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KPZ growth with conserved step density Marcel den Nijs (University of Washington) DMR 0341341.
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KPZ growth with conserved step density Marcel den Nijs (University of Washington) DMR 0341341 Non-equilibrium driven stochastic processes, such as asymmetric exclusion driven flow in narrow channels, and KPZ type interface growth, pose the fundamental problem that their stationary state probability distributions are unpredictable (unlike the familiar Gibbs equilibrium distributions). Moreover, in the above examples the process is critical in the sense that the stationary state is reached without any characteristic time scale with a dynamic exponent z=3/2. For this reason, studies in this area focus on the stability of this value of z and of the stationary state structure with respect to, clustering (traffic jams) using both numerical and analytic techniques. In this specific project we studied the generalization of KPZ type interface growth where the number of up and down steps are both conserved. We showed that this extra conservation law does not change the value z=3/2. It turns out that this process decouples into two independent Burgers equations, one for the left moving up-steps and another one for the right-moving down-steps. The large amount of step bunching (traffic jamming) does not affect the fluctuations at large length scales. We discovered this by numerical simulations and then proved it exactly using the so called matrix product ansatz method in terms of perfect screening in the stationary state step-step correlation functions.
KPZ growth with conserved step density Marcel den Nijs (University of Washington) DMR 0341341 The time evolution of the interface profile includes strong oscillations. To avoid these, we focused on the evolution of the step-step correlations, as shown in the figure. Note the soliton-like shaped traveling correlations. This project formed the core of Kyung Kim’s PhD thesis. Kyung is currently a post doc in bioinformatics at the UW. This type of rigorous statistical physics training can serve as an excellent starting point towards careers in areas like biophysics, bioinformatics, and neuroscience. “Dynamic Screening in a Two-Species Asymmetric Exclusion Process”, Kyung Hyuk Kim and Marcel den Nijs, Phys. Rev. E 76, 021107 (2007).