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Physics  2015 

Searching for the Tracy-Widom distribution in nonequilibrium processes

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Abstract:

While originally discovered in the context of the Gaussian Unitary Ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the Tracy-Widom distribution plays an important role. In our contribution we study one-dimensional systems with domain wall initial conditions. For an appropriate choice of parameters the profile develops a rarefaction wave, while maintaining the initial equilibrium states far to the left and right, which thus serve as infinitely extended thermal reservoirs. For two distinct model systems we will demonstrate that the properly projected time-integrated current has a deterministic contribution, linear in time $t$, and fluctuations of size $t^{1/3}$ with a Tracy-Widom distributed random amplitude.

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