Semiclassical approximations based on complex trajectories.
Semiclassical approximations based on complex trajectories.
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基于复杂轨迹的半经典近似。
DOI：
10.1103/physreve.69.066204
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
M. Baranger
中科院分区：
文献类型：
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作者：
A. D. Ribeiro;M. D. de Aguiar;M. Baranger
相干态传播子的半经典极限涉及哈密顿量H(u,v) =满足u(0) = z‘和v(T) = z’ *的复杂经典轨迹。在这项工作中，我们主要研究z' = z‘ ’的情况。传播子就是一个波包的返回概率振幅。我们证明了精确的返回概率图可以得到经典周期轨道的量子图像。然后比较了具有两个自由度的软混沌系统的精确返回概率及其半经典近似。我们发现在两种情况下，满足正确边界条件的经典轨迹必须从半经典公式中排除。第一个发生在轨迹对传播子的贡献呈指数增长的时候普朗克除以2趋向于零。第二次发生在贡献轨迹发生分叉的时候。在分岔点附近，半经典公式发散。更有趣的是，在研究的例子中，在分叉之后，存在多个满足边界条件的轨迹，实际上只有一个有助于半经典公式，这一现象与Stokes线密切相关。当这些轨迹的贡献被滤除后，半经典结果与精确计算结果非常吻合。
The semiclassical limit of the coherent state propagator involves complex classical trajectories of the Hamiltonian H(u,v) = satisfying u(0) = z' and v(T) = z"*. In this work we study mostly the case z' = z". The propagator is then the return probability amplitude of a wave packet. We show that a plot of the exact return probability brings out the quantal images of the classical periodic orbits. Then we compare the exact return probability with its semiclassical approximation for a soft chaotic system with two degrees of freedom. We find two situations where classical trajectories satisfying the correct boundary conditions must be excluded from the semiclassical formula. The first occurs when the contribution of the trajectory to the propagator becomes exponentially large as Planck's over 2 pi goes to zero. The second occurs when the contributing trajectories undergo bifurcations. Close to the bifurcation the semiclassical formula diverges. More interestingly, in the example studied, after the bifurcation, where more than one trajectory satisfying the boundary conditions exist, only one of them in fact contributes to the semiclassical formula, a phenomenon closely related to Stokes lines. When the contributions of these trajectories are filtered out, the semiclassical results show excellent agreement with the exact calculations.
DOI：
10.1088/0305-4470/34/36/309
发表时间：
2001-09-14
期刊：
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
影响因子：
--
作者：
Baranger, M;de Aguiar, MAM;Schellhaass, B
通讯作者：
Schellhaass, B