Weekly plans for week 5
Dear all, welcome back to FYS4411/9411. Here follows a quick review of what we did last week, with plans for this week and reading material.
Again, due to the present covid-19 situation, the lecture and the lab sessions are still online. We hope to be able to meet in person as soon as possible.
Last week we discussed the Metropolis algorithm with and without
importance sampling and derived the Metropolis-Hastings algorithm.
We replaced the brute force Metropolis algorithm with a walk in
coordinate space biased by the trial wave function. This approach is
based on the Fokker-Planck equation and the Langevin equation for
generating a trajectory in coordinate space. The link between the
Fokker-Planck equation and the Langevin equations and
importance sampling is non-trivial and perhaps almost impossible to
explain without a full semester course in for example statistical mechanics
and transport theory. However, we will try.
The plans for this week are:
o First we want to give you an overarching view on the equations we need to program in order to perform importance sampling with a simple Python code that demonstrates the essential elements.
o Secondly, we will go through the computational elements we need in order to program the local energy, the trial wave functions and the so-called _quantum force_ in the most efficient way (computationally).
o Finally, we will try to give a better connection between the equations for importance sampling and their links with the Fokker-Planck and Langevin equations.
The teaching material (slides) is at for example http://compphysics.github.io/ComputationalPhysics2/doc/pub/week4/html/week4.html
o You may find the following "Lecture on the Langevin and Fokker-Planck equations":"https://www.youtube.com/watch?v=H9I0PmXwhdo" as a useful introduction.
o The textbook of Gardiner on Stochastic Methods https://www.springer.com/gp/book/9783540707127 is a classic and chapters 4 and 5 are the most relevant ones in order to get a better understanding of these equations. The textbook can be downloaded via UiO's subscription to Springer.
o Another excellent reference on topics like Brownian motion, Markov chains, the Fokker-Planck equation and the Langevin equation is the text by Van Kampen http://www.elsevier.com/books/stochastic-processes-in-physics-and-chemistry/van-kampen/978-0-444-52965-7
Best wishes to you all,
Morten and ?yvind