Quantum dynamics in closed and open many-particle systems

这个项目属于物理科学主题和物理学大挑战领域“涌现和远离平衡的物理学”的福尔斯。第一行的工作是关于分析新的非平衡稳定状态，是可实现的冷原子实验。众所周知，吸引力Lieb-Liniger模型（具有吸引力δ函数相互作用的玻色子）在平衡态下是不稳定的，但由于守恒律的存在，量子猝灭后可以支持稳定的非平衡定态。在近似由Lieb-Liniger模型描述的冷原子系统中，这些对应于亚稳态。特别地，将相互作用强度从非常强的排斥力淬灭到非常强的吸引力实现了所谓的超级Tonks-Girardeau气体[E. Haller等人，Science 325，1224（2009）]。淬灭到不太强的吸引力的相互作用，预计将产生更多的异国情调的高度相关的稳定状态与复杂的层次结构的许多玻色子束缚态[L。Piroli等人，Phys.Rev.Lett. 116（7），070408（2016）]。该项目的这一部分的目的是通过使用最近开发的广义流体力学的框架来确定线性响应函数，并通过考虑扩展下的动态来表征这类状态的物理性质。下一步将是发展一个完整的理论相互作用淬火从基态的无限排斥的吸引力Lieb-Linger模型的淬火行动的方法。第二条工作线是关于用Lindblad方程描述开放量子系统。目的是用玻色化方法描述多粒子系统Lindblad方程的短时动力学。在第一种情况下，浴耦合将被视为退相噪声，而哈密顿部分允许自由玻色子（加上扰动）的描述。第一个目标是建立线性Luttinger液体理论提供了一个很好的描述的哈密尔顿部分的时间窗口。这将通过考虑精确可解模型和比较数值矩阵产品状态计算来完成。第二个目标是超越线性Luttinger液体的描述，并考虑不同类型的扰动所发挥的作用，通过使用运动方程技术。最终的目标是发展一个易于使用的扩展Luttinger液体理论开放的量子系统。

This project falls within the Physical Sciences Theme and the Physics grand challenge area "Emergence and Physics Far From Equilibrium". The first line of work is concerned with analysing novel non-equilibrium steady states that are realizable in cold atom experiments. It is well known that the attractive Lieb-Liniger model (bosons with attractive delta-function interaction) is thermodynamically unstable in equilibrium, but due to the existence of conservation laws can support stable non-equilibrium steady states after quantum quenches. In cold atom systems that are approximately described by the Lieb-Liniger model these correspond to metastable states. In particular, quenching the interaction strength from very strong repulsion to very strong attraction realizes the so-called super-Tonks-Girardeau gas [E. Haller et al, Science 325, 1224 (2009)]. Quenching to less strongly attractive interactions is expected to generate more exotic highly correlated steady states with an intricate hierarchical structure of many-boson bound states [L. Piroli et al, Phys. Rev. Lett. 116 (7), 070408 (2016)]. The aim of this part of the project is to characterize the physical properties of this class of states by using the recently developed framework of Generalized Hydrodynamics to determine linear response functions and by considering the dynamics under expansion. The next step will be to develop a full theory for an interaction quench from the ground state of the infinitely repulsive to the attractive Lieb-Linger model by means of the quench action approach. The second line of work is concerned with the description of open quantum systems by Lindblad equations. The aim is to describe the short-time dynamics of Lindblad equations for many-particle systems using bosonization methods. In the first instance the bath coupling will be taken to be dephasing noise, while the Hamiltonian part allows a description in terms of a free boson (plus perturbations). The first goal is to establish the time window over which linear Luttinger liquid theory provides a good description of the Hamiltonian part. This will be done by considering exactly solvable models and by comparing to numerical matrix product state computations. The second goal is to go beyond the linear Luttinger liquid description and consider the role played by different kinds of perturbations by using equation of motion techniques. The ultimate goal is to develop a readily useable extension of Luttinger liquid theory to open quantum systems.