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xvicontents14.15.2Exercise 2: Cache Flow 38714.15.3Exercise 3: Large-Matrix Multiplication 38815 Thermodynamic Simulations & FeynmanQuantum Path Integration 39015.1 Unit I. Magnets via the Metropolis Algorithm 39015.2 An Ising Chain (Model) 39015.3 Statistical Mechanics (Theory) 39315.3.1 Analytic Solutions 39315.4 Metropolis Algorithm 39415.4.1 Metropolis Algorithm Implementation 39715.4.2 Equilibration, Thermodynamic Properties (Assessment) 39715.4.3 Beyond Nearest Neighbors and 1-D (Exploration) 40015.5 Unit II. Magnets via Wang–Landau Sampling ⊙ 40015.6 Wang–Landau Sampling 40315.6.1 WLS Ising Model Implementation 40515.6.2 WLS Ising Model Assessment 40815.7 Unit III. Feynman Path Integrals ⊙ 40815.8 Feynman’s Space-Time Propagation (Theory) 40815.8.1 Bound-State Wave Function ( Theory) 41215.8.2 Lattice Path Integration (Algorithm) 41315.8.3 Lattice Implementation 41815.8.4 Assessment and Exploration 42015.9 Exploration: Quantum Bouncer’s Paths ⊙ 42116 Simulating Matter with Molecular Dynamics 42416.1 Molecular Dynamics ( Theory) 42416.1.1 Connection to Thermodynamic Variables 42816.1.2 Setting Initial Velocity Distribution 42916.1.3 Periodic Boundary Conditions and Potential Cutoff 42916.2 Verlet and Velocity-Verlet Algorithms 43116.3 1-D Implementation and Exercise 43216.4 Trajectory Analysis 43516.5 Quiz 43617 PDEs for Electrostatics & Heat Flow 43717.1 PDE Generalities 43717.2 Unit I. Electrostatic Potentials 43917.2.1 Laplace’s Elliptic PDE ( Theory) 439−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.34811_fm — 2008/2/13 — Page xvi