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Computational Physics Lectures: Random walks, Brownian motion and the Metropolis algorithm
Contents
Why Markov chains, Brownian motion and the Metropolis algorithm
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
A simple example (close to project 4) and some more jargon
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
An Illustrative Example, iterative steps
An Illustrative Example, what does it mean?
An Illustrative Example, understanding the basics
Simple c++ program to perform the above calculations
Entropy and the most likely state
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
The Metropolis Algorithm and Detailed Balance
Brief Summary
Simple example, particle in one dimension
Diffusion
Diffusion Equation
Diffusion Equation, continuity equation
Diffusion Equation, expectation values
Diffusion Equation, other expectation values
Diffusion Equation, normalization condition
Diffusion Equation
Diffusion Equation, the variance
Diffusion Equation, final expression for the variance
Diffusion Equation, interpretation
Diffusion Equation, simple illustration
Random Walks
Random Walks
Random Walks
Random Walks, simple program
Random walk
Simple python code with visualization of one-dimensional random walk
The Metropolis Algorithm and Detailed Balance
Another way of phrasing this is
\begin{equation} w(t=\infty) = Ww(t=\infty). \tag{3} \end{equation}
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