Models and Asymptotics of Non-equilibrium Steady States in Driven Diffusive Systems

该奖项将支持驱动扩散系统中非平衡稳态（NESS）的分析。此类中感兴趣的物理系统通常通过扩散非线性演化方程进行确定性建模，或者通过某些类型的马尔可夫过程进行随机建模。这里提到的 NESS 与线性动力学的平衡或详细平衡的不变测量不同，因为非平衡稳态表现出相分离（通常由边界动力学驱动）、自发对称性破缺和/或远离临界转变的长程相关性。要探索的具体环境包括条纹图案形成的强弯曲机制、空间随机分区和随机矩阵集合。非平衡稳态是许多物理系统和模型的典型特征，包括远离阈值的图案形成系统中的缺陷凝聚、经典分子形成、相互作用的玻色粒子系统、摇动的颗粒气体、无限等位基因模型、通过优先附着或重新布线形成的网络、随机增长模型和二维量子引力。该奖项将支持使用确定性（非随机）和随机（随机）技术的此类系统行为的研究方法。

This award will support the analysis of non-equilibrium steady states (NESS) in driven diffusive systems. Physical systems of interest in this general class are typically modeled either deterministically by diffusive nonlinear evolution equations or stochastically by certain types of Markov processes. The NESS referred to here differ from the equilibria of linear dynamics or the invariant measures of detailed balance in that the non-equilibrium steady states exhibit phase separation (often driven by boundary dynamics), spontaneous symmetry breaking and/or long range correlations away from critical transitions. Specific contexts to be explored include the strong bending regime of striped pattern formation, spatial random partitions, and random matrix ensembles. Non-equilibrium steady states are typical for a number of physical systems and models, including defect condensation in pattern forming systems driven far from threshold, classical molecule formation, a system of interacting Bose particles, shaken granular gasses, infinite allele models, network formation by preferential attachment or rewiring, stochastic growth models and two-dimensional quantum gravity. The award will support research approaches on the behavior of such systems that uses deterministic (non-random) as well as stochastic (random) techniques.