Fakultät für Physik
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Seminar: Selected Topics in Computational Physics – Topics

Selected topics and literature:

Extended description of topics supervised by Prof. Scrinzi

Topics Literature
Monte Carlo methods / Ruhl J. M. Thijssen, Computational Physics, Cambridge, ISBN-13 978-0-521-57588-1
Quantum transport equations and numerical integrators / Ruhl Michael Bonitz, Quantum transport theory, Teubner Texte
Relativistic quantum transport equations and numerical integrators / Ruhl S. R. De Groot, W. A. van Leeuwen, Ch.G. van Weert,Relativistic kinetic theory, North Holland, ISBN: 0 44485453 3, D. Vasak, M. Gylassy, H. T. Elze, Quantum Transport Theory for Abelian Plasma, Annals of Physics 173, 462 (1987).
Molecular Dynamics and integrators for ODEs / Ruhl

D. Vasak, M. Gylassy, H. T. Elze, Quantum Transport Theory for Abelian Plasma, Annals of Physics 173, 462 (1987).

Mean field methods: Hartree, Hartree-Fock, DFT, and Gross-Pitaevskii / Scrinzi

Present, compare and assess the various mean-field methods, literature: t.b.a

Non-linear wave dynamics / Scrinzi

Implement Hartree or Gross-Pitaevskii in tRecX or, alternatively Python, Matlab etc.

The H-matrix technique / Scrinzi

Study a general method for handling structured matrices, both in theory and in compuational practice, literature: M. Bebendorf, Hierarchical matrices: A means to efficiently solve elliptic boundary value prob-
lems, Springer (2008)

Efficient integrators for non-linear systems / Scrinzi

Implement and compare advanced methods for the numerical solutions of non-linear wave equations, literature: Starting point is the section on time-integrators in M. H. Beck, A. J ̈ackle, G. A. Worth, and H.-D.
Meyer, Phys. Rep. 324, 1, (2000)

Complementary reading: General numerical methods, software tools.

Additional literature:

  • F. Mandl and G. Shaw, Quantum field theory, WILEY.