非平衡态量子物质是近年来理论和实验研究的热点，涌现出多种方案，一种可行的思路是在强关联电子体系的量子临界点附近研究非平衡态现象。由于量子临界综合了静态和动态的平衡，其附近的非平衡态动力学必将与经典临界显著不同，最近基于Anti-de-Sitter/共性场论的研究也证实该观点。一般认为费米子系统的量子临界现象可以分为常规和非常规两类：前者在平衡态层面对应高维体系的经典连续相变；而后者则没有该对应关系，尚未发现普适分类。我们将应用基于Keldysh回路的动态重整化群方法，研究近藤塌陷临界点附近的稳态，并同常规量子临界点对比，从而理解有效温度现象和开放量子临界点中非平衡态耗散与经典行为等效的条件。我们也将对动态NCA方法进行扩展以描述含时现象、淬火和达到量子临界点附近稳态的过程，包括周期性驱动系统。本项目不仅对理解量子临界的非平衡态有重要的理论意义，而且与含时泵浦-探测光谱等实验紧密相关。

Quantum matter out-of-equilibrium is currently pursuit in many settings both experimentally and theoretically. A particular promising setting to explore non-equilibrium phenomena is the proximity of quantum criticality. We propose to study time-dependent and far-from-equilibrium phenomena near quantum criticality that occurs in systems of strongly correlated electrons. As quantum criticality already links statics and dynamics at the equilibrium level, it is expected that the non-equilibrium dynamics near quantum criticality differs significantly from that of classical critical systems. Recent results based on the Anti-de-Sitter/conformal field theory connection appear to be in line with this expectation. In recent years it has become clear that quantum criticality in fermionic systems can be of the conventional type which –at the equilibrium leve – corresponds to a classical continuous phase transition in elevated dimensions or can be unconventional, where no such quantum-to-classical correspondence exists. Importantly, this quantum-to-classical mapping only holds at equilibrium. For quantum critical points that defy the quantum-to-classical correspondence, no classification in terms of universality classes exists at the moment. We will use a dynamical renormalization group formulated on the Keldysh contour to address the steady states near critical Kondo destruction, a type of unconventional quantum criticality and will compare the results with that of conventional quantum criticality. This is done in order to understand the phenomena of effective temperatures and address under which conditions non-equilibrium dissipation in open quantum criticality can lead.to classical behavior. We will also generalize dynamical large-N and self-consistent methods (NCA) to describe time-dependent phenomena, quenches, and the approach to steady states near quantum criticality. As a step towards this goal we will study periodically driven systems..The motivation for the present proposal is in understanding if quantum criticality out-of-equilibrium allows for a description that resembles the one describing time-dependences near classical critical points, i.e. classical critical dynamics. This will be of theoretical importance but will also be relevant to e.g. describe time-dependent and pump-probe spectroscopies near quantum criticality.