Recent experimental advances in ultrafast phenomena have triggered renewed interest in the dynamics of correlated quantum systems away from equilibrium. We review non-equilibrium dynamical mean-field theory studies of both the transient and the steady states of a DC field-driven correlated quantum system. In particular, we focus on the non-equilibrium behavior and how it relates to the fluctuation-dissipation theorem. The fluctuation-dissipation theorem emerges as an indicator for how the system thermalizes and for how it reaches a steady state. When the system thermalizes in an infinite temperature steady state it can pass through a succession of quasi-thermal states that approximately obey the fluctuation-dissipation theorem. We also discuss the Wigner distribution and what its evolution tells us about the non-equilibrium many-body problem.

超快现象的最新实验进展已引起人们对相关量子系统动力学趋于平衡的新兴趣。我们回顾了直流场驱动相关量子系统的瞬态和稳态的非平衡动力学平均场理论研究。特别是，我们关注于非平衡行为及其与波动耗散定理的关系。波动耗散定理作为系统如何热化以及如何达到稳态的指标而出现。当系统在无限温度稳态下热化时，它可以通过一系列近似服从波动耗散定理的准热态。我们还将讨论Wigner分布及其演变如何告诉我们有关非平衡多体问题的信息。