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## SIMULATION METHODS APPLIED TO PHYSICS

CODE 98890 2022/2023 6 cfu during the 2nd year of 9012 FISICA(LM-17) - GENOVA 6 cfu during the 3nd year of 8758 FISICA (L-30) - GENOVA 6 cfu during the 1st year of 9012 FISICA(LM-17) - GENOVA FIS/01 GENOVA 2° Semester AULAWEB

## OVERVIEW

`The course provides an introduction to Monte Carlo simulation techniques for condensed matter and fundamental interactions physics.`

## AIMS AND CONTENT

### 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.

Lecture notes on the course web site

## TEACHERS AND EXAM BOARD

### Exam Board

RICCARDO FERRANDO (President)

FABRIZIO PARODI (President Substitute)

## LESSONS

### LESSONS START

The teaching will take place in the second semester.

### Class schedule

SIMULATION METHODS APPLIED TO PHYSICS

## EXAMS

### EXAM DESCRIPTION

`The oral exam consists in the discussion of an original essay and questions on the course program.`

### ASSESSMENT METHODS

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.