Sun Jing, Sasmal Sudip, Vendrell Oriol
Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Heidelberg, Germany.
J Chem Phys. 2021 Oct 7;155(13):134110. doi: 10.1063/5.0066740.
We consider the application of the original Meyer-Miller (MM) Hamiltonian to mapping fermionic quantum dynamics to classical equations of motion. Non-interacting fermionic and bosonic systems share the same one-body density dynamics when evolving from the same initial many-body state. The MM classical mapping is exact for non-interacting bosons, and therefore, it yields the exact time-dependent one-body density for non-interacting fermions as well. Starting from this observation, the MM mapping is compared to different mappings specific for fermionic systems, namely, the spin mapping with and without including a Jordan-Wigner transformation and the Li-Miller mapping (LMM). For non-interacting systems, the inclusion of fermionic anti-symmetry through the Jordan-Wigner transform does not lead to any improvement in the performance of the mappings, and instead, it worsens the classical description. For an interacting impurity model and for models of excitonic energy transfer, the MM and LMM mappings perform similarly, and in some cases, the former outperforms the latter when compared to a full quantum description. The classical mappings are able to capture interference effects, both constructive and destructive, that originate from equivalent energy transfer pathways in the models.
我们考虑将原始的迈耶 - 米勒（MM）哈密顿量应用于将费米子量子动力学映射到经典运动方程。当从相同的初始多体状态演化时，非相互作用的费米子和玻色子系统具有相同的单粒子密度动力学。MM 经典映射对于非相互作用的玻色子是精确的，因此，它也能给出非相互作用费米子精确的含时单粒子密度。基于这一观察结果，将 MM 映射与特定于费米子系统的不同映射进行比较，即包含和不包含约旦 - 维格纳变换的自旋映射以及李 - 米勒映射（LMM）。对于非相互作用系统，通过约旦 - 维格纳变换纳入费米子反对称性并不会提高映射的性能，反而会恶化经典描述。对于相互作用杂质模型和激子能量转移模型，MM 和 LMM 映射表现相似，并且在某些情况下，与完整量子描述相比，前者的表现优于后者。经典映射能够捕捉源于模型中等效能量转移路径的相长和相消干涉效应。
