Numerical integration of conservative systems. Molecular dynamics of Lennard-Jones gas. Chaotic systems and attractors. Stochastic systems, random walk and Markov processes. Monte Carlo method for spin systems. Disordered and neural networks.
Quantum dynamics of finite and infinite dimensional systems. Spin chains and entanglement. Quantum stocasticity and quantum random walks. Measurements and noise. Quantum Monte Carlo. Optimisation, control and quantum machine learning.
Werner Krauth, Statistical Mechanics: Algorithms and Computations (Oxford Master Series in Statistical, Computational, and Theoretical Physics) (2006)
Harvey Gould, Jan Tobochnik, and Wolfgang Christian, Introduction to Computer Simulation Methods, Addison-Wesley (1995)
Herman J. C. Berendsen, Simulating the Physical World: Hierarchical Modeling from Quantum Mechanics to Fluid Dynamics, Cambridge University Press (2007)
Luciano Maria Barone, Enzo Marinari, Giovanni Organtini, Federico Ricci-Tersenghi, Scientific Programming: C-Language, Algorithms and Models in Science, World Scientific (2013)
M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids, Oxford University Press (1989)
I. Joshua and W. Jingbo, Computational Quantum Mechanics, Springer (2018)
A. F. J. Levi, Applied Quantum Mechanics, Cambridge University Press (2006)
G. Lindblad, “Quantum Mechanics with MATLAB,” available on internet, http://mathphys.physics.kth.se/schrodinger.html
Introduction to Matlab: https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/intro.pdf
and File Exchange su http://www.mathworks.com/matlabcentral/
Learning Objectives
The course aims to provide the basic elements of the scientific programming in the field of physics. During the course one will face problems of classical and quantum physics from a computational point of view. We will analyze the deterministic and stochastic dynamical classical and quantum systems with few and many degrees of freedom.
Those who follow this course could usefully combine it with: Physics of Complex Systems, Statistical Physics and Information Theory, Quantum Information (Curriculum of Condensed Matter); Statistical Mechanics I and II , Theory of Dynamical Systems (Curriculum of Theoretical Physics). In addition, there are strong links to the courses in physics of solids, liquids and phase transitions.
- Writing of a scientific program and its execution.
- Numerical simulation of a physical model.
- Analysis, visualization and interpretation of the data.
- Comparison of numerical results with physical theories.
Prerequisites
- Basic knowledge of: mathematical analysis and linear algebra, physics, classical and quantum statistical mechanics.
- Basic elements of C and Matlab programming languages
- Use of an operating system
Teaching Methods
6 credits, with lab lectures.
The theory is only hinted at, you can find a more extensive discussion in other courses (Statistica Mechanics, Critical Phenomena, Physics of Complex Systems, Out of Equilibrium Statistical Physics, Theory of Dynamical Systems, Quantum Information, Quantum Optics, Photonics, Ultracold Atoms, Quantum Gases). In the workshop will present practical problems, given a sample implementation and prompted the development of a program working in small groups.
Further information
Office hours by appointment. Emails: franco.bagnoli@unifi.it
filippo.caruso@unifi.it
Available for receptions via skype / google hangout.
Refer also to the e-learning system http://e-l.unifi.it .
Type of Assessment
The exams is based on a laboratory test where one has to write down a C and/or Matlab numerical code to solve one problem of classical computational physics and one related to quantum physics.
Course program
Part I
- Numerical integration of differential equations (RK and Verlet). Harmonic oscillator and pendulum.
- Molecular dynamics of a Lennard-Jones gas. Measurements and observables.
- Bifurcations and chaos: logistic map and Lorenz model.
- Lyapunov exponents for maps and continuous systems. Attractors.
- Stochastic systems: random walks. Probability distributions.
- Percolation: Markov process. Mean field theory.
- Monte-Carlo Method. Ising Model. Phase transitions, fluctuations, etc.
- Disordered systems, spin glasses. Neural networks and learning (basic notions).
Part II
- Introduction to Matlab/Octave
- Time-independent Scroedinger equation
- Quantum particle in a potential hole
- Quantum harmonic oscillator
- Spin chain dynamics: entanglement
- Composite quantum systems and partial trace
- Quantum stochastic systems: quantum random walks
- Lindblad equation and noise
- Quantum Monte Carlo and applications
- Quantum Zeno effects
- Optimisation, control and quantum machine learning