Microscopic State

Microscopic State:: N coordinates q₁, q₂, ..., q_N, and N momenta p₁, p₂ ,..., p_N. It is point in the phase space .
Phase Space:: All points in phase space

Examples

1.

One-dimensional Harmonic Oscillator.
$\begin{figure*} \InputIfFileExists{harmonic.pstex_t}{}{}\end{figure*}$
Energy conservation:

$\begin{displaymath} \frac{q^2}{2k}+\frac{p^2}{2m} = E\end{displaymath}$

This is the equation of ellipse (see also problem 5 from the Quiz):
$\begin{figure*} \InputIfFileExists{ellipse.pstex_t}{}{}\end{figure*}$

2.

N particles in a cubic volume.
$\begin{figure*} \InputIfFileExists{idealgas.pstex_t}{}{} \end{figure*}$

6N-dimensional phase space.
$\begin{figure*} \InputIfFileExists{idealgas_trajectory.pstex_t}{}{}\end{figure*}$

3.

Discrete Phase Space-Ising spins
$\begin{figure*} \InputIfFileExists{3spins.pstex_t}{}{}\end{figure*}$
General case: N spins:
$\begin{figure*} \InputIfFileExists{ising.pstex_t}{}{}\end{figure*}$
Phase trajectory: discrete hops
$\begin{figure*} \InputIfFileExists{3spins_trajectory.pstex_t}{}{}\end{figure*}$