量子能谱中的长程关联

LONG-RANGE CORRELATIONS IN QUANTUM SPECTRA

从可积系统求迹公式出发 ,运用Einstein Brillouin Keller(EBK)量子化条件 ,导出了二维无关联振子系统周期轨道作用量量子化条件 ,由此发现了量子能级与周期轨道之间的对应关系 .这种对应关系表明 ,如果两条能级对应的周期轨道的拓扑相同 ,这两条能级对回归函数的贡献相干 .回归谱中的一个峰是量子能谱中一组与具有相同拓扑的周期轨道相对应的能级之间相干的结果 ,这一组能级间存在着长程关联 .

Starting From Berry-Tabor trace formula, Einstein-Brillouin-Keller (EBK) quantization condition is adopted to derive action quantization conditions of periodic orbits in two dimensional uncoupled oscillators. The correspondence relations between quantum levels and periodic orbits are found. They indicate that two levels' cotributions to recurrence function coherently interfere with each other if the two levels correspond to periodic orbits with identical topology. The peaks in recurrence spectra results from coherent interference among levels whose corresponding periodic orbits have identical topology. There are long-range correlations among these levels.