Non-equilibrium dynamics and single-particle spectral functions in low-dimensional fermion systems

这一提议的目标是探索强关联量子物质中的动力学过程。为此，我将研究低维几何结构中的相互作用电子。这些电子的性质将在真实空间和实时进行数值和解析分析。这些令人向往的结果将为能量和量子信息如何在物质中分布提供新的见解，因此与未来量子设备的发展高度相关。低维电子系统表现出许多有趣的关联效应。例如，在一个维度上，Luttinger液体理论预测分离的自旋密度波和电荷密度波的显著现象是基本的低能量激发。在过去的几年里，低维系统的实验实现取得了巨大的进步，在许多情况下，这与精确的理论预测齐头并进。这一总体图景将在这个项目中进一步完成。当前感兴趣的一个焦点是强关联系统的动力学。最近，利用超冷气体的实验者令人印象深刻地成功地观察到了一个远离平衡的孤立量子系统。然而，从理论的角度来看，要完全理解非平衡中的动力学过程，必须知道整个激发谱，这是一个远远超出目前知识状态的挑战。然而，通过移动杂质对Luttinger液体理论的扩展，使得能够计算更高能量下的单粒子光谱函数。此外，高效算法的出现允许在一维上以数字方式跟踪可观测对象的时间相关性。我将使用这两种方法来回答关于一维非平衡相互作用费米子系统的基本开放问题。在局域单粒子激发后，超冷气体中的自旋密度波和电荷密度波是如何随时间演化的？这个问题也将推广到二维系统。如果在某个初始时刻，一个自旋方向的粒子密度局部投射到零，系统将如何演化？在较高能量下，局域单粒子谱函数有什么特征？

This proposal targets the exploration of dynamical processes in strongly correlated quantum matter. To this end I will study interacting electrons in low dimensional geometries. The properties of these electrons will be analyzed numerically and analytically in real space and real time. The aspired results will provide new insights into how power and quantum information is distributed in matter and therefore be highly relevant for the development of future quantum devices. Low-dimensional electron systems exhibit a number of intriguing correlation effects. In one dimension, for example, Luttinger liquid theory predicts the remarkable phenomenon of separate spin- and charge-density waves as the fundamental low-energy excitations. The enormous progress in the experimental realization of low-dimensional systems of the last years has in many cases gone hand in hand with precise theoretical predictions. This overall picture will be further completed in this project.A focus of current interest is the dynamics of strongly correlated systems out of equilibrium. Recently, experimentalists with ultra-cold gases impressively succeeded to observe an isolated quantum system far away from equilibrium. However, from the theory point of view to fully understand the dynamical processes in non-equilibrium the entire spectrum of excitations has to be known, a challenge that is far beyond the present state of knowledge. The extension of the Luttinger liquid theory by a mobile impurity, though, enables the calculation of the single-particle spectral function at higher energies. Additionally, the advent of efficient algorithms allows for numerically tracking the time dependence of observables in one dimension. I will use both methods to answer fundamental open questions on one-dimensional systems of interacting fermions in non-equilibrium. How do the spin- and charge density waves in ultra-cold gases evolve in time after a local single-particle excitation? This problem will also be generalized to two-dimensional systems. How does the system evolve if at some initial time the particle density of one spin direction is locally projected onto zero? What are the characteristics of the local single-particle spectral function at higher energies?