Week 4 January 22-26, Building a Variational Monte Carlo program
Contents
Overview of week 4, January 22-26
Code templates for first project
Basic Quantum Monte Carlo, repetition from last week
Multi-dimensional integrals
Trail functions
Variational principle
Tedious parts of VMC calculations
Bird's eye view on Variational MC
Linking with standard statistical expressions for expectation values
The local energy
The Monte Carlo algorithm
Example from last week, the harmonic oscillator in one dimension (best seen with jupyter-notebook)
Why Markov chains, Brownian motion and the Metropolis algorithm
Brownian motion and Markov processes
Brownian motion and Markov processes, Ergodicity and Detailed balance
Brownian motion and Markov processes, jargon
Brownian motion and Markov processes, sequence of ingredients
Applications: almost every field in science
Markov processes
Markov processes
Markov processes, the probabilities
Markov processes
An Illustrative Example
An Illustrative Example
An Illustrative Example, next step
An Illustrative Example, the steady state
Code for the iterative process
Small exercise
What do the results mean?
Understanding the basics
Basics of the Metropolis Algorithm
The basic of the Metropolis Algorithm
More on the Metropolis
Metropolis algorithm, setting it up
Metropolis continues
Detailed Balance
More on Detailed Balance
Dynamical Equation
Interpreting the Metropolis Algorithm
Gershgorin bounds and Metropolis
Normalizing the Eigenvectors
More Metropolis analysis
Final Considerations I
Final Considerations II
Final Considerations III
The system: two particles (fermions normally) in a harmonic oscillator trap in two dimensions
Separating the degrees of freedom
Variational Monte Carlo code (best seen with jupyter-notebook)
First code attempt for the two-electron case
Code templates for first project
The C++ template
The python template, using JAX
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