周期轨道的量子化与量子能谱中的长程关联

用二维可积系统的半经典量子化方案和二维无关联振子系统的量子能级与周期轨道之间的对应关系,讨论了一组量子能级之间具有长程关联的内在机制,在二维无关联振子系统中,发现了具有相同拓扑M(M1,M2)的周期轨道相对应的量子能级之间存在着长程关联,并以二维4次无关联振子系统为例做了具体说明.

Quantization of the Periodic Orbits and Long-Range Correlations in Quantum Spectra

Using the classical quantization way in a two dimensional integrable system and quantized energies periodic orbits correspondence relationship, the long range correlation among the quantum lavels has been discussed in detail. Making use of Berry Tabor trace formula, the quantization conditions of the action of the periodic orbits in two dimensional integrable systems have been obtained. Furthermore, considering the periodicity conditions for the periodic orbits on reasonable torus, the correspondence relations between quantum levels and classical periodic orbits in the two dimensional uncoupled oscillators have been established. It is also shown that there exist the long range correlations among these quantum levels which correspond to the group of the classical periodic orbits with same topology M (M 1,M 2) . To concert state the new points, an example has been given.