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Computational Physics II

Robert Zillich

lecture:    Wed. 10:15-11:45, P 215
exercise:    Wed. 14:30-15:15, P 215


This second course in computational physics deals with simulations of classical and quantum mechanical systems of many particles. Applications of the methods introduced in this class include all branches of physics: solid state physics (crystal growth, surfaces,...), soft matter physics (polymers,...), liquid state physics (solute-solvent systems,...), phase transitions, ab initio calculations of atomic interactions, quantum fluids, and even astrophysics.
The concepts of classical and quantum mechanics and of statistical physics which are needed in the class will be recapitulated.
Attendance of the lecture Computational Physics I is not a requirement.

Table of Contents:

Part 1: Molecular Dynamics (MD)
    Steps of an MD simulation
    Integrating the equation of motion - Liouville formalism
    Force Fields
    Some MD tricks
    Calculation of Physical Properties
    Linear Response Theory
    Canonical ensemble MD: extended system methods

Part 2: Classical Monte Carlo Methods
    Pseudo Random numbers
    Probability distribution functions
    Metropolis algorithm
    (Magnetism: The Ising model)

Part 3: Quantum Monte Carlo Methods
    Variational Monte Carlo
    Diffusion Monte Carlo
    Excited states and the Fermion sign problem
    (Excited states and ill-posed inverse problems)


The contents of the lecture may be subject to minor changes.  You will work on 2 projects, each
consisting of (i) writing a program, (ii) conducting 'experiments' with the program and obtaining results,
and (iii) writing a report about it.
The final grade for the lecture and exercise class is based on your 2 written reports and on your
participation in class discussion

Literature:

part I,II:
    M. P. Allen & D. J. Tildesley "Computer Simulations of Liquids", Oxford Science Pub.
    D. Frenkel & B. Smit "Understanding Molecular Simulation", Academic Press
    advanced: D. J. Evans & G. P. Morriss "Statistical Mechanics of Nonequilibrium Liquids", Academic Press
                   M. Griebel et al. "Numerische Simulation in der Molekueldynamik", Springer

part III:
    R. Guardiola in "Microscopic Quantum Many-Body Theories and their Applications", Lecture
        Notes in Physics, Springer
    B. L. Hammond et al. "Monte Carlo Methods in Ab Initio Quantum Chemistry", World Scientific Pub.