About this course: In this course you will learn a whole lot of modern physics (classical and quantum) from basic computer programs that you will download, generalize, or write from scratch, discuss, and then hand in. Join in if you are curious (but not necessarily knowledgeable) about algorithms, and about the deep insights into science that you can obtain by the algorithmic approach.
Created by: École normale supérieure
Taught by: Werner Krauth, Directeur de recherches au CNRS
Department of physics
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
Monte Carlo algorithms (Direct sampling, Markov-chain sampling)
Dear students,
welcome to the first week of Statistical Mechanics: Algorithms and Computations!
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Here are a few details about the structure of the course: For each week, a lecture and a tutorial videos will be presented, together with a downloadable copy o...
3 videos, 2 readings, 1 practice quiz
Graded: From the one-half rule to the bunching method
WEEK 2
Hard disks: From Classical Mechanics to Statistical Mechanics
In Week 2, you will get in touch with the hard-disk model, which was first simulated by Molecular Dynamics in the 1950's. We will describe the difference between direct sampling and Markov-chain sampling, and also study the connection of Monte Carlo and Molecu...
3 videos, 1 reading, 1 practice quiz
Graded: Paradoxes of hard-disk simulations in a box
WEEK 3
Entropic interactions and phase transitions
After the hard disks of Week 2, in Week 3 we switch to clothe-pins aligned on a washing line. This is a great model to learn about the entropic interactions, coming only from statistical-mechanics considerations. In the tutorial you will see an example of a ty...
3 videos, 2 readings, 1 practice quiz
Graded: Two-dimensional liquids and solids
WEEK 4
Sampling and integration
In Week 4 we will deepen our understanding of sampling, and its connection with integration, and this will allow us to introduce another pillar of statistical mechanics (after the equiprobability principle): the Maxwell and Boltzmann distributions of velocitie...
3 videos, 1 reading, 1 practice quiz
Graded: Sampling and integration in high dimensions
WEEK 5
Density matrices and Path integrals (Quantum Statistical mechanics 1/3)
Week 5 is the first episode of a three-weeks journey through quantum statistical mechanics. We will start by learning about density matrices and path integrals, fascinating tools to study quantum systems. In many cases, the Trotter approximation will be useful...
3 videos, 1 reading, 1 practice quiz
Graded: Quantum statistical mechanics and Quantum Monte Carlo
WEEK 6
Lévy Quantum Paths (Quantum Statistical mechanics 2/3)
In Week 6, the second quantum week, we will introduce the properties of bosons, indistinguishable particles with peculiar statistics. At the same time, we will also go further by learning a powerful sampling algorithm, the Lévy construction, and in the homewor...
3 videos, 1 reading, 1 practice quiz
Graded: Path sampling: A firework of algorithms
WEEK 7
Bose-Einstein condensation (Quantum Statistical mechanics 3/3)
At the end of our quantum journey, in Week 7, we discuss the Bose-Einstein condensation phenomenon, theoretically predicted in the 1920's and observed in the 1990's in experiments with ultracold atoms. In the path-integral framework, an elegant description of ...
3 videos, 1 reading, 1 practice quiz
Graded: Bosons in a trap - Bose-Einstein condensation
WEEK 8
Ising model - Enumerations and Monte Carlo algorithms
In Week 8 we come back to classical physics, and in particular to the Ising model, which captures the essential physics of a set of magnetic spins. This is also a fundamental model for the development of sampling algorithms, and we will see different approache...
3 videos, 1 reading, 1 practice quiz
Graded: Cluster sampling, perfect sampling in the Ising model
WEEK 9
Dynamic Monte Carlo, simulated annealing
Continuing with simple models for spins, in Week 9 we start by learning about a dynamic Monte Carlo algorithm which runs faster than the clock. This is easily devised for a single-spin system, and can also be generalized to the full Ising model from Week 8. In...
3 videos, 1 reading
Graded: Simulated Annealing for sphere packings and the travelling salesman problem
WEEK 10
The Alpha and the Omega of Monte Carlo, Review, Party
The lecture of Week 10 includes the alpha and the omega of our course. First we repeat the experiment of Buffon's needle, already performed in the 18th century, and then we touch the sophisticated theory of Lévy stable distributions, and their connection with ...
2 videos, 1 reading
Graded: Final Exam 2016
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École normale supérieure
L’École normale supérieure (ENS) est un établissement d'enseignement supérieur pour les études prédoctorales et doctorales (graduate school) et un haut lieu de la recherche française. L'ENS offre à 300 nouveaux étudiants et 200 doctorants chaque année une formation de haut niveau, largement pluridisciplinaire, des humanités et sciences sociales aux sciences dures. Régulièrement distinguée au niveau international, l'ENS a formé 10 médailles Fields et 13 prix Nobel.
Ratings and Reviews
A good combination of physics and programming.
I learned a bunch of things, thank you very much.
The lectures are great, and the material covered is awesome. I do not own a copy of the accompanied textbook, but I imagine that this course would be even better if I did.
Sometimes the homework sessions felt a little contrived - but I am fairly certain that this was just an artifact of making them peer-gradable.
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A great introduction to the ideas of statistical mechanics and Monte Carlo methods. I also like Dr. Krauth's sense of humour. He begins by imagining children on the beach in Monte Carlo, computing pi by throwing pebbles.
If you're looking for a nice set of lectures followed by easy multiple choice questions, this course isn't for you. The lectures and tutorials are very professional, Dr. Krauth & his students have done a great job, but the assignments are where you will learn the most. They are hard work, and I found I had to think hard. Don't leave them until the last minute: start early, and break for a walk outside when you get stuck. They really teach the ideas.
I started this course to support other coursework as was doing, as I felt my command of thermodynamics was a bit shaky. I've found it enjoyable in its own right. I've learned to appreciate Monte Carlo methods, and apply them to my own work on Molecular Diagnosis.