.5 The problem of rare events 8.6 Collective variables 8.7 The blue moon ensemble approach 8.8 Umbrella sampling and weighted histogram methods 8.9 Wang-Landau sampling 8.10 Driven adiabatic free-energy dynamics 8.11 Metadynamics 8.12 The committor distribution and the histogram test 8.13 Problems 9 Quantum mechanics 9.1 Introduction: Waves and particles 9.2 Review of the fundamental postulates of quantum mechanics 9.3 Simple examples 9.4 Identical particles in quantum mechanics: Spin statistics 9.5 Problems 10 Quantum ensembles and the density matrix 10.1 The difficulty of many-body quantum mechanics 10.2 The ensemble density matrix 10.3 Time evolution of the density matrix 10.4 Quantum equilibrium ensembles 10.5 Problems 11 Quantum ideal gases: Fermi-Dirac and Bose-Einstein statistics 11.1 Complexity without interactions 11.2 General formulation of the quantum-mechanical ideal gas 11.3 An ideal gas of distinguishable quantum particles 11.4 General formulation for fermions and bosons 11.5 The ideal fermion gas 11.6 The ideal boson gas 11.7 Problems 12 The Feynman path integral 12.1 Quantum mechanics as a sum over paths 12.2 Derivation of path integrals for the canonical density matrix and the time evolution operator 12.3 Thermodynamics and expectation values from path integrals 12.4 The continuous limit: Functional integrals 12.5 How to think about imaginary time propagation 12.6 Many-body path integrals 12.7 Quantum free-energy profiles 12.8 Numerical evaluation of path integrals 12.9 Problems 13 Classical time-dependent statistical mechanics 13.1 Ensembles of driven systems 13.2 Driven systems and linear response theory 13.3 Applying linear response theory: Green-Kubo relations for transport coefficients 13.4 Calculating time correlation functions from molecular dynamics 13.5 The nonequilibrium molecular dynamics approach 13.6 Problems 14 Quantum time-dependent statistical mechanics 14.1 Time-dependent systems in quantum mechanics 14.2 Time-dependent perturbation theory in quantum mechanics 14.3 Time correlation functions and frequency spectra 14.4 Examples of frequency spectra 14.5 Quantum linear response theory 14.6 Approximations to quantum time correlation functions 14.7 Problems 15 The Langevin and generalized Langevin equations 15.1 The general model of a system plus a bath 15.2 Derivation of the generalized Langevin equation 15.3 Analytically solvable examples 15.4 Vibrational dephasing and energy relaxation in simple fluids 15.5 Molecular dynamics with the Langevin equation 15.6 Designing memory kernels for specific tasks 15.7 Sampling stochastic transition paths 15.8 Mori-Zwanzig theory 15.9 Problems 16 Discrete models and critical phenomena 16.1 Phase transitions and critical points 16.2 The critical exponents α, β, γ, and δ 16.3 Magnetic systems and the Ising model 16.4 Universality classes 16.5 Mean-field theory 16.6 Ising model in one dimension 16.7 Ising model in two dimensions 16.8 Spin correlations and their critical exponents 16.9 Introduction to the renormalization group 16.10 Fixed points of the renormalization group equations in greater than one dimension 16.11 General linearized renormalization group theory 16.12 Understanding universality from the linearized renormalization group theory 16.13 Other uses of discrete models 16.14 Problems 17 Introduction to machine learning in statistical mechanics 17.1 Machine learning in statistical mechanics: What and why? 17.2 Three key probability distributions 17.3 Simple linear regression as a case study 17.4 Kernel methods 17.5 Neural networks 17.6 Weighted neighbor methods 17.7 Demonstrating machine learning in free-energy simulations 17.8 Clustering algorithms 17.9 Intrinsic dimension of a data manifold 17.10 Problems Appendix A Properties of the Dirac delta-function Appendix B Calculus of functionals Appendix C Evaluation of energies and forces Appendix D Proof of the Trotter theorem Appendix E Laplace transforms References Index |
| Type de document : | Livres |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| PHY/890 | Livre | bibliothèque sciences exactes | Consultable |
