Quantum dynamics in closed and open many-particle systems

该项目属于物理学主题和物理学重大挑战领域“浮现和物理远离平衡”。第一项工作是分析在冷原子实验中可实现的新的非平衡稳态。众所周知，具有吸引力的Lieb-Liniger模型(具有吸引力的Delta函数相互作用的玻色子)在热力学上是不稳定的，但由于守恒定律的存在，在量子猝灭后可以支持稳定的非平衡稳态。在由Lieb-Liniger模型近似描述的冷原子系统中，它们对应于亚稳态。特别是，将相互作用强度从很强的排斥力淬灭到很强的吸引力实现了所谓的超级Tonks-Girardeau气体[E.Haller等人，科学325,1224(2009)]。猝灭到不那么有吸引力的相互作用有望产生更奇异的高度关联的稳态，具有复杂的多玻色子束缚态的层级结构[L.Pieroi等，Phys.莱特牧师。第116(7)、070408(2016年)]。本项目这一部分的目的是通过使用最近开发的广义流体动力学框架来确定线性响应函数并考虑膨胀下的动力学，来表征这类状态的物理特性。下一步将是发展一个完整的理论，通过猝灭作用的方法，从无限排斥的基态到吸引的利勃-林格模型的相互作用猝灭。第二项工作是关于用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，浴缸耦合将被认为是退相噪声，而哈密顿部分允许用自由玻色子(加上微扰)来描述。第一个目标是建立一个时间窗口，在这个时间窗口上，线性Luttinger液体理论可以很好地描述哈密顿部分。这将通过考虑精确可解的模型并通过与数值矩阵乘积状态计算进行比较来实现。第二个目标是超越线性的Luttinger液体描述，使用运动方程技术来考虑不同类型的扰动所起的作用。最终目标是将Luttinger液体理论推广到开放的量子系统。

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.