Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
J Chem Phys. 2013 Sep 28;139(12):124110. doi: 10.1063/1.4820880.
The dephasing relation (DR), a linearization of semiclassical fidelity, is generalized to include the overlap of "off-diagonal" elements. The accuracy of the formulation is tested in integrable and chaotic systems and its scaling with dimensionality is studied in a Caldeira-Leggett model with many degrees of freedom. It is shown that the DR is often in very good agreement with numerically analytic quantum results and frequently outperforms an alternative semiclassical treatment. Most importantly, since there is no computationally expensive prefactor, and Monte Carlo Metropolis sampling is used to facilitate the calculation, the DR is found to scale remarkably well with increasing dimension. We further demonstrate that a propagator based on the DR can include more quantum coherence and outperform other popular linearized semiclassical methods, such as forward-backward semiclassical dynamics (FBSD) and the linearized semiclassical initial value representation (LSC-IVR).
去相位关系 (DR)，即半经典保真度的线性化，被推广到包括“非对角”元素的重叠。该公式的准确性在可积和混沌系统中进行了测试，并在具有多个自由度的 Caldeira-Leggett 模型中研究了其与维度的标度关系。结果表明，DR 通常与数值解析量子结果非常吻合，并且经常优于替代的半经典处理。最重要的是，由于没有计算上昂贵的预因子，并且使用蒙特卡罗 Metropolis 抽样来促进计算，因此发现 DR 随着维度的增加而显著地良好标度。我们进一步证明，基于 DR 的传播子可以包含更多的量子相干性，并优于其他流行的线性化半经典方法，例如前向-后向半经典动力学 (FBSD) 和线性化半经典初始值表示 (LSC-IVR)。
