Single pair bound state experiments
**Previous:** Temperature
**Up:** Observations

## Single pair bound state experiments

Plot 4 shows a single pair of quarks. Any algorithm that produces an
answer must produce the same answer (), so
the effects of incorrect pairings from other possible problems can
isolated.
Plot 4 shows the position of each particle as a function of
time. The maximum positions can seen easily to getting further and further
apart from each other. This increase in separation corresponds to
an increase in maximum potential energy. The period of the oscillation
can also be observed to increase slightly in plot 4.

Plot 4 incorporates the numerical integration step size adjustments,
but not the velocity constraint on step size. This constraint is that
the step size be small when the quarks pass through their centre of
mass. The velocity at that point is at its largest, and the quarks are
easily accelerated well beyond the centre of mass. This overshoot can
be seen to increase the kinetic energy slightly, at no cost in
potential energy.

Plot 5 shows the position as a function of time with the velocity
constraint. It can be seen in this plot that the increase in maximum
separation is only appreciable over very long time scales. The
increase in plot 5 is some of plot 4. More importantly, if
higher precision is required, the smallest step size permitted can be decreased.
The step size in this simulation was constrained to be between 1 and 10000.

*mcr@ccs.carleton.ca*