The decay dynamic of an excited quantum emitter(QE)is one of the most important contents in quantum optics.It has been widely applied in the field of quantum computing and quantum state manipulation.When the electroma...The decay dynamic of an excited quantum emitter(QE)is one of the most important contents in quantum optics.It has been widely applied in the field of quantum computing and quantum state manipulation.When the electromagnetic environment is described by several pseudomodes,the effective Hamiltonian method based on the multi-mode Jaynes-Cummings model provides a clear physical picture and a simple and convenient way to solve the decay dynamics.However,in previous studies,only the resonant modes are taken into account,while the non-resonant contributions are ignored.In this work,we study the applicability and accuracy of the effective Hamiltonian method for the decay dynamics.We consider different coupling strengths between a two-level QE and a gold nanosphere.The results for dynamics by the resolvent operator technique are used as a reference.Numerical results show that the effective Hamiltonian method provides accurate results when the two-level QE is resonant with the plasmon.However,when the detuning is large,the effective Hamiltonian method is not accurate.In addition,the effective Hamiltonian method cannot be applied when there is a bound state between the QE and the plasmon.These results are of great significance to the study of the decay dynamics in micro-nano structures described by quasi-normal modes.展开更多
A numerically efficient broadband, range-dependent propagation model is proposed, which incorporates the Hamiltonian method into the coupled-mode model DGMCM. The Hamiltonian method is highly efficient for finding bro...A numerically efficient broadband, range-dependent propagation model is proposed, which incorporates the Hamiltonian method into the coupled-mode model DGMCM. The Hamiltonian method is highly efficient for finding broadband eigenvalues, and DGMCM is an accurate model for range-dependent propagation in the frequency domain. Consequently, the proposed broadband model combining the Hamiltonian method and DGMCM has significant virtue in terms of both efficiency and accuracy. Numerical simulations are also provided. The numerical results indicate that the proposed model has a better performance over the broadband model using the Fourier synthesis and COUPLE, while retaining the same level of accuracy.展开更多
Based on Hamiltonian formulation, this paper proposes a design approach to nonlinear feedback excitation control of synchronous generators with steam valve control, disturbances and unknown parameters. It is shown tha...Based on Hamiltonian formulation, this paper proposes a design approach to nonlinear feedback excitation control of synchronous generators with steam valve control, disturbances and unknown parameters. It is shown that the dynamics of the synchronous generators can be expressed as a dissipative Hamiltonian system, based on which an adaptive H-infinity controller is then designed for the systems by using the structure properties of dissipative Hamiltonian systems. Simulations show that the controller obtained in this paper is very effective.展开更多
Dirac's method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.
The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic Runge- Kutta （RK） method is an important part of the former, and the ...The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic Runge- Kutta （RK） method is an important part of the former, and the continuous finite element method （CFEM） belongs to the later. We find and prove the equivalence of one kind of the implicit RK method and the CFEM, give the coefficient table of the CFEM to simplify its computation, propose a new standard to measure algorithms for Hamiltonian systems, and define another class of algorithms --the regular method. Finally, numerical experiments are given to verify the theoretical results.展开更多
Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective H...Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.展开更多
An analytical method for predicting chaos in perturbed planar non Hamiltonian integrable systems with slowly varying parameters was developed. Based on the analysis of the geometric structure of unperturbed systems, ...An analytical method for predicting chaos in perturbed planar non Hamiltonian integrable systems with slowly varying parameters was developed. Based on the analysis of the geometric structure of unperturbed systems, the condition of transversely homoclinic intersection was given. The generalized Melnikov function of the perturbed system was found by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters.展开更多
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved hav...By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudo- symplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agree-ment with theory.展开更多
Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are establi...Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.展开更多
Introduction Frequency-dependent dielectric response is one of the important properties of ferroelectrics,reflecting the polarization response to high-frequency electric fields.Polarizations are closely related to fer...Introduction Frequency-dependent dielectric response is one of the important properties of ferroelectrics,reflecting the polarization response to high-frequency electric fields.Polarizations are closely related to ferroelectric domain structures,such as single domain,which represents the region with homogeneous polarizations direction.Ferroelectrics usually possess complex domain structures with domain walls(DWs)separating adjacent homogeneously polarized domains.DWs have attracted much attention during the past two decades due to their properties and potential for device designing.The related issues include DW motion,nonvolatile memory,topological defects,enhanced susceptibility,enhanced quality factor,low dielectric loss,and others.(Ba0.8,Sr0.2)TiO3(BST0.8)is a ferroelectric usually with multi-domain structures.Previous work identified two typical types of domain walls(DWs),i.e.,90°DWs and 180°DWs.The enhancement of dielectric response in systems with 90°DWs is now well understood,and the behavior of dielectric response in multi-domain systems with 180°DWs remains unclear.Therefore,gaining insights into how 180°DWs affect the dielectric response can clarify the effects in multidomain systems.Methods We performed molecular dynamics simulations using the ALFE-H code with the first-principles-based effective Hamiltonian method to study the BST0.8 system.All the calculations were performed in the NPT ensemble using the Evans-Hoover thermostat,and periodic boundary condition(PBC)along all three directions.To simulate the substrate,a uniform biaxial strain was fixed to the 1.55%in-plane strain.To analyze the multi-domain with different DWs,the simulations started with a self-constructed initial multi-domain polarization configuration.Subsequent 50 ps MD simulation was performed under chosen strains for structural relaxation.In the initial configuration,the magnitude of non-zero components of soft mode on each site was set to 0.1Å,atomic occupations(alloying)were randomized,and unless otherwise specified,all other mode variables were set to zero.The trajectory of local mode averaged over the supercell during MD simulations was extracted to calculate the dielectric response.The 8 ns MD simulations were performed to obtain an autocorrelation function for any time t ranging from 0 to 1 ns by one step of 10 fs.The fast Fourier transformation(FFT)was performed to calculate the dielectric response.Then two uncoupled damped harmonic oscillators(DHOs)were used to fit the data of dielectric response.Results and discussion The dielectric response of single domain at 300 K with the different electric fields along[110]from 0 to 2 MV/cm was computed.The computational results can be well fitted with the model of two uncoupled DHOs.The real and imaginary parts of the predicted dielectric response at each chosen electric field both exhibit two peaks.As the electric field increases,the low-frequency mode with 300 GHz at zero field in the system gradually disappears,and a high-frequency mode of larger than 8 THz appears when electric field is larger than 1 MV/cm.The high frequencies modes of 3 THz at zero filed and 8 THz under 1 MV/cm shift towards higher frequencies as the electric field increases.In other words,the present simulations reveal that it is possible to manipulate the frequency of peaks in dielectric response via changing the magnitude of the external electric field.The dielectric responses of multi-domain with 90°DWs and 180°DWs are further analyzed.According to the experimental PFM results,the multi-domain structures are simulated and the dielectric response through MD simulations is calculated.The analysis of the dielectric response of single domain structure and multi-domain structures shows that the single domain structures exhibit high-frequency peaks at>300 GHz,whereas the multi-domain structures exhibit low-frequency peaks at 8 GHz and 120 GHz for 180°DWs system and at 10 GHz for 90°DWs system,revealing that there exists a low-frequency mode related to collective oscillation of DWs in multi-domain structures.In addition,the frequencies of peaks in multi-domain with DWs are in a gigahertz range,whereas the single domain structure exhibits peaks in a terahertz range.The contribution of DWs to the dielectric response primarily arises from the timescale of DWs motion,such as sliding or breathing,which differs significantly from the high-frequency vibrations of optical phonon modes.The vibrational frequency of DWs is much lower,with relaxation times in the order of nanoseconds,resulting in a response frequency in GHz range,which is far below the terahertz range of optical phonon modes.Therefore,DWs oscillations dominate the dielectric response at a low frequency.Moreover,multi-domain structure with 180°DWs exhibits a unique low frequency mode at 120 GHz,which is significantly different from single domain and 90°DWs system.In other words,multi-domain structures with 180°DWs and 90°DWs exhibit different dielectric responses.There exists a common low-frequency mode related to the oscillations of DWs in BST0.8.Conclusions It was possible to manipulate the frequency of peaks in dielectric response of single domain through changing the magnitude of the external electric field.Domain walls oscillations dominated the dielectric response in a low frequency gigahertz range,whereas the single domain structures exhibited resonant peaks in a terahertz range.Moreover,multi-domain structures with different domain walls in BST0.8 had different dielectric responses,but the both have a same low-frequency mode at 10 GHz related to the domain walls oscillations.The results of this study indicated the dielectric response behaviors of ferroelectrics induced in an external electric field and internal multi-domain configurations and provided the potential mechanisms and guidance for optimizing application performance.展开更多
运用辛叠加方法求出相邻两边固支其他两边自由(two adjacent edges clamped and the other edges free, CCFF)正交各向异性矩形薄板屈曲问题的级数展开解。首先,将原屈曲问题的控制方程转化为哈密顿系统,通过分析边界条件,将原屈曲问题...运用辛叠加方法求出相邻两边固支其他两边自由(two adjacent edges clamped and the other edges free, CCFF)正交各向异性矩形薄板屈曲问题的级数展开解。首先,将原屈曲问题的控制方程转化为哈密顿系统,通过分析边界条件,将原屈曲问题分解为两个子屈曲问题,再利用辛本征函数展开法分别求得两个子屈曲问题的通解;然后,利用叠加方法得到原屈曲问题的辛叠加解;最后,应用所得辛叠加解分别计算了单/双向载荷作用下的CCFF各向同性和正交各向异性矩形薄板的屈曲问题。计算结果表明,所得辛叠加解是正确的并且其收敛速度较快。展开更多
基金Project supported by the National Natural Science Foundation of China(11964010,11564013 and 11464014)the Natural Science Foundation of Hunan Province(2020JJ4495)+1 种基金the Scientific Research Fund of Hunan Provincial Education Department(22A0377 and 21A0333)the Jishou University Innovation Foundation for Postgraduate(Jdy20038)。
文摘The decay dynamic of an excited quantum emitter(QE)is one of the most important contents in quantum optics.It has been widely applied in the field of quantum computing and quantum state manipulation.When the electromagnetic environment is described by several pseudomodes,the effective Hamiltonian method based on the multi-mode Jaynes-Cummings model provides a clear physical picture and a simple and convenient way to solve the decay dynamics.However,in previous studies,only the resonant modes are taken into account,while the non-resonant contributions are ignored.In this work,we study the applicability and accuracy of the effective Hamiltonian method for the decay dynamics.We consider different coupling strengths between a two-level QE and a gold nanosphere.The results for dynamics by the resolvent operator technique are used as a reference.Numerical results show that the effective Hamiltonian method provides accurate results when the two-level QE is resonant with the plasmon.However,when the detuning is large,the effective Hamiltonian method is not accurate.In addition,the effective Hamiltonian method cannot be applied when there is a bound state between the QE and the plasmon.These results are of great significance to the study of the decay dynamics in micro-nano structures described by quasi-normal modes.
基金supported by the National Natural Science Foundation of China(Grant No.11125420)the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘A numerically efficient broadband, range-dependent propagation model is proposed, which incorporates the Hamiltonian method into the coupled-mode model DGMCM. The Hamiltonian method is highly efficient for finding broadband eigenvalues, and DGMCM is an accurate model for range-dependent propagation in the frequency domain. Consequently, the proposed broadband model combining the Hamiltonian method and DGMCM has significant virtue in terms of both efficiency and accuracy. Numerical simulations are also provided. The numerical results indicate that the proposed model has a better performance over the broadband model using the Fourier synthesis and COUPLE, while retaining the same level of accuracy.
基金This work was supported by the National Natural Science Foundation of China (No.G60474001) the Research Fund for Doctoral Program of Chinese Higher Education (No.G20040422059).
文摘Based on Hamiltonian formulation, this paper proposes a design approach to nonlinear feedback excitation control of synchronous generators with steam valve control, disturbances and unknown parameters. It is shown that the dynamics of the synchronous generators can be expressed as a dissipative Hamiltonian system, based on which an adaptive H-infinity controller is then designed for the systems by using the structure properties of dissipative Hamiltonian systems. Simulations show that the controller obtained in this paper is very effective.
文摘Dirac's method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.
基金Project supported by the National Natural Science Foundation of China (No. 11071067)the Hunan Graduate Student Science and Technology Innovation Project (No. CX2011B184)
文摘The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic Runge- Kutta （RK） method is an important part of the former, and the continuous finite element method （CFEM） belongs to the later. We find and prove the equivalence of one kind of the implicit RK method and the CFEM, give the coefficient table of the CFEM to simplify its computation, propose a new standard to measure algorithms for Hamiltonian systems, and define another class of algorithms --the regular method. Finally, numerical experiments are given to verify the theoretical results.
基金supported by the National Natural Science Foundation of China (Grant No. 11774328)。
文摘Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.
文摘An analytical method for predicting chaos in perturbed planar non Hamiltonian integrable systems with slowly varying parameters was developed. Based on the analysis of the geometric structure of unperturbed systems, the condition of transversely homoclinic intersection was given. The generalized Melnikov function of the perturbed system was found by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters.
基金Project supported by the National Natural Science Foundation of China (No.10471038)
文摘By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudo- symplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agree-ment with theory.
基金Project supported by the National Natural Science Foundation of China(No.11432010)the Doctoral Program Foundation of Education Ministry of China(No.20126102110023)+2 种基金the 111Project of China(No.B07050)the Fundamental Research Funds for the Central Universities(No.310201401JCQ01001)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(No.CX201517)
文摘Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.
文摘Introduction Frequency-dependent dielectric response is one of the important properties of ferroelectrics,reflecting the polarization response to high-frequency electric fields.Polarizations are closely related to ferroelectric domain structures,such as single domain,which represents the region with homogeneous polarizations direction.Ferroelectrics usually possess complex domain structures with domain walls(DWs)separating adjacent homogeneously polarized domains.DWs have attracted much attention during the past two decades due to their properties and potential for device designing.The related issues include DW motion,nonvolatile memory,topological defects,enhanced susceptibility,enhanced quality factor,low dielectric loss,and others.(Ba0.8,Sr0.2)TiO3(BST0.8)is a ferroelectric usually with multi-domain structures.Previous work identified two typical types of domain walls(DWs),i.e.,90°DWs and 180°DWs.The enhancement of dielectric response in systems with 90°DWs is now well understood,and the behavior of dielectric response in multi-domain systems with 180°DWs remains unclear.Therefore,gaining insights into how 180°DWs affect the dielectric response can clarify the effects in multidomain systems.Methods We performed molecular dynamics simulations using the ALFE-H code with the first-principles-based effective Hamiltonian method to study the BST0.8 system.All the calculations were performed in the NPT ensemble using the Evans-Hoover thermostat,and periodic boundary condition(PBC)along all three directions.To simulate the substrate,a uniform biaxial strain was fixed to the 1.55%in-plane strain.To analyze the multi-domain with different DWs,the simulations started with a self-constructed initial multi-domain polarization configuration.Subsequent 50 ps MD simulation was performed under chosen strains for structural relaxation.In the initial configuration,the magnitude of non-zero components of soft mode on each site was set to 0.1Å,atomic occupations(alloying)were randomized,and unless otherwise specified,all other mode variables were set to zero.The trajectory of local mode averaged over the supercell during MD simulations was extracted to calculate the dielectric response.The 8 ns MD simulations were performed to obtain an autocorrelation function for any time t ranging from 0 to 1 ns by one step of 10 fs.The fast Fourier transformation(FFT)was performed to calculate the dielectric response.Then two uncoupled damped harmonic oscillators(DHOs)were used to fit the data of dielectric response.Results and discussion The dielectric response of single domain at 300 K with the different electric fields along[110]from 0 to 2 MV/cm was computed.The computational results can be well fitted with the model of two uncoupled DHOs.The real and imaginary parts of the predicted dielectric response at each chosen electric field both exhibit two peaks.As the electric field increases,the low-frequency mode with 300 GHz at zero field in the system gradually disappears,and a high-frequency mode of larger than 8 THz appears when electric field is larger than 1 MV/cm.The high frequencies modes of 3 THz at zero filed and 8 THz under 1 MV/cm shift towards higher frequencies as the electric field increases.In other words,the present simulations reveal that it is possible to manipulate the frequency of peaks in dielectric response via changing the magnitude of the external electric field.The dielectric responses of multi-domain with 90°DWs and 180°DWs are further analyzed.According to the experimental PFM results,the multi-domain structures are simulated and the dielectric response through MD simulations is calculated.The analysis of the dielectric response of single domain structure and multi-domain structures shows that the single domain structures exhibit high-frequency peaks at>300 GHz,whereas the multi-domain structures exhibit low-frequency peaks at 8 GHz and 120 GHz for 180°DWs system and at 10 GHz for 90°DWs system,revealing that there exists a low-frequency mode related to collective oscillation of DWs in multi-domain structures.In addition,the frequencies of peaks in multi-domain with DWs are in a gigahertz range,whereas the single domain structure exhibits peaks in a terahertz range.The contribution of DWs to the dielectric response primarily arises from the timescale of DWs motion,such as sliding or breathing,which differs significantly from the high-frequency vibrations of optical phonon modes.The vibrational frequency of DWs is much lower,with relaxation times in the order of nanoseconds,resulting in a response frequency in GHz range,which is far below the terahertz range of optical phonon modes.Therefore,DWs oscillations dominate the dielectric response at a low frequency.Moreover,multi-domain structure with 180°DWs exhibits a unique low frequency mode at 120 GHz,which is significantly different from single domain and 90°DWs system.In other words,multi-domain structures with 180°DWs and 90°DWs exhibit different dielectric responses.There exists a common low-frequency mode related to the oscillations of DWs in BST0.8.Conclusions It was possible to manipulate the frequency of peaks in dielectric response of single domain through changing the magnitude of the external electric field.Domain walls oscillations dominated the dielectric response in a low frequency gigahertz range,whereas the single domain structures exhibited resonant peaks in a terahertz range.Moreover,multi-domain structures with different domain walls in BST0.8 had different dielectric responses,but the both have a same low-frequency mode at 10 GHz related to the domain walls oscillations.The results of this study indicated the dielectric response behaviors of ferroelectrics induced in an external electric field and internal multi-domain configurations and provided the potential mechanisms and guidance for optimizing application performance.
文摘运用辛叠加方法求出相邻两边固支其他两边自由(two adjacent edges clamped and the other edges free, CCFF)正交各向异性矩形薄板屈曲问题的级数展开解。首先,将原屈曲问题的控制方程转化为哈密顿系统,通过分析边界条件,将原屈曲问题分解为两个子屈曲问题,再利用辛本征函数展开法分别求得两个子屈曲问题的通解;然后,利用叠加方法得到原屈曲问题的辛叠加解;最后,应用所得辛叠加解分别计算了单/双向载荷作用下的CCFF各向同性和正交各向异性矩形薄板的屈曲问题。计算结果表明,所得辛叠加解是正确的并且其收敛速度较快。
