For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The propose...For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.展开更多
Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space devel...Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.展开更多
Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions v...Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions via direct sampling of the dis-order distribution,leading to high computational costs.In this work,we extend the auxiliary degree-of-freedom based matrix product state(MPS)method to handle system-bath correlated thermal equilibrium initial states,which can capture static disorder effects using a one-shot quantum dynamical simulation.We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates.Our results show that the one-shot method is very accu-rate with only a moderate increase in MPS bond dimension,thereby significantly reducing computational cost.Moreover,it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost,thus reducing sta-tistical errors.This method provides a broadly useful tool for calculating equilibrium time cor-relation functions in system-bath coupled models with static disorder.展开更多
The microstructure, IR spectrum, as well as rotation dynamics of water molecule in sodium tetrafluoroborate （NaBF4）/water mixture at room temperatures were studied with molecular dynamics simulation. Different conce...The microstructure, IR spectrum, as well as rotation dynamics of water molecule in sodium tetrafluoroborate （NaBF4）/water mixture at room temperatures were studied with molecular dynamics simulation. Different concentrations of water （6.25%, 25.0%, 50.0%, 75.0%, 90.0%, and 99.6%） in NaBF4/water mixture were simulated to understand the structure and dynamics. It was shown that water molecules tend to be isolated from each other in mixtures with more ions than water molecules in both liquids. With increase of the molar fraction of water in the mixture, the rotation bands and the bending bands of water display red shift whereas the O-H stretch bands show blue shift, and the decay of the reorientation correlation function becomes slower. This suggests that the molecules are hindered and their motions are difficult and slow, due to the hydrogen-bond interactions and the inharmonic interactions between the interor intra-molecular modes.展开更多
基金Project supported by the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(Grant No.GZC20231050)the National Natural Science Foundation of China(Grant Nos.12175193 and 11905183)the 13th Five-year plan for Education Science Funding of Guangdong Province(Grant No.2021GXJK349)。
文摘For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.
文摘Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.
基金supported by the National Natural Science Foundation of China(No.22273005 and No.22422301)the Innovation Program for Quantum Science and Technology(No.2023ZD0300200)+1 种基金the National Security Academic Foundation(No.U2330201)the Fundamental Research Funds for the Central Universities.
文摘Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions via direct sampling of the dis-order distribution,leading to high computational costs.In this work,we extend the auxiliary degree-of-freedom based matrix product state(MPS)method to handle system-bath correlated thermal equilibrium initial states,which can capture static disorder effects using a one-shot quantum dynamical simulation.We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates.Our results show that the one-shot method is very accu-rate with only a moderate increase in MPS bond dimension,thereby significantly reducing computational cost.Moreover,it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost,thus reducing sta-tistical errors.This method provides a broadly useful tool for calculating equilibrium time cor-relation functions in system-bath coupled models with static disorder.
基金The authors are grateful to Professor Jiu-shu Shao at Beijing Normal University for his encourage and help reading the manuscript. We also would like to thank Prof. Jian-min Tao and Guo-bao Li for their kind help. This work was supported by the National Natural Science Foundation of China （No.50564006）, the Key program of Natural Science Foundation of Yunnan Provine （No.2005EOOO4Z）, the Natural Science Foundation of Yunnan Provine （No.2008E0049M）, the Foundation of the Education Department of Yunnan Province （No.07Z40082）, and the Foundation of Kunming University of Science and Technology （No.2007-16）.
文摘The microstructure, IR spectrum, as well as rotation dynamics of water molecule in sodium tetrafluoroborate （NaBF4）/water mixture at room temperatures were studied with molecular dynamics simulation. Different concentrations of water （6.25%, 25.0%, 50.0%, 75.0%, 90.0%, and 99.6%） in NaBF4/water mixture were simulated to understand the structure and dynamics. It was shown that water molecules tend to be isolated from each other in mixtures with more ions than water molecules in both liquids. With increase of the molar fraction of water in the mixture, the rotation bands and the bending bands of water display red shift whereas the O-H stretch bands show blue shift, and the decay of the reorientation correlation function becomes slower. This suggests that the molecules are hindered and their motions are difficult and slow, due to the hydrogen-bond interactions and the inharmonic interactions between the interor intra-molecular modes.
