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机制下的量子动力学产生了越来越大的兴趣。在各个研究领域都取得了令人印象深刻的理论进展。在实验方面，许多固态实验室正在开发和完善的尖端脉冲激光泵浦探测技术为更多的量子动力学研究打开了大门。最近对强相互作用物质中的普朗克输运和标度不变输运的观察进一步表明了在一大类非常不同的相互作用凝聚态中的普遍输运现象。观测到的输运动力学进一步表明，普适普朗克输运与黑洞附近最快的信息传播之间可能存在密切联系。狄拉克费米子的流体动力学也在石墨烯中被观察到，几个月前，由于狄拉克费米子之间的相互作用而产生的粘性流动被成像。这些理论和实验研究揭示了动力学中令人惊奇和意想不到的方面，这些密集的实验努力和令人印象深刻的成功进一步要求对强相互作用机制中的非平衡量子现象进行新的理论研究。 在这个计划中，我们将研究量子动力学，包括输运动力学和流体动力学在强相互作用量子临界制度是（几乎）标度不变。我们将探索在这些相互作用的系统中潜在和自然出现的通用传输动力学和量子流体动力学。我们将专门研究和确定新的参数空间的尺寸，从普遍的动力学偏差可以在一个可控的和明显的方式进行研究。主要目的是测试潜在的普遍动力学现象对实验变量的鲁棒性，并了解量子临界状态下的动力学，运输和流体动力学。为了实现这些目标，我们将建议分为两个部分，每个部分都强调动态现象的一些特定的普遍方面，如下所述。这些方面将在包括冷气体在内的不同凝聚态系统中进行研究，这取决于哪些系统在实验上更相关，在实验室中更实用。第一部分讨论了电荷中性点附近的二维和三维半金属中强相互作用狄拉克费米子的普朗克输运现象和流体力学。狄拉克点可以被认为是临界点，并且进一步的强相互作用可以导致在杂质和声子散射可以忽略的超清洁半金属中的普朗克输运和相对论粘性流体动力学流动。第二部分涉及紧急通用共形动力学在强相互作用的冷气体和费米-玻色量子混合物附近的Feshbach共振，以及在相互作用的固体状态附近的Lifshitz转变。

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.