The Semiclassical Dynamics of Small Quantum Systems

9305582汤姆索维奇最近在介观、原子和其他系统中进行了出色的实验，正在探索量子力学和经典力学世界之间的深层联系。连接两个世界的理论是半经典近似的领域，许多长期存在的基本问题仍然没有解决。尽管半经典力学的大部分工作都集中在能量领域，但人们直接感兴趣的往往是系统的时间演化。直到最近，还只存在非常初级的依赖时间的半经典技术。这项工作将集中于将新的、更强大的半经典传播方法(我们开发的)扩展到更高的维度(这对物理应用很重要)，简化由混沌运动引起的问题，研究领先的修正，并将该方法应用于静止的量子力学问题。好了！G2 U F v F@~F F^t 0.U H F~u F H F v F.V v N‘U v？F F x*v 0=\F t=/t v v 0=：t N F@^S v？86 8！！A 8 8(Times新罗马符号&amp；Arial“h；%；%/Terri L.Hicks Terri L.Hicks

9305582 Tomsovic Recent elegant experiments in mesoscopic, atomic and other systems are probing the deep connections between the quantum mechanical and classical mechanical worlds. The theory bridging the two worlds is the realm of semiclassical approximations for which many long-standing, fundamental problems remain unresolved. Although the bulk of the work on semiclassical mechanics has been concentrated in the energy domain, often the direct interest is in the time evolution of a system. Until very recently only very rudimentary time dependent semiclassical techniques existed. This work will focus on extending new, more powerful semiclassical propagation methods (which we developed) to apply to higher dimensions (which is important for physical applications), simplifying the problems arising from chaotic motion, investigating the leading corrections, and adapting the method to apply to stationary quantum mechanical problems. ! G 2 U F v F @ ~ F F ^ t 0 .u H F ~ u F H F v F . v v N Õ U v Õ F F x* v 0 =\ F t =/ t v v 0 =: t N F @ ^ S v Õ 8 6 8 ! ! A 8 8 ( Times New Roman Symbol & Arial " h ; % ; % / terri l. hicks terri l. hicks