驱动混沌系统的能量跃迁密度：一个复合迹公式
Energy transition density of driven chaotic systems: A compound trace formula
摘要：
在经典窄能量范围内的混沌哈密顿量的本征态的量子跃迁的概率密度的振荡已被证明取决于封闭的复合轨道。这些是由一对轨道段形成的，一个在原始哈密顿量的能量壳层中，另一个在驱动哈密顿量的能量壳层中，端点重合。从时域来看，在复合传播子的迹的半经典计算中也会出现相同的一对轨迹段：原始哈密顿量的复指数与其驱动镜像的乘积。它在这里示出的概率密度是双重傅立叶变换的这条轨迹，使封闭的复合轨道模仿的作用所发挥的周期轨道Gutzwiller的轨迹公式在其半经典的评价。振荡的相位与能量或演化参数与先前获得的一致，而每个闭合复合轨道的贡献的幅度更紧凑，并且独立于进行计算的Weyl-Wigner表示的任何特征。
英文摘要：
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.
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