Simulation Methods in Statistical Physics, spring 2013
Book: J.M. Thijssen, Computational Physics.
Frenkel and Smit's book (Understanding Molecular Simulations, available electronically from the library website) is well-written, and useful to read for this course. However, it does not cover everything that I am planning to discuss. In particular, there is no mention of Quantum MC.
Discussed so far
- Lecture 1, introduction
- basic structure of a simulation (for MD see Thijssen section 8.1)
- molecular Dynamics (MD) vs. Monte Carlo (MC); example: Lorentz gas
- Lecture 2, MD (Thijssen, parts of chapter 8)
- example for resource scaling: hard-sphere gas
- soft interactions: Lennard-Jones potential (Thijssen section 8.3)
- integration algorithms for MD: Verlet, Runge-Kutta (Thijssen section 8.2, Appendix A page 570-573)
- Lecture 3
- symplectic integration (Frenkel & Smit, appendix A.3.1, A.3.2)
- Lyapunov instability (Frenkel & Smit, section 4.3.4)
- inter-molecular interactions with cutoffs and long-range interactions (Thijssen pages 203 - 205, section 8.7 ; Ewald summations are also described in detail in Frenkel & Smit chapter 12)
- Lecture 4
- discussing programming projects
- exercise: hangman (entropy, resource scaling)
- Lecture 5
- interactions within molecules, particularly chemical bonds (Thijssen section 8.6)
- constraints (Thijssen section 8.6, Frenkel & Smit section 15.1)
- intro to Quantum MD (Thijssen section 9.1)
- Car-Parinello (Thijssen section 9.2, Frenkel & Smit section 15.2)
- Lecture 6
- finished the discussion on Car-Parinello (example from Frenkel & Smit section 15.2)
- the foundation of statistical mechanics: ergodicity, ergodic measure
- ensembles in statistical mechanics (Thijssen section 7.1)
- thermostats: langevin thermostat (Thijssen section 8.8)
- Lecture 7
- thermostats and barostats: Nosé-Hoover thermostat (Frenkel & Smit section 6.1.2, 6.1.3, 6.2)
- finite-size effects: in general and near phase transition (Thijssen chapter 7)
- Lecture 8
- correlation length and time, time averages (Thijssen chapter 7)
- Monte Carlo introduction: direct MC, MC integration (Thijssen section 10.1, 10.2)
- Drawing random variables with nonuniform distribution (Thijssen appendix B3)
- Lecture 9
- Importance sampling (Frenkel & Smit section 3.1.1)
- markov chains (Thijssen section 10.3)
- Metropolis, detailed balance (Frenkel & Smit section 3.1.2, 3.2.3)
- Ising model as example (Thijssen section 10.3.1)
- Lecture 10
- trial moves in the monatomic gas (Thijssen section 10.3.2, Frenkel & Smit section 3.3.1)
- trial moves with internal degrees of freedom (3.3.2)
- cluster moves (Frenkel & Smit section 14.3)
- Lecture 11
- discussing the programming projects
- Lecture 12
- more ensembles in Monte-Carlo (Frenkel & Smit chapter 5, Thijssen section 10.4)
- free-energy and chemical potential calculations (Frenkel & Smit sections 7.1 and 7.2, Thijssen section 10.5)
- Lecture 13, Quantum Monte Carlo
- variational Quantum Monte Carlo (Thijssen sections 3.1, 3.2, 12.1, 12.2)
- diffusion Monte Carlo (Thijssen section 12.3)
- Lecture 14, Quantum Monte Carlo
- Diffusion Monte Carlo continued (Thijssen section 12.3)
- Path integral Monte Carlo (Thijssen section 12.4.1)
- Lecture 15, Question hours
Programming projects. The classical MC and MD projects are related. Read both descriptions all the way through before you start writing your code. The project reports are due a little less than 2 weeks before the exam, the 11th of March. If you hand in your report later, but before the 1st of April, 08:00, you can still get a minimum passing grade for the programming project in question. There will be no third programming project. Include your code electronically. You can send it in by email. Here is a list of things you might want to think about if you have bugs or get stuck.
There are exercises for bonus points. They are meant to give you an opportunity to practice the basic concepts from this course. Ask me questions about them any time. Hand them in one week after they have been posted.
If you do these well enough, you get a bonus on the exam, or on the programming projects, wherever you need it the most.
The bonus is proportional to the amount of exercises you have done well, so it pays to do them, even if you have not done the others. It will be a maximum of 15% of the total score. I will not hand out solutions, but you can continue to ask me questions about the exercises after the deadline, by email or in person.
Note that the exam questions will be similar in style.
As mentioned in the first lecture, the weight of the exam and programming projects in the final grade is 50-50. You have to clear both to pass the course.