Exact factorization of a many-body wavefunction beyond the electron-nuclear problem
Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；Eindhoven University of Technology（埃因霍温理工大学）；Sorbonne Université, CNRS, LCT UMR 7616（索邦大学，法国国家科学研究中心，LCT联合研究实验室）
This Review is devoted to the presentation of the exact factorization as a framework employed to study a variety of quantum-mechanical many-body problems. Since its original formulation in the 70s, the main applications of the exact factorization were directed towards understanding the properties of multi-component systems, e.g. electron-nuclear systems. Especially in the electron-nuclear case, the exact factorization is viewed as an exactification of the Born-Oppenheimer approximation, thus it was, and still is, largely employed in nonadiabatic dynamics. Nonetheless, as early as the 80s, the formalism was employed to study many-electron interacting systems and, quite recently, i.e. less than a decade ago, it was extended to study the behavior of molecules in the context in cavity quantum electrodynamics. These formulations, perhaps less popular than the electron-nuclear formulation, have attracted a lot of attention over the years. Therefore, we review here the exact electron-only factorization and the exact photon-electron-nuclear factorization.
Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function
Quantum Mechanical Analysis of Neutron Wavefunction Overlap and Nuclear Interaction Probability with Carborane Cage ($^{10}$B10) in Boron Neutron Capture Therapy
The use of the Born-Oppenheimer factorization in the phase-space representation of the time-independent Schrödinger equation for bilinearly coupled harmonic oscillators
本文用Born-Oppenheimer（BO）乘积波函数分析法和相空间束缚轨线法解析地求解了两个双线性耦合谐振子系统[J. S. Molano等人，化学物理快报\textbf{76}（12），138171（2021）]。双线性耦合振荡器系统允许获得量子系统的解析表达式，便于与使用BO拟积的结果进行比较。解析和BO波函数作为抛物柱面函数的乘积得到。精确和BO波函数的抛物柱面函数的自变量通过线性变换与物理坐标相关，分别由矩阵$\mathsf{G}$和$\mathsf{\tilde{G}}$表示。矩阵$\mathsf{G}$的$QU$分解输出与BO $\mathsf{\tilde{G}}$矩阵密切相关的上三角矩阵$\mathsf{U}$。分析了BO非绝热耦合对相空间运动方程稳定性的影响。由Born-Oppenheimer相空间轨迹法得到的本征值和本征函数与解析解非常吻合。
Accurate molecular dynamics and nuclear quantum effects at low cost by multiple steps in real and imaginary time: using density functional theory to accelerate wavefunction methods
Permutation invariant multi-scale full quantum neural network wavefunction
Peking University（北京大学）；Advanced Energy Science and Technology Guangdong Laboratory（广东实验室先进能源科学与技术）；ByteDance Seed（字节跳动种子）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；State Key Laboratory of Heavy Ion Science and Technology（重离子科学和技术国家重点实验室）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
NucleoNet: A Nuclear-Aware Determinant Ansatz for Multi-Geometry Neural Variational Monte Carlo
School of Artificial Intelligence and Data Science, University of Science and Technology of China（中国科学技术大学人工智能与数据科学学院）；University of Science and Technology of China（中国科学技术大学）；Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）；Singapore University of Technology and Design（新加坡科技设计大学）；AI for Science Institute（北京智源人工智能研究院）；School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）；National Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究部计算物理国家实验室）；HEDPS, CAPT, College of Engineering, Peking University（北京大学工学院）
