LEARNING OUTCOMES

The course aims at providing an introduction to Monte Carlo simulation techniques

   applied to condended matter and fundamental interations physics.

AIMS AND LEARNING OUTCOMES

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)

PREREQUISITES

No formal prerequisites, but a good knowledge of a programming language is recomended

TEACHING METHODS

Theoretical lectures and practical exercitations 

SYLLABUS/CONTENT

- 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.

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes on the course web site