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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=567926
• 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.

量子现象的开发有望在通信、数据存储和计算技术方面取得进步。在量子设备上执行操作通常需要改变外部控制参数，如磁场和电场或温度。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这样的进展都是至关重要的。过去的一个主要障碍是固体中极快的动力学，典型的时间尺度在飞秒范围内。直到最近，实验技术才得到广泛应用，这些技术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由超冷量子气体在光学晶格上制成的人造晶体。在这样的系统中，晶格势和原子之间的相互作用可以在很大的参数范围内改变，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，因此实验数据经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，极大地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。它由量子动力学模拟部分和使用有效场论分析这些模拟结果的部分组成。这项研究是在一些基本问题的指导下进行的，这些问题包括驰豫动力学、量子系统长时间的热化以及动力学量子相变。对于这项研究来说，重要的是我们在模拟无限长的一维量子系统方面的专业知识。与有限系统相反，在时间演化中不会出现复苏或重现，因此系统才能真正实现平衡。该研究计划的分析部分将建立在我们之前关于强关联量子系统中输运的场论工作的基础上并加以扩展。我们的目标是在外部控制参数之一发生微小变化--即所谓的量子猝灭--之后，获得对长时间量子动力学的普遍描述。我将从专注于简单的一维晶格模型中的量子动力学开始我的拟议研究，这些模型与周围环境完全隔离，也不包含任何杂质。在研究的后期阶段，我将把我的工作扩展到开放量子系统，也包括无序。这两种影响在任何真实的设备中都是不可避免的。最后，我想要考虑到设备所用材料的特定属性。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以硅为基础的电子产品的材料之一。在授权期结束时，我预计我的工作将对驰豫动力学和动力学相变的新普遍理论做出重大贡献--通过数值模拟和冷原子气体实验进行检验--这将有助于指导我们探索利用量子现象来实现技术进步。