Quantum Techniques for Stochastic Mechanics, by Jacob Biamonte, QIC 890/891 Selected Advanced Topics in Quantum Information, The University of Waterloo, Waterloo Ontario, Canada, (Spring term 2012).

Given Aug 9th, 2012 in Waterloo Canada

Lecture Content

Review of lecture 1

Probabilities vs amplitudes (chapter 4)

Operators (creation and annihilation)

Amoeba field theory

Preamble to stochastic mechanics vs quantum mechanics

Note: the lecture content here is to be read along with the youtube video of the course. It should contain what was written on the board. Without the video, it might not make sense.

The master equation vs the rate equation

A stochastic petri net has

$k$ species

$x_i$ is the concetration of the ith species

we want to know

$\frac{d}{d t} x_i = ???$

one for each $1\leq i \leq k$.

The RHS: sum of terms, one term for each transition in the Petri net

For each transition we end up with a term like this

$\frac{d}{d t} x_i = r (n_i - m_i)x_1^{m_1}\cdots x_k^{m_k}$

$n_i$ is the number of times species $x_i$ appears in the output