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master degree course in PHYSICS – FISICA

Course year 2
Teaching units Unit Atomistic simulation methods
Theory and Foundations of Physics (lesson)
  • TAF: Compulsory subjects, characteristic of the class SSD: FIS/02 CFU: 6
Teachers: Mauro FERRARIO
Exam type oral
Evaluation final vote
Teaching language Italiano
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To expose students to a range of numerical applications of the MonteCarlo and Molecular Dynamics methods in theoretical and computational physics

To give all students experience of code development for MonteCarlo and Molecular Dynamics modeling of physical processes on a computer and of using established numerical codes to simulate physical systems.

To provide experience in writing with appropriate technical language and mathematical formalism a report of numerical modeling.

To provide what is needed to deepen understanding of the Monte Carlo and Molecular Dynamics numerical methods and its uses in atomistic modelling in physics.

Admission requirements

Basic knowledge of Numerical calculus, Classical and Quantum Mechanics, Thermodynamics and Statistical Physics

Course contents

Theoretical lectures and numerical laboratory activities will introduce and illustrate numerical modelling applied to simulate systems of particles at the level of the atomistic description. The course will deal with:
- numerical methods, algorithms and scientific programming in python.
- generation of random numbers with predefined probability distribution and correlation.
- stochastic processes, Markov chains and Brownian motion.
- introduction to the Monte Carlo method, importance sampling, acceptance-rejection schemes,
- Metropolis and Wang-Landau MonteCarlo sampling schemes.
- introduction to the Molecular Dynamics method, integration schemes, deterministic and brownian dynamics,
- empirical force-fields and order-N methods in condensed matter,
- thermodynamic constraints and numerical Statistical Mechanics
- Applications to phase transitions, Ising and hard-sphere fluid model, static and dynamics properties of molecular systems, free-energy calculations, ground state search for many body quantum systems by Variational & Diffusion Monte Carlo.

Teaching methods

Traditional lectures with the possible aid of multimedia supports and practical classes in the computer laboratory with online learning support through DataCamp. Attendance is highly recommended, but not compulsory. Planning and technical info, together with the teaching material and student support will be made available on a suitable e-learning platform. According to the evolution of the coronavirus pandemic lectures/practical may be delivered as webinars to comply with the restrictions of social distancing.

Assessment methods

Written report of a numerical modeling project, final oral examination. Written report of an autonomously developed numerical modelling project chosen from a given set and to be discussed in the final oral examination. According to the evolution of the coronavirus pandemic assessments may be carried out online to comply with the restrictions of social distancing.

Learning outcomes

At the end of the course the student will have acquired/developed

1. Knowledge and understanding:
knowledge of the MonteCarlo simulation approach for atomistic systems
knowledge of the Molecular Dynamics simulation approach for atomistic systems
understanding of the basic modelling approaches of Computational Statistical Physics

2. Ability to apply knowledge and understanding:
basic programming ability to develop and execute a MonteCarlo or Molecular Dynamics computer code to simulate atomistic models

3. Autonomy of judgment:
ability to analyse and autonomously choose the appropriate numerical approach for modelling one of the proposed physical problems

4. Communication skills:
ability to write scientific reports and talk about both the setup and the results of numerical simulation experiments

5. Learning skills:
ability of further learn and develop, autonomously, theoretical modelling skills using advanced computational physics approaches.


Handouts and web-based teaching material, selected chapters from the following textbooks:
D. Frenkel and B. Smit, "Understanding Molecular Simulation - Second Edition", (Academic Press, 2002)
D. P. Landau and K. Binder, "A Guide to Monte Carlo Simulations in Statistical Physics" (Cambridge, 2013)