含时自洽谐波近似：非谐核量子动力学和时间关联函数
Time-Dependent Self Consistent Harmonic Approximation: Anharmonic nuclear quantum dynamics and time correlation functions
摘要：
大多数具有重要物理意义的材料性质与核动力学直接相关，例如离子热导率，拉曼/红外振动光谱，非弹性X射线和中子散射。一个能够从第一原理计算出这些性质的理论，解释了核能景观中的非谐性和量子涨落，可以在数百个原子的系统中实现，现在还没有。在这里，我们推导出一个近似理论的量子晶格振动在有限温度下的时间演化。该理论在自洽谐波近似（SCHA）中引入了时间动力学，并与静态情况共享相同的计算成本。它是非经验的，因为纯态根据狄拉克最小作用量原理演化，并且热系综的动力学保持能量和熵。静态SCHA恢复为动力学方程的稳态解。我们将微扰理论应用于静态SCHA解，并推导出一种有效计算量子动力学响应函数的算法。由于这种新的算法，我们可以访问任何一般的外部依赖于时间的扰动的响应函数，使声子谱的模拟，而无需遵循任何微扰扩展的核势或经验方法。我们基准的算法上的红外和拉曼光谱的高压氢相III，与96个原子的模拟细胞。我们的工作还探索了动态核运动的非线性机制，提供了一个范例来模拟与强或多个探针的相互作用，如泵浦-探测光谱，或涉及轻原子的化学反应，如生物分子中的质子转移
英文摘要：
Most material properties of great physical interest are directly related to nuclear dynamics, e.g. the ionic thermal conductivity, Raman/IR vibrational spectra, inelastic X-ray, and Neutron scattering. A theory able to compute from first principles these properties, accounting for the anharmonicity and quantum fluctuations in the nuclear energy landscape that can be implemented in systems with hundreds of atoms is missing. Here, we derive an approximate theory for the quantum time evolution of lattice vibrations at finite temperature. This theory introduces the time dynamics in the Self-Consistent Harmonic Approximation (SCHA) and shares with the static case the same computational cost. It is nonempirical, as pure states evolve according to the Dirac least action principle and the dynamics of the thermal ensemble conserves both energy and entropy. The static SCHA is recovered as a stationary solution of the dynamical equations. We apply perturbation theory around the static SCHA solution and derive an algorithm to compute efficiently quantum dynamical response functions. Thanks to this new algorithm, we have access to the response function of any general external time-dependent perturbation, enabling the simulation of phonon spectra without following any perturbative expansion of the nuclear potential or empirical methods. We benchmark the algorithm on the IR and Raman spectroscopy of high-pressure hydrogen phase III, with a simulation cell of 96 atoms. Our work also explores the nonlinear regime of the dynamical nuclear motion, providing a paradigm to simulate the interaction with intense or multiple probes, as in pump-probe spectroscopy, or chemical reactions involving light atoms, as the proton transfer in biomolecules
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