The Quantized Baker's Map and Its Long Time Behavior (Physics)

量化贝克图及其长期行为（物理）

• 批准号: 8816234
• 负责人: Nandor Balazs
• 金额: $ 5.65万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-15 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8816234&HistoricalAwards=false
• 关键词: Quantized; Baker; Map; Its; Long

In classical mechanics discrete area preserving maps give information on chaotic motion. The corresponding map in quantum systems is a unitary transformation giving the evolution of the state in a discrete time step. Balazs, and his collaborator, Voros, have discussed two such maps, the map for motion on a pseudosphere, a relatively nonphysical system, and the quantized Baker's map. It is proposed to complete this work, in particular to look at the large time behavior, and the passage to the classical limit, to test the correspondence between chaotic motion in the classical and quantum system.

在经典力学中，离散区域保持映射给出混沌运动的信息。量子系统中对应的映射是一个给出状态在离散时间步长的演化的酉变换。Balazs和他的合作者Voros已经讨论了两种这样的地图，一种是伪球（一个相对非物理系统）上的运动地图，另一种是量子化的Baker地图。建议完成这项工作，特别是观察大时间行为，并通过经典极限，以测试经典和量子系统中混沌运动之间的对应关系。