Low-dimensional quantum systems out of equilibrium

失衡的低维量子系统

• 批准号: RGPIN-2014-06615
• 负责人: Sirker, Jesko
• 金额: $ 2.26万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=633530
• 关键词: Low; dimensional; quantum; systems; out

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.

量子现象的利用预示着通信、数据存储以及计算技术的进步。在量子器件上执行操作通常需要改变外部控制参数，例如磁场和电场或温度。这种变化总是会使量子系统脱离平衡。因此，对量子系统的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固体中具有飞秒范围内典型时间尺度的极快动力学。直到最近，实验技术才变得广泛可用，从而可以在这样的时间尺度上解决量子动力学问题。最近另一个重要的进展是在光学晶格上用超冷量子气体制成的人工晶体。在这样的系统中，晶格势和原子之间的相互作用可以在很宽的参数范围内改变，使得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。更具体地说，我的研究计划致力于低维量子系统中非平衡动力学的理论研究。它包括一个部分，其中量子动力学将被模拟和一个部分，这些模拟的结果将使用有效场理论进行分析。该研究是由有关弛豫动力学，量子系统在长时间的热化，和动态量子相变的基本问题。对于这项研究来说，重要的是我们在模拟无限长一维量子系统方面的专业知识。与有限系统相反，在时间演化中不会发生回复或递归，因此系统可以真正平衡。该研究计划的分析部分将建立在我们以前关于强相关量子系统中传输的理论工作的基础上。我们的目标是获得一个通用的描述的量子动力学在很长一段时间后，一个小的变化-所谓的量子淬火-的外部控制参数之一。我将开始我所提出的研究集中在量子动力学在简单的一维晶格模型是完全孤立的，从他们的周围，不包含任何杂质。在研究的后期阶段，我将把我的工作扩展到开放的量子系统，也包括无序。这两种效应在任何真实的设备中都是不可避免的。最后，我想考虑到制造设备的材料的具体属性。特别是，我将研究碳纳米管中的量子动力学，这是一种可能彻底改变我们目前硅基电子产品的材料。在授予期结束时，我预计我的工作对弛豫动力学和动力学相变的新的普遍理论做出了重大贡献-通过数值模拟和冷原子气体实验进行了测试-这将有助于指导我们探索利用量子现象促进技术进步。