可积系统——求迹公式和逆谱分析(英文)

Integrable Systems——Trace Formulas and Inverse-Spectroscopy

研究了二维无关联四次振子系统 ,有理环面上积分 Hamiltonian运动方程给出了系统一系列周期轨道和经典物理量 ,使用半经典近似下的 Berry- Tabor求迹公式 ,得到了半经典的态密度 .应用 Fourier变换分析了每条周期轨道对态密度的贡献 ,并与量子态密度的

Periodic orbits of two dimensional uncoupled quartic oscillator were calculated by inte grating Hamiltonian equations of motion on reasonable tori, and several classical quantities were also computed. Inserting them into Berry Tabor trace formula, a trace, i.e., the semiclassical density of states of the corresponding quantum system, was obtained. Finally, Fourier transform was adopted to verify the contribution of each periodic orbit. Good agreement between the semiclassical action function and the quantum action function indicates the validity of Berry Tabor trace formula.