IDI fluctuation, probability density and PP plots.

<p>(a)-(c) for the experiment with pump parameter <i>p</i> = <i>I</i>/<i>I</i>_<i>th</i> = 1.0145 and threshold -1.5, (d)-(e) for the LK model simulation with pump parameter <i>μ</i> = 1.020 and threshold -1.0. In the density plots, the red curve is the fitted non-Gaussian stable density, the blue curve is the Gaussian density with the sample mean and variance, and the dotted curve is the smoothed data density. In the PP plots, a 45-degree red line is also drawn for reference.</p

Fitted stable-parameters.

<p><i>α</i> and <i>γ</i>, versus the pump parameter for two thresholds: (a), (b) experimental data; (c), (d) simulated data. For the experimental data, the maximum values of the 95% confidence interval half-widths are quite small, 0.007 and 0.003 for <i>α</i> and <i>γ</i>, respectively. For the simulated data, the maximum half-widths are also quite small, 0.01 and 0.004, respectively, and therefore the error bars (parameter +/− confidence interval) are also not plotted because they are all too small to be seen.</p

Comparison of position standard deviations for the first example.

<p>Natural-log of the Newtonian (squares) and special-relativistic (diamonds) position standard deviations for the first example.</p

Comparison of probability densities for the first example.

<p>Newtonian (shaded grey) and special-relativistic (bold line) position (top plot) and momentum (bottom plot) probability densities for the first example at kick 17.</p

Trajectories for the third example.

<p>Quasiperiodic Newtonian, special-relativistic and general-relativistic phase-space trajectories, plotted for the first 1000 impacts, from the non-chaotic third example. The three trajectories are still close to one another at impact 1000 and thus they are indistinguishable in the plot.</p

Difference between the special-relativistic and general-relativistic trajectories for the second example.

<p>Natural-log of the magnitude of the difference between the special-relativistic and general-relativistic positions (squares) and velocities (diamonds) for the chaotic second example. Straight-line fits up to impact 61 are also plotted.</p

Difference between the mean trajectories for the first example.

<p>Natural-log of the absolute value of the difference between the Newtonian and special-relativistic mean positions (top plot) and mean momentums (bottom plot) for the first example. The mean-position differences at kick 22 and 24 cannot be resolved with the accuracy we have for the Newtonian and special-relativistic mean positions at those kicks.</p

Difference between the Newtonian and general-relativistic trajectories for the third example.

<p>Magnitude of the difference between the Newtonian and general-relativistic positions (top plot) and velocities (bottom plot) for the non-chaotic third example. Straight-line fits are also plotted.</p

Newtonian trajectory for the second example.

<p>Top: Chaotic Newtonian phase-space trajectory, plotted for the first 210 impacts, from the second example. Bottom: Natural-log of the magnitude of the difference [position difference (squares), velocity difference (diamonds)] between the chaotic Newtonian trajectory and another Newtonian trajectory which differed initially by 10⁻¹⁴ in position and 10⁻¹² in velocity. Straight-line fits up to impact 84 are also plotted.</p

Comparison of trajectories for the second example.

<p>Comparison of the Newtonian (squares), special-relativistic (diamonds) and general-relativistic (triangles) positions (top plot) and velocities (bottom plot) for the chaotic second example.</p