激发态量子相变动力学性质研究

A natural extension of the ground state quantum phase transitions is the excited-state quantum phase transitions (ESQPTs), which refer to quantum phase transitions that take place at the excited levels when the control parameter of the system is varied. Recently, with the further studies of ESQPTs, the dynamical properties of ESQPT have received lots of attention. To date, however, a better and deep understanding of the dynamical properties of ESQPTs is still lacking. In this proposal, in order to reveal the universal properties of the dynamics of ESQPT, a detailed and deep analysis on the transition probability near the critical point of ESQPT will be made. Meanwhile, in order to get a more general understand of the dynamical properties of ESQPT, we will discuss the feasibility and applicable condition of semiclassical theory to study the dynamical properties of ESQPT. By using the numerical and theoretical approach, the universal properties of transition probability will be studied in different models with the control parameter is changed in two different ways, i.e., sudden quench and slow quench, respectively. Moreover, the validity and degree of application of the semiclassical theory will be analyzed in detail.

激发态量子相变作为基态量子相变的自然延伸，它指的是系统激发态能级性质随着控制参数的改变而发生显著改变的相变。近年来，伴随着人们对激发态相变研究的不断深入，有关激发态相变动力学性质的研究吸引了越来越多的注意。然而，到目前为止，关于激发态相变的动力学性质依然缺乏深入而具体的了解。本申请拟通过具体而深入地分析系统在激发态临界点附近的跃迁概率，得到关于激发态相变动力学性质的一些普适规律。同时，为了从更一般的角度理解激发态量子相变的动力学性质，我们将探讨半经典理论被用来研究激发态相变动力学性质的可行性及具体的适用条件。在两种具有代表性的参数改变方式下，即快速淬火（sudden quench）和缓慢淬火（slow quench），我们将在不同的模型中运用数值和解析的方法分析系统跃迁概率的普适性质，探寻半经典理论的适用条件和适用程度。

近年来，大量的研究投入到了关于激发态相变特性的探讨中。在本项目中，我们具体且深入地对激发态相变的动力学性质进行了研究。具体研究成果及其科学意义概括如下：1）揭示了激发态相变对量子调控以及量子信息过程的重要影响；2）拓展了已有的关于激发态量子相变的认识与理解，首次从动力学角度给出了刻画相变的序参量；3）从研究物理量统计分布的角度给出了研究激发态量子相变性质及其普适性的新思路；4）建立了关于激发态相变的量子—经典对应，为从经典方面深入分析相变特性铺平了道路。总结起来，我们的研究不仅拓展了关于激发态量子相变的理解，同时也为进一步更深入地研究激发态相变提供了新的思路。