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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.