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Principles of computer simulations for condensed matter systems

Informations pratiques


Discipline :

Physique

Niveau :

Master 2

Semestre :

S3a

Crédits ECTS :

6

Volume Horaire :

24h Cours
10h TD

Responsable :

Ralf Everaers

École Normale Supérieure de Lyon, Laboratoire de Physique.

Intervenants :

Ralf Everaers
Daniel Jost

This course will be given in English

Objectives

Introduction of the principles underlying numerical simulations methods in statistical physics, condensed matter phyics, physical chemistry and biophysics. This course will be taught in English.

Outline

1. Brief review of Statistical Mechanics
Canonical and microcanonical ensembles, entropy, temperature, fluctuations, why not brute force ? Time vs. ensemble averages

2. Classical Molecular Dynamics
Numerical integration of Newton’s equations of motion : Euler vs Verlet algorithm, Liouville formulation of time-reversible algorithms, Calculation of short and long-range forces, transition to chaos: Fermi-Pasta-Ulam problem, Thermostats

3. Classical Monte Carlo
Simple sampling, importance sampling, reweighting methods, MC for different thermodynamic ensembles, MC methods for calculating free energies and chemical potentials

4. Quantum Monte Carlo
Sampling path integrals

5. Ab-initio Molecular Dynamics
Born-Oppenheimer approximation, Hartree-Fock, Density functional theory, Car-Parinello Molecular Dynamics

6. Multiscale Modeling
Force fields for atomistic simulations, Coarse-graining: (Iterative) Boltzmann inversion, Force-matching, Inverse Monte Carlo Methods

7. Non-equilibrium Methods
Driven lattice gases, cellular automata, non-equilibrium Molecular Dynamics

Pré-requis

Physique statistique L3, thermodynamique L2, mécanique quantique L3

Modalité de l'examen

Oral