The low-order harmonic generation of hydrogen molecular ion interacting with a linearly polarized laser field has been investigated theoretically by using a simple two-state model. The validity of the two-state model ...The low-order harmonic generation of hydrogen molecular ion interacting with a linearly polarized laser field has been investigated theoretically by using a simple two-state model. The validity of the two-state model is carefully examined by comparing the harmonic spectra of hydrogen molecular ion obtained from this model with those from the three-dimensional time-dependent Schr¨odinger equation. When combined with the Morlet transform of quantum time-frequency spectrum,the two-state model can be used to study the dynamical origin of the low-order harmonic generation of hydrogen molecular ion driven by low-frequency pulses. In addition, some interesting structures of the time profiles for low order harmonics are obtained.展开更多
This paper studies the two-vibron bound states in the β- Fermi Pasta-Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site ...This paper studies the two-vibron bound states in the β- Fermi Pasta-Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site and mixed two-vibron bound states may exist in the model. Specially, wave number has a significant effect on such bound states, which may be considered as the quantum effects of the localized states in quantum systems.展开更多
We consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the v-dimensional integer valued lattice Z<sup>v</sup>. We proved the essen...We consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the v-dimensional integer valued lattice Z<sup>v</sup>. We proved the essential spectrum of the system in the singlet state is consists of union of no more then three intervals, and the discrete spectrum of the system in the singlet state is consists of no more then five eigenvalues. We show that the discrete spectrum of the system in the triplet and singlet states differ from each other. In the singlet state the appear additional two eigenvalues. In the triplet state the discrete spectrum of the system can be empty set, or is consists of one-eigenvalue, or is consists of two eigenvalues, or is consists of three eigenvalues. For investigation the structure of essential spectra and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model.展开更多
The model of two two level atoms interact with a single mode cavity was investigated. The formulation of the time evolution operator for the two atom Jaynes Cummings model is pressented by the bare states approach. Be...The model of two two level atoms interact with a single mode cavity was investigated. The formulation of the time evolution operator for the two atom Jaynes Cummings model is pressented by the bare states approach. Besides, the time evolution of the two atom common population probabilities is studied, and some novel features are obtained.展开更多
The paper deals with analytical fracture mechanics to consider elastic thermal stresses acting in an isotropic multi-particle-matrix system. The multi-particle-matrix system consists of periodically distributed spheri...The paper deals with analytical fracture mechanics to consider elastic thermal stresses acting in an isotropic multi-particle-matrix system. The multi-particle-matrix system consists of periodically distributed spherical particles in an infinite matrix. The thermal stresses originate during a cooling process as a consequence of the difference αm - αp in thermal expansion coefficients between the matrix and the particle, αm and αp, respectively. The multi-particle-matrix system thus represents a model system applicable to a real two-component material of a precipitation-matrix type. The infinite matrix is imaginarily divided into identical cubic cells. Each of the cubic cells with the dimension d contains a central spherical particle with the radius R, where d thus corresponds to inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent microstructural characteristics of a twocomponent material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural characteristics. The analytical fracture mechanics includes an analytical analysis of the crack initiation and consequently the crack propagation both considered for the spherical particle （q = p） and the cell matrix （q = m）. The analytical analysis is based on the determination of the curve integral Wcq of the thermal-stress induced elastic energy density Wq. The crack initiation is represented by the determination of the critical particle radius Rqc = Rqc（V）. Formulae for Rqc are valid for any two-component mate- rial of a precipitate-matrix type. The crack propagation for R 〉 Rqc is represented by the determination of the function fq describing a shape of the crack in a plane perpendicular展开更多
Time-dependent hybrid density functional theory in combination with polarized continuum model is applied to study the solvent effects on the geometrical and electronic structures as well as one- and two-photon absorpt...Time-dependent hybrid density functional theory in combination with polarized continuum model is applied to study the solvent effects on the geometrical and electronic structures as well as one- and two-photon absorption processes, of a newly synthesized asymmetrical charge-transfer organic molecule bis-（4-bromo-phenyl）-[4-（2-pyridin-4-yl-vinyl）phenyl]-amine （BPYPA）. There exist two charge-transfer states for the compound in visible region. The two-photon absorption cross section calculated by a three-state model and solvatochromic shift of the charge-transfer states are found to be solvent-dependent, where a nonmonotonic behaviour with respect to the polarity of the solvents is observed. The numerical results show that the organic molecule exhibits a rather large two-photon absorption cross section as compared with the compound 4-trans-[p-（N, N-Di-n-butylamino）-p-stilbenyl vinyl] pyridine （DBASVP） reported previously, and is predicted to be a good two-photon polymerization initiator. The hydrogen-bond effect is analysed. The computational results are in good agreement with the measurements.展开更多
On the level of the time-dependent hybrid density functional theory, the one- and two-photon absorption properties of a series of symmetric 4-bis{2-[4-（2-aryl） phenyl]vinyl）-2,5-bisdialkoxybenzenes are studied resp...On the level of the time-dependent hybrid density functional theory, the one- and two-photon absorption properties of a series of symmetric 4-bis{2-[4-（2-aryl） phenyl]vinyl）-2,5-bisdialkoxybenzenes are studied respectively utilizing the analytic response theory and the few-state model methods. The calculated results show that the planarity of the geometrical structure plays a great role in enhancing the linear and nonlinear optical abilities of the molecule. However the effect of the length of the chain linked to the π-centre on the optical property is very little. For the investigated compounds, the A-π-A type charge-transfer molecules display more superior one- and two-photon absorption characteristics than the D-π-D type ones. Furthermore, the two-photon absorption results by use of few-state model are generally consistent with those by analytic response theory, demonstrating the reliability of the few-state model for evaluating the two-photon absorption cross section. The numerical simulations are in good agreement in tendency with the available experimental measurements.展开更多
We consider a three-magnon system in the isotropic ferromagnetic Non-Heisenberg model with spin one and with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the syste...We consider a three-magnon system in the isotropic ferromagnetic Non-Heisenberg model with spin one and with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in a ν-dimensional lattice are investigated. We obtain the lower and upper estimates for the number of three-magnon bound states of the system.展开更多
We theoretically study the transition dynamics of a two-component Bose-Einstein condensate driven by a train of weak δ-shaped laser pulses. We find that the atomic system can experience peculiar resonant transition e...We theoretically study the transition dynamics of a two-component Bose-Einstein condensate driven by a train of weak δ-shaped laser pulses. We find that the atomic system can experience peculiar resonant transition even under weak optical excitations and derive the resonance condition by the perturbation method. Employing this mechanism, we propose a scheme to obtain an atomic ensemble with desired odd/even atom number and also a scheme to prepare a nonclassical state of the many-body system with fixed atom number.展开更多
The optimal conditions for two-stage Kalman estimator with random bias of anARMA model is considered in this paper.First,the optimal augmented state Kalman fil-ter and the two-stage Kalman estimator are given.Second,u...The optimal conditions for two-stage Kalman estimator with random bias of anARMA model is considered in this paper.First,the optimal augmented state Kalman fil-ter and the two-stage Kalman estimator are given.Second,under an algebraic constraint,the equivalence between the two-stage Kalman estimator and the optimal augmented stateKalman filter is proved.Finally,because the given algebraic constraint are restrictive inpractice,the results thus obtained implies that two-stage Kalman estimator is suboptimal.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11465016,11674268,and 11764038)
文摘The low-order harmonic generation of hydrogen molecular ion interacting with a linearly polarized laser field has been investigated theoretically by using a simple two-state model. The validity of the two-state model is carefully examined by comparing the harmonic spectra of hydrogen molecular ion obtained from this model with those from the three-dimensional time-dependent Schr¨odinger equation. When combined with the Morlet transform of quantum time-frequency spectrum,the two-state model can be used to study the dynamical origin of the low-order harmonic generation of hydrogen molecular ion driven by low-frequency pulses. In addition, some interesting structures of the time profiles for low order harmonics are obtained.
基金Project supported by the Key Project of Hunan Provincial Educational Department of China (Grant No 04A058)
文摘This paper studies the two-vibron bound states in the β- Fermi Pasta-Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site and mixed two-vibron bound states may exist in the model. Specially, wave number has a significant effect on such bound states, which may be considered as the quantum effects of the localized states in quantum systems.
文摘We consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the v-dimensional integer valued lattice Z<sup>v</sup>. We proved the essential spectrum of the system in the singlet state is consists of union of no more then three intervals, and the discrete spectrum of the system in the singlet state is consists of no more then five eigenvalues. We show that the discrete spectrum of the system in the triplet and singlet states differ from each other. In the singlet state the appear additional two eigenvalues. In the triplet state the discrete spectrum of the system can be empty set, or is consists of one-eigenvalue, or is consists of two eigenvalues, or is consists of three eigenvalues. For investigation the structure of essential spectra and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model.
基金Supported by National Natural Science Foundation of China （10571036） the Key Discipline Development Program of Beijing Municipal Commission （XK100080537）
基金SupportedbytheFoundationofAnhuiprovincialeducationalcommittee (No .2 0 0 1kj2 63 )
文摘The model of two two level atoms interact with a single mode cavity was investigated. The formulation of the time evolution operator for the two atom Jaynes Cummings model is pressented by the bare states approach. Besides, the time evolution of the two atom common population probabilities is studied, and some novel features are obtained.
基金supported by the Slovak Research and Development Agency under the contracts No. COST-0022-06, No.COST-0042-06, No. APVV-51-061505, No. APVV-0034-07, No.APVV-0171-06by the 6th FP EU NESPA+17 种基金by FP7-EGPOT-2007-3 DEMATEN 204953 (05/08-04/11)by IMPROVING 229625by HANCOC-MNT.ERA-NET 01/09-12/11by NANOSMART Centre of Excellence (01/2007-12/2010) Slovak Academy of Sciencesby the Slovak Grant Agency VEGA (2/7197/27, 2/7194/27, 2/7195/27,1/4107/07)by iNTeg-Risk CP-IP 213345-2by European Structural Fund-Center of Excellence (Progressive Materials with Nano-and Submicron-Structure): ITMS NFP code 262200120019by COST Action 536by COST Action 538by OTKA Foundation (No. T043704,T043685, T 048593, T 63609)by HPRT-CT-2000-00037by EC5 Center of Excellence ICAI-CT-2000-70029by OTKA Postdoctoral Research Grant (D38478)by Swedish Research Council (No. 621-2002-4299)by NSF-OTKA-MTA (No. MTA: 96 OTKA: 049953)by GVOP-3.2.1.-2004-04-0224/3.0by Janos Bolyai Research Grant.96/OTKA04953, OTKA 63609.
文摘The paper deals with analytical fracture mechanics to consider elastic thermal stresses acting in an isotropic multi-particle-matrix system. The multi-particle-matrix system consists of periodically distributed spherical particles in an infinite matrix. The thermal stresses originate during a cooling process as a consequence of the difference αm - αp in thermal expansion coefficients between the matrix and the particle, αm and αp, respectively. The multi-particle-matrix system thus represents a model system applicable to a real two-component material of a precipitation-matrix type. The infinite matrix is imaginarily divided into identical cubic cells. Each of the cubic cells with the dimension d contains a central spherical particle with the radius R, where d thus corresponds to inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent microstructural characteristics of a twocomponent material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural characteristics. The analytical fracture mechanics includes an analytical analysis of the crack initiation and consequently the crack propagation both considered for the spherical particle （q = p） and the cell matrix （q = m）. The analytical analysis is based on the determination of the curve integral Wcq of the thermal-stress induced elastic energy density Wq. The crack initiation is represented by the determination of the critical particle radius Rqc = Rqc（V）. Formulae for Rqc are valid for any two-component mate- rial of a precipitate-matrix type. The crack propagation for R 〉 Rqc is represented by the determination of the function fq describing a shape of the crack in a plane perpendicular
基金Project supported by the National Natural Science Foundation of China （Grant No 10274044） and Shandong Natural Science Foundation （Grant No Y2004A08）.
文摘Time-dependent hybrid density functional theory in combination with polarized continuum model is applied to study the solvent effects on the geometrical and electronic structures as well as one- and two-photon absorption processes, of a newly synthesized asymmetrical charge-transfer organic molecule bis-（4-bromo-phenyl）-[4-（2-pyridin-4-yl-vinyl）phenyl]-amine （BPYPA）. There exist two charge-transfer states for the compound in visible region. The two-photon absorption cross section calculated by a three-state model and solvatochromic shift of the charge-transfer states are found to be solvent-dependent, where a nonmonotonic behaviour with respect to the polarity of the solvents is observed. The numerical results show that the organic molecule exhibits a rather large two-photon absorption cross section as compared with the compound 4-trans-[p-（N, N-Di-n-butylamino）-p-stilbenyl vinyl] pyridine （DBASVP） reported previously, and is predicted to be a good two-photon polymerization initiator. The hydrogen-bond effect is analysed. The computational results are in good agreement with the measurements.
基金Project supported by the State Key Development Program for Basic Research of China(Grant No.2006CB806000)the Open Fund of the State Key Laboratory of High Field Laser Physics(Shanghai Institute of Optics and Fine Mechanics),Higher Educational Science and Technology Program of Shandong Province(Grant No.J09LA13)
文摘On the level of the time-dependent hybrid density functional theory, the one- and two-photon absorption properties of a series of symmetric 4-bis{2-[4-（2-aryl） phenyl]vinyl）-2,5-bisdialkoxybenzenes are studied respectively utilizing the analytic response theory and the few-state model methods. The calculated results show that the planarity of the geometrical structure plays a great role in enhancing the linear and nonlinear optical abilities of the molecule. However the effect of the length of the chain linked to the π-centre on the optical property is very little. For the investigated compounds, the A-π-A type charge-transfer molecules display more superior one- and two-photon absorption characteristics than the D-π-D type ones. Furthermore, the two-photon absorption results by use of few-state model are generally consistent with those by analytic response theory, demonstrating the reliability of the few-state model for evaluating the two-photon absorption cross section. The numerical simulations are in good agreement in tendency with the available experimental measurements.
文摘We consider a three-magnon system in the isotropic ferromagnetic Non-Heisenberg model with spin one and with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in a ν-dimensional lattice are investigated. We obtain the lower and upper estimates for the number of three-magnon bound states of the system.
基金Project supported by the National Key Research and Development Program of China(Grant No.2016YFA0301504)the National Natural Science Foundation of China(Grant Nos.61835013 and 11774362)
文摘We theoretically study the transition dynamics of a two-component Bose-Einstein condensate driven by a train of weak δ-shaped laser pulses. We find that the atomic system can experience peculiar resonant transition even under weak optical excitations and derive the resonance condition by the perturbation method. Employing this mechanism, we propose a scheme to obtain an atomic ensemble with desired odd/even atom number and also a scheme to prepare a nonclassical state of the many-body system with fixed atom number.
文摘The optimal conditions for two-stage Kalman estimator with random bias of anARMA model is considered in this paper.First,the optimal augmented state Kalman fil-ter and the two-stage Kalman estimator are given.Second,under an algebraic constraint,the equivalence between the two-stage Kalman estimator and the optimal augmented stateKalman filter is proved.Finally,because the given algebraic constraint are restrictive inpractice,the results thus obtained implies that two-stage Kalman estimator is suboptimal.
