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首页> 外文期刊>Annales Henri Poincare >Canonical Quantum Observables for Molecular Systems Approximated by Ab Initio Molecular Dynamics
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Canonical Quantum Observables for Molecular Systems Approximated by Ab Initio Molecular Dynamics

机译：AB Initio分子动力学近似的分子系统的规范量子可观察

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It is known that ab initio molecular dynamics based on the electron ground-state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temperature is low compared to the first electron eigenvalue gap. This work proves that a certain weighted average of the different ab initio dynamics, corresponding to each electron eigenvalue, approximates quantum observables for any temperature. The proof uses the semiclassical Weyl law to show that canonical quantum observables of nuclei-electron systems, based on matrix-valued Hamiltonian symbols, can be approximated by ab initio molecular dynamics with the error proportional to the electron-nuclei mass ratio. The result covers observables that depend on time correlations. A combination of the Hilbert-Schmidt inner product for quantum operators and Weyl's law shows that the error estimate holds for observables and Hamiltonian symbols that have three and five bounded derivatives, respectively, provided the electron eigenvalues are distinct for any nuclei position and the observables are in the diagonal form with respect to the electron eigenstates.
机译：众所周知，基于电子接地状态特征值的AB Initio分子动力学可用于在与第一电子特征值间隙相比的温度低时近似典型集合中的量子可观察。该工作证明，对应于每个电子特征值的不同AB初始动力学的某个加权平均值近似于任何温度的量子可观察。该证据使用了半思法的Weyl定律，表明基于基于矩阵值的Hamiltonian符号的核电子系统的规范量子可观察可以通过AB Initio分子动力学来近似与电子核质量比成比例的误差。结果涵盖依赖于时间相关性的可观察到。 Hilbert-Schmidt内部产品用于量子运营商和Weyl的法律的组合表明，分别具有三个和五个有界衍生物的可观察到和Hamiltonian符号的误差估计，只要电子特征值对于任何细胞核位置和可观察到的观察者而言在对角线形式方面相对于电子特征酯。

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