Quantum Dynamics with Classically Chaotic Limit

9412706 Sundaram本研究建议的重点是理解经典和半经典方法在描述强耦合量子系统动力学中的使用、有效性和局限性。由于相互作用的强度排除了量子微扰理论在这些系统中的应用，非微扰直觉是从动力学的经典描述中推导出来的，这通常是不可积的或混沌的。具有经典混沌极限的动力学量子化产生了许多具有实际和形式意义的重要问题。特别是，我们建议研究1)从量子传播子轨迹的精确表达式出发的周期轨道展开，解析连续轨道的贡献以及与这些所谓的“幽灵”轨道相关的凝聚(疤痕波函数)的可能性，2)通过参数涨落引入的噪声对去稳定疤痕波函数的影响，3)高维疤痕波函数，具体应用于超强激光场中基态原子的稳定问题和里德堡原子与微波相互作用中的噪声谱。***

9412706 Sundaram The focal point of this research proposal is the understanding of the use, efficacy and limitations of classical and semi-classical methods in describing the dynamics of strongly coupled quantum systems. Since the strength of the interaction precludes the use of quantum perturbation theory in these systems, non-perturbative intuition is derived from a classical description of the dynamics, which is most often nonintegrable or chaotic. A number of important issues of both practical and formal consequence arise from the quantization of dynamics with a classically chaotic limit. In particular, we propose to investigate 1) the periodic orbit expansion starting from exact expressions of the trace of quantum propagators, the contributions of analytically continued orbits and the possibility of conherence (scarred wave functions) associated with these so-called 'ghost' orbits,2) the effects of noise introduced via parametric fluctuations on de stabilizing scarred wave-functions and 3) scarred wave functions in higher dimensions with specific application to the problems of stabilization of ground state atoms in super-intense laser fields and to the noise spectroscopy in the interaction of Rydberg atoms with microwaves. ***