## LecturerDénes Sexty & Alexander Rothkopf, Summer term 2015## Date- Lecture: Monday, 11:30-13:00, Phil 19 / Seminarraum
- Exercises: Monday,14:15-16:00, CIP-Pool Phil 12 (starting Mon. April 20th)
You will need your 'Uni-ID' to log in to the computer system. -
**Klausur**: Preliminary date**July 31st, 13:00h****in the CIP-Pool Phil 12** **Programming****take-home exam**: PDF hand in solutions until July 30th or at the Klausur on July 31st.
## Topics- Introduction
- The Ising Model
- Monte Carlo Methods
- Solving the linear and non-linear Schroedinger equation
- Path integral on the lattice
- Scalar Fields I
- Scalar Fields II
- Scalar Fields III - Data Analysis
- Gauge fields on the lattice I
- Gauge fields on the lattice II
- Fermions on the lattice
- Non-equilibrium QFT
- Nonzero chemical potential
- Field content of the standard model, non-perturbative phenomena of current interest, the concept of lattice discretization, development of computational ressources
Lecture note as PDF - 1d solution: direct and transfer-matrix, 2d-Ising low- and high-temperature expansion, dimerization, phase diagram
Lecture note as PDF Tutorial - Introduction to C: Note as PDF - Markov chains, Detailed balance, Metropolis algorithm, Hybrid Monte Carlo, Langevin equation, Fokker-Planck equation
Lecture note as PDF (incl. complete proof of detailed balance, see also Bhanot 1986.) Tutorial - Towards 1d-Ising with Metropolis: Note as PDF, Sample Program: source - Recap on partial differential equations, physics motivation: quantum mechaniscs, Bose-Einstein condensation, discretization schemes
Lecture note as PDF Tutorial - Solving the 2d-Poisson equation: Note as PDF, Sample Program: source - PDE solvers continued; path integral for quantum mechanics, euclidean formulation, partition function (transfer matrix, reflection positivity)
Lecture note as PDF (typo corrected in last line of ADI solver) Tutorial - Eigenvalues and -vectors for the 1d-harmonic oscillator, forward Euler time evolution, Sample Program Eigenvectors, -values: source - reflection positivity, transfer operator, free scalar field, continuum limit
Lecture note as PDF Tutorial - Thomas algorithm for periodic boudnary conditions, Crank-Nicolson time evolution, Sample Program : source - spontaneous symmetry breaking, spin system, critical point, continuum limit, lattice perturbation theory, renormalization hopping parameter expansion, triviality
Lecture note as PDF Tutorial - HMC algorithm for O(1) theory in 1 Euclidean dimension, Sample Program : source - Lüscher-Weisz solution and triviality; autocorrelation, covariance matrix, likelihood fitting, jackknife resampling, reweighting
Lecture note as PDF (changed the autocorrelation FFT formula)Tutorial - Decorrelated exponential fitting : Updated Exercise Sheet - Data Sets Sample programs: autocorrelation, Exponential Fit (with Jackknife and Decorrelation) - Concept of gauge theory, parallel transport, Haar measure, Wilson action, Gauge fixing
Lecture note as PDF Tutorial - Simulating SU(2) gauge theory : Exercise Sheet - Landau gauge fixing, Kogut-Sussking Hamiltonian, Improved actions, Wilson loop and strong coupling expansion, Polyakov loop and center symmetry, scale setting
Lecture note as PDF Tutorial - Heatbath for SU(2) - Simulating SU(3) gauge theory : Exercise Sheet - Naive fermions, doubling, Chiral symmetry,
Wilson fermions, staggered fermions,Fermion matrix inversion
Lecture note as PDF Tutorial - Conjugate Gradient algorithm for sparse matrices: code , Exercise Sheet - scalar fields in cosmology and in cold atom systems, gauge fields in heavy-ion collisions, path integral on the Schwinger-Keldysh time contour, classical statistical approximation and its simulation, classical gauge fields in Hamiltonian and Lagrangian formulation
Lecture note as PDF Tutorial - High performance computing with OpenMPI: Exercise Sheet Sample program: code, Guide to collective communication - sign problem, dual variables and worm algorithm,
stochastic quantisation
Lecture note as PDF Tutorial - Complex Langevin Exercise Sheet ## Literature- Lecture notes on lattice theory by Prof. M. Laine (recommended reading)
Homepage - I. Montvay, G. Münster: Quantum Fields on a Lattice
Cambridge, UK: Univ. Pr. (1994) 491 p. (Cambridge monographs on mathematical physics) - Heinz J. Rothe: Lattice Gauge Theories, An introduction
World Scientific Lecture Notes in Physics - Vol 74 - Jan Smit: Introduction to quantum fields on a lattice: A robust mate
Cambridge Lect.Notes Phys. 15 (2002) - C. Gattringer, C.B. Lang: Quantum Chromodynamics on the Lattice
Lecture Notes in Physics 788, Springer - For those with no C programming experience please work through:
C programming tutorial - Brian W. Kernighan, Dennis M. Ritchie: The C Programming Language (2nd edition)
ISBN-13: 007-6092003106 ISBN-10: 0131103628 Solution to exercises Examples - K.N. King: C Programming: A Modern Approach
ISBN-13: 978-0393969450 ISBN-10: 0393969452 - K. Reek: Pointers on C
ISBN-13: 978-0673999863 ISBN-10: 0673999866 - Z. A. Shaw: Learn C The Hard Way
Website See especially Chapter 4 for the use of the debugger "Valgrind" - W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, Third Edition (2007)
ISBN-10: 0521880688 ISBN-13: 978-0521880688
## Lattice theory## C Programming## Algorithms and Implementations## PrerequisitesKnowledge of quantum mechanics and statistical physics is required. Basic knowledge of quantum field theories is useful. |