Fig. 4: Reaching the coarsening speed limit.
a, The growth of ℓ2 for the same initial state (P1) and gas density but different a. All curves start at t = 0 and plotting them versus t − t* (with a-dependent t*) collapses them in the universal scaling regime. The dashed line shows ℓ2 = D(t − t*). For weaker interactions, the system approaches this speed limit slower and reaches it at a larger ℓ; the solid lines show exponential fits to the early-time data. b, When expressed in the interactions-set units of length, \(\xi =1/\sqrt{8{\rm{\pi }}na}\), and time, tξ ≡ mξ2/ħ, all of our data for different Pi, a, V, and n (see Fig. 3) collapse onto a single curve, meaning that the speed limit is always reached at the same ℓ/ξ. The solid line shows exponential growth with a time constant τ = 56tξ and the dashed line has slope mD/ħ = 3.4. c, Numerically differentiating the data in b, we eliminate the non-universal t* and show as a function of (ℓ/ξ)2 how dℓ2/dt approaches the universal D = 3.4ħ/m and then stops growing; the solid and dashed lines are the same functions as in b. For weaker interactions (larger ξ), observing this speed limit requires a larger physical system. The data points show averages based on at least 20 measurements. All error bars show standard errors of the measurements.
