Course Book

Computer simulation of physical systems II

Course Book

Lecturer(s) :

Language:

English

Learning outcomes

To provide the student with basic methods of computational condensed-matter physics.

Content

[b]Diffusion-limited aggregation:[/b] description of the model, fractal dimension, dielectric breakdown.[br/][br/][b]Boundary and eigenvalue problems:[/b] Numerov's integration algorithm, solution of the radial Poisson equation and of the one-dimensional Schrödinger equation.[br/][br/][b]Density-functional theory:[/b] Hohenberg-Kohn theorem, Kohn-Sham equations, local-density approximation.[br/][br/][br/][b]First-principles calculations:[/b] selfconsistent solutions for isolated atoms; selfconsistent solution for periodic systems, plane-wave basis sets, pseudopotentials; applications to atoms, clusters, solids, surfaces, chemical reactions.[br/][br/][b][i]Ab initio[/i] molecular dynamics:[/b] Car-Parrinello method and applications.[br/][br/][br/][b]Variational Monte Carlo:[/b] solution of Schrödinger equation through the variational Monte Carlo method, variance minimization, application to quantum systems.[br/][br/][b]Diffusion Monte Carlo:[/b] solution of Schrödinger equation through evolution in imaginary time, Green-Function Monte Carlo method, guide function, fixed node approximation, application to quantum systems.[br/][br/][br/][b]Minimization in multidimensions:[/b] steepest-descent and conjugate-gradient methods.[br/]

Required prior knowledge

Quantum mechanics, Statistical physics

Type of teaching

Ex cathedra

Links