|SCIENTIFIC DISCIPLINARY SECTOR||FIS/01|
The course provides an introduction to Monte Carlo simulation techniques for condensed matter and fundamental interactions physics.
The course aims at providing an introduction to Monte Carlo simulation techniques
applied to condended matter and fundamental interations physics.
The course aims at providing the basic knowledge of Monte Carlo simulation techniques with application to condended matter and fundamental interactions physics. For condensed matter physics the learning outcomes are: - Markov chain simulation (Metropolis algorithm) - Simulation of phase transition in reticulated gas - Continuos-time Monte Carlo for equilibrium and non-equilibrium transitions - Simulation of aggregate creation. Fractals. For the physics of fundamental interactions the learning outcomes are: - Simulation of the transport of particles in matter - Simulation of the interaction and decay of particles in Lorentz-invariant phase space - Parametric simulation of a detector - Simulation of experiments (past and present)
No formal prerequisites, but a good knowledge of a programming language is recomended
Theoretical lectures and practical exercitations
- Introduction to the Monte Carlo method. Sampling methods: rejection, inversion. Variance reduction. Importance sampling.
- Markov chains. Homogeneity condition. Requirements for the convergence of Markov chains. Metropolis algorithm.
- Simulation of the reticular gas in two dimensions with repulsive interactions using the Metropolis algorithm. Order-disorder phase transitions. Order parameter.
- Continuous-time Monte Carlo for equilibrium simulations. Continous time Monte Carlo for non-equilibrium simulations.
- Simulation of the growth of two-dimensional aggregates with Monte Carlo in continuous time. DDA model. Scale laws for the density of free atoms and aggregates. Generalities on fractals and definition of non-integer dimensionality. Measurement of the fractal size of the aggregates.
- Simulation of the transport of particles in matter. Detailed and condensed simulation.
- Methods for variance reduction in the transport of particles in matter
- Simulation of particle decay and interaction in Lorentz-invariant phase space. Two-body decay. Three-body decay. Factorization.
- Parametric simulation of detectors and experiments. Applications to past and present experiments.
Lecture notes on the course web site
Office hours: Every day after appointment request.
RICCARDO FERRANDO (President)
FABRIZIO PARODI (President Substitute)
The teaching will take place in the second semester.
The oral exam consists in the discussion of an original essay and questions on the course program.
The original essay consists in the development of a program which, applying concepts and techniques acquired in the course, solves a physical problem.
The final score will take into account the results obtained, their presentation and answers to general questions.