论文标题
驱动混沌系统的能量过渡密度：复合痕量公式
Energy transition density of driven chaotic systems: A compound trace formula
论文作者
论文摘要
在经典狭窄的能量范围内，混乱的哈密顿量的量子过渡的概率密度的振荡已证明取决于封闭的化合物轨道。这些是由一对轨道片段形成的，一个轨道片段在原始哈密顿量的能量壳中，另一个在驱动的哈密顿式驱动的驱动器壳中，端点重合。在时间域中查看，同一对轨迹段出现在对复合传播器的痕迹的半经典评估中：原始哈密顿量及其驱动图像的复杂指数的乘积。这里显示的概率密度是该迹线的双重傅立叶变换，因此闭合的复合轨道模仿了Gutzwiller在Gutzwiller的痕量公式中在其半经典评估中所起的作用。具有能量或演化参数的振荡的相位与先前获得的振动参数一致，而每个封闭的化合物轨道的贡献的幅度更紧凑，并且与进行计算的Weyl-wigner表示的任何特征无关。
Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit segments, one in the energy shell of the original Hamiltonian and the other in the energy shell of the driven Hamiltonian, with endpoints which coincide. Viewed in the time domain, the same pair of trajectory segments arises in the semiclassical evaluation of the trace of a compound propagator: the product of the complex exponentials of the original Hamiltonian and of its driven image. It is shown here that the probability density is the double Fourier transform of this trace, so that the closed compound orbits emulate the role played by periodic orbits in Gutzwiller's trace formula in its semiclassical evaluation. The phase of the oscillations with the energies or evolution parameters agree with those previously obtained, whereas the amplitude of the contribution of each closed compound orbit is more compact and independent of any feature of the Weyl-Wigner representation in which the calculation was carried out.
