Semiclassical accuracy in phase space for regular and chaotic dynamics.
Semiclassical accuracy in phase space for regular and chaotic dynamics.
复制标题
规则和混沌动力学相空间的半经典精度。
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
L. Kaplan
中科院分区：
文献类型：
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作者：
L. Kaplan
一个相空间半经典近似有效O（h）在短时间内被用来比较半经典精度的长期和稳定的观测量在混沌，稳定和混合系统。给定相同水平的半经典精度的短时间行为，平方半经典误差的混沌系统中的线性增长的时间，在经典稳定的系统中的二次增长。在混沌系统中，在海森堡时间的相对平方误差与h（eff）呈线性关系，允许明确的半经典确定的本征值和波函数的高能量限制，而在稳定的情况下，本征值误差总是保持的平均水平间距的顺序。对于一个混合的经典相空间，与混沌海相关联的特征值可以用半经典方法计算，其精度比与稳定岛屿相关联的特征值高。
A phase-space semiclassical approximation valid to O(h) at short times is used to compare semiclassical accuracy for long-time and stationary observables in chaotic, stable, and mixed systems. Given the same level of semiclassical accuracy for the short time behavior, the squared semiclassical error in the chaotic system grows linearly in time, in contrast with quadratic growth in the classically stable system. In the chaotic system, the relative squared error at the Heisenberg time scales linearly with h(eff), allowing for unambiguous semiclassical determination of the eigenvalues and wave functions in the high-energy limit, while in the stable case the eigenvalue error always remains of the order of a mean level spacing. For a mixed classical phase space, eigenvalues associated with the chaotic sea can be semiclassically computed with greater accuracy than the ones associated with stable islands.