Low-dimensional quantum systems out of equilibrium

利用量子现象有望在通信、数据存储和计算技术方面取得进步。在量子器件上进行操作通常需要改变外部控制参数，如磁场、电场或温度。这样的变化总是会使量子系统失去平衡。因此，对量子系统非平衡动力学的基础研究对于任何此类进展都至关重要。过去的一个主要障碍是在飞秒范围内典型时间尺度的固体中非常快的动力学。直到最近，实验技术才变得广泛可用，允许在这样的时间尺度上解决量子动力学问题。另一个重要的最新进展是用光学晶格上的超冷量子气体制成人工晶体。在这样的系统中，晶格势和原子之间的相互作用可以在一个很宽的参数范围内改变，使量子动力学很容易观察到。此外，这些人造晶体非常干净，因此实验数据通常可以直接与理论和模拟进行比较。这打开了一扇机会之窗，大大提高了我们对量子系统非平衡动力学的认识。

The exploitation of quantum phenomena promises progress in communication, data storage as well as computing technology. Performing operations on a quantum device generally requires the change of external control parameters such as magnetic and electric fields or temperature. Such a change will always drive the quantum system out of equilibrium. Fundamental research on the non-equilibrium dynamics of quantum systems is therefore vital for any such progress. A major obstacle in the past has been the extremely fast dynamics in solids with typical timescales in the femtosecond range. Only recently have experimental techniques become widely available which allow to resolve quantum dynamics on such timescales. Another important recent progress are artificial crystals made out of ultracold quantum gases on optical lattices. In such systems the lattice potential and the interaction between the atoms can be changed over a wide parameter range making quantum dynamics readily observable. Furthermore, these artificial crystals are extremely clean so that experimental data can often be directly compared with theories and simulations. This opens a window of opportunity to significantly advance our knowledge about the non-equilibrium dynamics of quantum systems. More specifically, my research program is devoted to theoretical studies of non-equilibrium dynamics in low-dimensional quantum systems. It consists of a part where quantum dynamics will be simulated and a part where the results of these simulations will be analyzed using effective field theories. The research is guided by fundamental questions about the relaxation dynamics, the thermalization of quantum systems at long times, and dynamical quantum phase transitions. Important for this research is our expertise in simulating infinitely long one-dimensional quantum systems. Contrary to a finite system, revivals or recurrences do not occur in the time evolution so that the system can truly equilibrate. The analytical part of the research program will build on and extend our previous field theoretical works on transport in strongly correlated quantum systems. Our aim is to obtain a universal description of the quantum dynamics at long times after a small change - a so-called quantum quench - of one of the external control parameters. I will start my proposed research by concentrating on the quantum dynamics in simple one-dimensional lattice models which are completely isolated from their surroundings and do not contain any impurities. During later stages of the research I will extend my work to open quantum systems and also include disorder. Both effects are unavoidable in any real device. Finally, I want to take the specific properties of the material the device is made of into account. In particular, I will study quantum dynamics in carbon nanotubes which is one of the materials which could potentially revolutionize our current silicon-based electronics. At the end of the granting period I anticipate that my work has significantly contributed to new universal theories of relaxation dynamics and dynamical phase transitions - tested by numerical simulations and by experiments on cold atomic gases - which will help in guiding our quest to exploit quantum phenomena for technological advances.