Quantum transport and hydrodynamics in strongly interacting systems: Symmetries, Quantum criticality and Entanglement

在过去十年左右的时间里，理论家和各种实验物理团体对强相互作用体系中的量子动力学产生了巨大的兴趣。在各个研究前沿都取得了令人瞩目的理论进展。在实验方面，许多固体实验室正在发展和完善的基于脉冲激光的前沿泵浦探测技术为更多的量子动力学研究打开了一扇门。最近对强相互作用物质中的普朗克输运和尺度不变输运的观测进一步表明，在一类非常不同的相互作用凝聚态中存在普遍输运现象。观测到的输运动力学进一步表明，普朗克输运和黑洞附近最快的信息传播之间可能存在密切联系。在石墨烯中也观察到了狄拉克费米子的流体动力学，几个月前，由于狄拉克费米子之间的相互作用，人们对粘性流动进行了成像。这些理论和实验研究揭示了动力学的迷人和意想不到的方面。这些密集的实验工作和令人印象深刻的成功进一步要求在强相互作用状态下对非平衡量子现象进行新的理论研究。

Over the last decade or so, there has been enormous growing interest from both theorists and various experimental physics communities in quantum dynamics in strongly interacting regimes. Impressive theoretical progress has been made on various research fronts. On the experimental side, the cutting edge pulsed-laser based pump-probe technique that many solid state labs are developing and perfecting is opening a door to more studies of quantum dynamics. Very recent observation of Planckian transport and scale invariant transport in strongly interacting materials further indicates universal transport phenomena in a broad class of very different interacting condensed matter states. The transport dynamics observed further suggest a possible intimate connection between the universal Planckian transport and fastest information spreading near a black hole. Hydrodynamics of Dirac fermions had also been observed in graphene and a few months ago, viscous flow due to mutual-interactions between Dirac fermions was imaged. These studies, theoretical and experimental ones, have revealed fascinating and unexpected aspects of dynamics.These intensive experimental efforts and impressive successes further demand new theoretical efforts on non-equilibrium quantum phenomena in strongly interacting regimes. In this proposal, we will research on quantum dynamics including transport dynamics and hydrodynamics in strongly interacting quantum critical regimes that are (nearly) scale invariant. We will explore universal transport dynamics and quantum hydrodynamics that can potentially and naturally emerge in these interacting systems. We will specially examine and identify new dimensions in parameter spaces where deviations from universal dynamics can be studied in a controllable and pronounced way. The main objective of is to test the robustness of potential universal dynamic phenomena against experimental variables and understand the resultant dynamics, transport and hydrodynamics in quantum critical regimes. To achieve these objectives, we divide the proposal into two parts, each of which emphasizes a few particular universal aspects of dynamic phenomena as outlined below. And these aspects will be examined in different condensed matter systems including cold gases, depending on which are experimentally more relevant and more practical to realize in labs. Part I addresses Planckian transport phenomena and hydrodynamics in strongly interacting Dirac fermions in 2D and 3D semi-metals near charge neutrality points. Dirac points can be considered to be critical ones and further strong interactions can result in Planckian transport and relativistic viscous hydrodynamic flow in ultra clean semi-metals where impurity and phonon scatterings are negligible. Part II concerns emergent universal conformal dynamics in strongly interacting cold gases and Fermi-Bose quantum mixtures near Feshbach resonance, as well as in interacting solid states near Lifshitz transitions.