Computational
Condensed Matter Physics
(Monte Carlo related techniques)
The course consists of 7 lectures (2 hours
each) and 7 Lab sessions (4 hours each) related to the lectures. Grades are
based on the performance during the Labs (50 % of the final grade) and the
accomplishment of an individual (final) project (50 % of the final
grade).
Lecture 1:
Introduction to computer modeling. Basic notions from the theory of probability
and statistical physics. Time and ensemble averages. Computing of statistical
integrals by Monte Carlo.
Lab1: Computing of definitive integrals
by Monte Carlo. Random number generators. (in Fortan, PASCAL or Basic)
Lecture 2: Modeling of microcanonical,
canonical and grand canonical ensembles. Algorithms, strategies, initial &
boundary conditions. Accuracy of the Monte Carlo estimates.
Lab 2: Phase transitions in a two-dimensional
Ising model. (in Fortan, PASCAL or Basic)
Lecture 3: Monte Carlo simulation
of magnetic phase diagrams, spin glasses, order/disorder phenomena in alloys
and proteins, crystal growth.
Lab 3: Growth of a two-dimensional
crystal described by the model of Kosell. (in Fortan, PASCAL or Basic)
Lecture 4: Modeling of classical &
quantum liquids and soft solids (polymers).
Lab 4: Vapour-liquid-solid phase transitions
in a two-dimensional hard-disk-like liquid. Boltzmann distribution by the
algorithm of von Neumann. (in Fortan, PASCAL or Basic)
Lecture 5: Kinetic processes by Monte
Carlo.
Lab 5: Self-diffusion on a two-dimensional
square lattice. (in Fortan, PASCAL or Basic)
Lecture 6: Scattering, implantation,
sputtering, radiation damages modeled by Monte Carlo. Principles of reverse
Monte Carlo.
Lab 6: Optimization of the characteristics
of a photomultiplyer (dynode) by Monte Carlo simulations. (in Fortan, PASCAL
or Basic)
Lecture 7. Geometrical phase transitions
and percolation phenomena by Monte Carlo. Image reconstruction by Monte Carlo.
Lab 7: Simulation of percolation clusters
with fractal dimensions. (in Fortan, PASCAL or Basic)
8. Individual project. (end semester)
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