从经典、半经典和量子模拟计算谱密度
On Computing Spectral Densities from Classical, Semiclassical and Quantum Simulations
摘要：
Caldeira-Leggett模型在谱密度函数方面提供了热环境的紧凑表征。这种简单性导致了各种数值精确的量子方法减少密度矩阵传播。当使用这些方法时，必须从系统和环境的动力学性质计算谱密度，这通常使用经典的分子动力学模拟来完成。然而，在某些情况下，量子效应可能会发挥作用。因此，我们重新制定我们最近开发的傅立叶方法，以使光谱密度计算半经典模拟近似考虑量子效应。我们提出了两种可能的协议的基础上，无论是关联函数或期望值。这些协议进行了测试的线性化半经典初值表示（LSC-IVR），解冻高斯波包动力学（TGWD）和混合计划相结合的两个更准确的Herman-Kluk（HK）公式。令人惊讶的是，从LSC-IVR方法的谱密度，基于一个完全经典的传播，是非常准确的，而那些从单轨迹TGWD是质量差的非谐波制度。当系统接近经典状态时，混合方法提供了合理的质量，尽管在有限温度下，期望值的计算协议变得更加鲁棒。如果观察到更强的量子效应，两种混合方法都太不准确了。
英文摘要：
The Caldeira-Leggett model provides a compact characterization of a thermal environment in terms of a spectral density function. This simplicity has led to a variety of numerically exact quantum methods for reduced density matrix propagation. When using these methods, a spectral density has to be computed from dynamical properties of system and environment, which is commonly done using classical molecular dynamics simulations. However, there are situations, where quantum effects could play a role. Therefore, we reformulate our recently developed Fourier method in order to enable spectral density calculations from semiclassical simulations which approximately consider quantum effects. We propose two possible protocols based on either correlation functions or expectation values. These protocols are tested for the linearized semiclassical initial-value representation (LSC-IVR), the thawed Gaussian wave packet dynamics (TGWD) and hybrid schemes combining the two with the more accurate Herman-Kluk (HK) formula. Surprisingly, spectral densities from the LSC-IVR method, based on a completely classical propagation, are extremely accurate whereas those from the single-trajectory TGWD are of poor quality in the anharmonic regime. The hybrid methods provide reasonable quality when the system is close to the classical regime, although, at finite temperature, the computation protocol from expectation values turns out to be more robust. If stronger quantum effects are observed, both hybrid methods turn out as too inaccurate.
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