A single semiconductor quantum dot under continuous excitation randomly switches ("blinks") between a bright, radiative ON state and a dark OFF state where an Auger-ejected charge carrier quenches emission. The defining experimental fact (Nirmal et al. 1996; Kuno et al. 2000) is that ON- and OFF-time durations follow a truncated power law, not an exponential:
P_on(t) ∝ t^(-α_on) · exp(-t/τ_c)
P_off(t) ∝ t^(-α_off) · exp(-t/τ_c)
This 2D version simulates an ensemble of independent dots arranged on a grid — a synthetic single-molecule fluorescence microscopy field — each running its own truncated-power-law telegraph process with the same random-duration sampler as the underlying model. Because a power law has no characteristic timescale, no two dots blink in sync, and the population never settles onto a simple exponential decay the way ordinary two-state (Poisson) kinetics would.
Below the grid, every ON-duration ever recorded across the whole ensemble is binned into a live log-log survival-function plot: P(T>t), the fraction of ON-events longer than t, plotted against t on log-log axes. A pure power law appears as a straight line of slope −(αon−1); the fitted slope (dashed reference line) is compared live against this theoretical value, and the cutoff τc shows up as a downward bend once t approaches it — exactly the diagnostic real single-dot spectroscopy papers use to extract α from measured blinking traces.
- αon / αoff — steeper exponents bias the ensemble toward many short flickers; shallower exponents (α near 1) let rare, very long excursions survive.
- τc — larger τc pushes the log-log bend further right, letting the straight-line power-law region extend to longer times.
- Durations are drawn by rejection sampling from a pure power law weighted by exp(-t/τc) — the same statistical model, and same sampler, used in the companion 3D single-dot simulation, here applied independently to every dot in the grid.