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 method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The metho...The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A(αl),then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio,and use the minimum ratio among the group of ratios to measure the multi collinearity of A.According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix,the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm.The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit,the size of the measure reflects the multi collinearity of column vectors objectively.It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.展开更多
We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode rep...We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.展开更多
We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quant...We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.展开更多
A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical...A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.展开更多
State transition matrix is an important concept in modern control system. It studies the motion law of linear control system from initial state to any state at time t. In this paper, joining an engineering example, an...State transition matrix is an important concept in modern control system. It studies the motion law of linear control system from initial state to any state at time t. In this paper, joining an engineering example, an approach to determine zero-input responses is developed, and the design of simulation experiments with the aid of Matlab is used to illustrate the physical meaning of it. Furthermore, during the engineering application, for the discrimination of state transition matrix, a discrimination method of state transition matrix is proposed based on related theorems and an effective method is derived by calculating characteristics during tedious verification of theorem. The simulation results have proved the correctness of system analysis by using such discrimination method under different parameter models.展开更多
In terms of reflection transformation of a matrix product state （MPS）, the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state ｜ψe〉 and the odd-p...In terms of reflection transformation of a matrix product state （MPS）, the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state ｜ψe〉 and the odd-parity state ｜ψσ〉. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state ｜ψe〉 and the odd-parity state ｜ψo〉 constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states ｜ψe〉 and ｜ψo〉 is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.展开更多
The matrix product state （MPS） is utilized to investigate the ground state properties and quantum phase transitions （OPTs） of the dimerized antiferromagnetic Heisenberg （DAH） model. The ground state MPS wavefunc...The matrix product state （MPS） is utilized to investigate the ground state properties and quantum phase transitions （OPTs） of the dimerized antiferromagnetic Heisenberg （DAH） model. The ground state MPS wavefunctions determined by the infinite time-evolving block decimation （iTEBD） algorithm are shown to be very efficient descriptions of DAH model. In the thermodynamic limit, the quantum entanglement, the bond energy~ and the nearest-neighbor correlations are calculated. It is revealed that the singular behavior of the bipartite entanglement can detect the QPTs directly. The critical point J2c= 1.0 is determined evidently, and the quantum phase transition is argued to belong to the second-order category. At the critical point, logarithmic divergent character of the block entanglement is observed, and the system can be described by a free bosonic field theory.展开更多
For our proposed composite parity-conserved matrix product state(MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. B...For our proposed composite parity-conserved matrix product state(MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.展开更多
This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from un...This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.展开更多
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Project(40144018)supported by the National Natural Science Foundation of China
文摘The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A(αl),then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio,and use the minimum ratio among the group of ratios to measure the multi collinearity of A.According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix,the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm.The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit,the size of the measure reflects the multi collinearity of column vectors objectively.It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.
基金supported by the National Natural Science Foundation of China through the Project "Science Center for Luminescence from Molecular Aggregates(SCELMA)" (No.21788102)the Ministry of Science and Technology of China through the National Key R&D Plan (No.2017YFA0204501)supported by the National Natural Science Foundation of China (No.22003029)
文摘We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.
文摘We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.
文摘A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.
基金Supported by the National Natural Science Foundation of China(11605147)the Education and Teaching Reform Project of Xianyang Normal University(2015Z006).
文摘State transition matrix is an important concept in modern control system. It studies the motion law of linear control system from initial state to any state at time t. In this paper, joining an engineering example, an approach to determine zero-input responses is developed, and the design of simulation experiments with the aid of Matlab is used to illustrate the physical meaning of it. Furthermore, during the engineering application, for the discrimination of state transition matrix, a discrimination method of state transition matrix is proposed based on related theorems and an effective method is derived by calculating characteristics during tedious verification of theorem. The simulation results have proved the correctness of system analysis by using such discrimination method under different parameter models.
基金Supported by the Scientific Research Foundation of CUIT under Grant No.KYTZ201024the National Natural Science Foundation of China under Grant Nos.10775100,10974137 the Fund of Theoretical Nuclear Center of HIRFL of China
文摘In terms of reflection transformation of a matrix product state （MPS）, the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state ｜ψe〉 and the odd-parity state ｜ψσ〉. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state ｜ψe〉 and the odd-parity state ｜ψo〉 constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states ｜ψe〉 and ｜ψo〉 is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.
基金Supported by the Chinese National Science Foundation under Grant Nos.11047160 and 10874003It is also partially supported by the National Basic Research Program of China under Grant No.2009CB939901
文摘The matrix product state （MPS） is utilized to investigate the ground state properties and quantum phase transitions （OPTs） of the dimerized antiferromagnetic Heisenberg （DAH） model. The ground state MPS wavefunctions determined by the infinite time-evolving block decimation （iTEBD） algorithm are shown to be very efficient descriptions of DAH model. In the thermodynamic limit, the quantum entanglement, the bond energy~ and the nearest-neighbor correlations are calculated. It is revealed that the singular behavior of the bipartite entanglement can detect the QPTs directly. The critical point J2c= 1.0 is determined evidently, and the quantum phase transition is argued to belong to the second-order category. At the critical point, logarithmic divergent character of the block entanglement is observed, and the system can be described by a free bosonic field theory.
基金Supported by the National Natural Science Foundation of China under Grant No.10974137the Major Natural Science Foundation of the Educational Department of Sichuan Province under Grant No.14ZA0167
文摘For our proposed composite parity-conserved matrix product state(MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.
基金supported by National Basic Research Program of China (973 Program) (No. 6138101004-3)Key Project of Innovation Knowledge of Chinese Academy of Sciences (No. YYYJ-0917)Innovation Knowledge of Chinese Academy of Sciences (No.O7A6210601)
文摘This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.
