On the integrable dynamical systems in statistical mechanics

Zheng, Yu

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On the integrable dynamical systems in statistical mechanics

Date

2016

Authors

Zheng, Yu

Abstract

Mathematical details of stochastic process are reviewed, before one-dimensional Ising model is introduced and solved statistical mechanically by partition function, quantum mechanically by Bethe ansatz and algebraic Bethe ansatz, and stochastically by master equation. Bethe ansatz are also applied to mass transport models including asymmetric simple exclusion process and zero range process. Several two-dimensional surface growth models and their corresponding universality classes are discussed.