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Condensed Matter Physics on the Computer -

A Laboratory Style Graduate Course


Michael Schreiber and Thomas Vojta

Institut für Physik, Technische Universität Chemnitz,

D-09107 Chemnitz, Germany





1. Teaching Computational Physics

2. Design of the course

3. Physics and computational topics

4. Example problems



Teaching Computational Physics, Trest, 31 August 2000





Teaching computational physics:

What do we want to achieve?


Teach students to solve a physical problem using a computer simulation

This includes:

- analyzing the physical problem

- reformulating the problem in a way suitable for a simulation

- choosing an efficient numerical algorithm

- writing the computer code

- running the computer simulation

- analyzing and interpreting the data obtained






A laboratory style computational condensed

matter physics course


Structure of the course:


What it is not ...


Course concentrates on computational physics aspects

It is therefore




Implementational details:





Summary of topics


Algorithmic preliminaries

Random walks and growth models



Phonons

Electronic states

Thermodynamics and related problems


Summary of computational techniques



Conclusions


course consists of a set of separate physics problems the students solve by



selection of problems is made to


Condensed Matter Physics on the Computer -

Example problems


Michael Schreiber and Thomas Vojta

Institut für Physik, Technische Universität Chemnitz,

D-09107 Chemnitz, Germany









Hopping conductivity and damage spreading:

extensions and generalizations of basic equilibrium Monte Carlo (Metropolis) algorithms as taught in the Ising model problem

Hopping conductivity: dynamics close to equilibrium

Damage spreading: dynamics far from equilibrium



Anderson localization of disordered electrons:

transfer matrix methods, finite size scaling M. Schreiber (Saturday)


Example: Hopping conductivity in semiconductors


Prerequisites: Problems on random numbers and on the Monte Carlo simulation of the Ising model

Goal: Investigation of the electrical transport in weakly doped semiconductors at low temperatures





Physics background:

Specific tasks:




A simple model for the hopping transport problem


(a = localization length of impurity state, T = temperature)




Schedule for the computer work


First day:

Second day:

Optional:




Connection to state-of-the-art research


Course problem: hopping transport of non-interacting electrons

well understood in general



However: real electrons interact via Coulomb potential

hopping transport of interacting electrons not fully understood today



Questions: What are the hopping entities, single electrons, pairs, clusters?

How do they couple to the phonons?

What is the temperature dependence of the resulting conductivity?