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In this course, you will learn a lot of modern physics (classical and quantum) by downloading, generalising, or writing from scratch basic computer programmes, discussing them, and then handing them in. Join if you're curious (but not necessarily knowledgeable) about algorithms and the deep insights into science that the algorithmic approach can provide.
Syllabus :
1. Monte Carlo algorithms (Direct sampling, Markov-chain sampling)
- Introduction to Monte Carlo algorithms
- Exponential convergence and the 3x3 pebble game
- From the one-half rule to the bunching method
2. Hard disks: From Classical Mechanics to Statistical Mechanics
- Hard disks: from Classical Mechanics to Statistical Mechanics
- Equiprobability, partition functions, and virial expansions for hard disks
- Paradoxes of hard-disk simulations in a box
3. Entropic interactions and phase transitions
- Entropic interactions, phase transitions
- Algorithms, exact solutions, thermodynamic limit
- Two-dimensional liquids and solids
4. Sampling and integration
- Sampling and Integration - From Gaussians to the Maxwell and Boltzmann distributions
- Sampling discrete and one-dimensional distributions
- Sampling and integration in high dimensions
5. Density matrices and Path integrals (Quantum Statistical mechanics 1/3)
- Density matrices and path integrals
- Trotter decomposition and quantum time-evolution
- Quantum statistical mechanics and Quantum Monte Carlo
6. Lévy Quantum Paths (Quantum Statistical mechanics 2/3)
- Lévy sampling of quantum paths
- Bosonic statistics (with wave functions)
- Path sampling: A firework of algorithms
7. Bose-Einstein condensation (Quantum Statistical mechanics 3/3)
- Quantum indiscernability and Bose-Einstein condensation
- Permutation cycles and ideal Bosons
- Bosons in a trap - Bose-Einstein condensation
8. Ising model - Enumerations and Monte Carlo algorithms
- Ising model - From enumeration to Cluster Monte Carlo Simulations
- Ising model - Heat bath algorithm, coupling of Markov chains
- Cluster sampling, perfect sampling in the Ising mode
9. Dynamic Monte Carlo, simulated annealing
- Dynamical Monte Carlo and the Faster-than-the-Clock approach
- Simulated Annealing and the 13-sphere problem
- Simulated Annealing for sphere packings and the travelling salesman problem
10. The Alpha and the Omega of Monte Carlo, Review, Party
- The Alpha and the Omega of Monte Carlo
- Review - Party - Best of
