By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-Xi Liu et al. [Phys. Rev. A 63 (2001) 033816]....By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-Xi Liu et al. [Phys. Rev. A 63 (2001) 033816]. The influence of the external laser field on the quantum decoherence of a mesoscopically superposed state of the excitons is investigated. Our result shows that, the classical field can compensate the energy dissipation of the excitons. Although the decoherence rate of the excitonic Schr?dinger cat state does not depend on the external field, the phase of the decoherence factor can be well controlled by adjusting the amplitude of the external field as well as the detuning between the field and the transition frequency of the atom.展开更多
We obtain a new relation between Green's functions of the time-dependent Schrōdinger equation forstationary potentials and Green's functions of the same equation for certain time-dependent potentials. The rel...We obtain a new relation between Green's functions of the time-dependent Schrōdinger equation forstationary potentials and Green's functions of the same equation for certain time-dependent potentials. The relationobtained here emerges very easily from a transformation introduced by Ray [J.R. Ray, Phys. Rev. A26 (1982) 729] andgeneralizes former work of Dodonov et al. [V.V. Dodonov, V.I. Man'ko, and D.E. Nikonov, Phys. Lett. A162 (1992)359.]展开更多
The hierarchical stochastic Schrodinger equations(HSSE)are a kind of numerically exact wavefunction-based approaches suitable for the quantum dynamics simulations in a relatively large system coupled to a bosonic bath...The hierarchical stochastic Schrodinger equations(HSSE)are a kind of numerically exact wavefunction-based approaches suitable for the quantum dynamics simulations in a relatively large system coupled to a bosonic bath.Starting from the influence-functional description of open quantum systems,this review outlines the general theoretical framework of HSSEs and their concrete forms in different situations.The applicability and efficiency of HSSEs are exemplified by the simulations of ultrafast excitation energy transfer processes in large-scale systems.展开更多
The numerical calculation of the energy distribution of electrons emitted by the tungsten, for a triangular barrier and given reflection images, has been carried out. It is shown that the numerical solution of Schrodi...The numerical calculation of the energy distribution of electrons emitted by the tungsten, for a triangular barrier and given reflection images, has been carried out. It is shown that the numerical solution of Schrodinger equation is the most effective method of calculation of the transparency of potential barrier among those used in work. I-V characteristics, which were calculated by the application of this method under different conditions, match the experimental data the best. The application of the numerical solution of Schrodinger equation for the calculation of transparency of the potential barrier enables the in-depth analysis of the tunnels phenomena and allows forecasting the effects which can not be received by application of Wentzel-Kramers-Brillouin approximation.展开更多
The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonie oscillator, due to diodes included in the circuit. In this paper, using the advanced quantum theory of mesoseopie circuits, which based o...The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonie oscillator, due to diodes included in the circuit. In this paper, using the advanced quantum theory of mesoseopie circuits, which based on the fundamental fact that the electric charge takes discrete value, the diode included mesoscopic circuit is firstly studied. Schrodinger equation of the system is a four-order difference equation in p rep asentation. Using the extended perturbative method, the detail energy spectrum and wave functions axe obtained and verified, as an application of the results, the current quantum fluctuation in the ground state is calculated. Diode is a basis component in a circuit, its quantization would popularize the quantum theory of mesoscopie circuits. The methods to solve the high order difference equation are helpful to the application of mesoscopic quantum theory.展开更多
The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eig...The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.展开更多
We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schr¨odinger equation.The accuracy of the solution is explored as it varies with the range of the numerical domai...We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schr¨odinger equation.The accuracy of the solution is explored as it varies with the range of the numerical domain.The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires.Also,the model of a linear harmonic oscillator is considered for comparison reasons.It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range,which is thus considered to be optimal.This range is found to depend on the number of mesh nodes N approximately as α_0 log_e^(α1)(α_2N),where the values of the constants α_0,α_1,and α_2are determined by fitting the numerical data.And the optimal range is found to be a weak function of the diffusion length.Moreover,it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schr¨odinger equation.展开更多
文摘By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-Xi Liu et al. [Phys. Rev. A 63 (2001) 033816]. The influence of the external laser field on the quantum decoherence of a mesoscopically superposed state of the excitons is investigated. Our result shows that, the classical field can compensate the energy dissipation of the excitons. Although the decoherence rate of the excitonic Schr?dinger cat state does not depend on the external field, the phase of the decoherence factor can be well controlled by adjusting the amplitude of the external field as well as the detuning between the field and the transition frequency of the atom.
文摘We obtain a new relation between Green's functions of the time-dependent Schrōdinger equation forstationary potentials and Green's functions of the same equation for certain time-dependent potentials. The relationobtained here emerges very easily from a transformation introduced by Ray [J.R. Ray, Phys. Rev. A26 (1982) 729] andgeneralizes former work of Dodonov et al. [V.V. Dodonov, V.I. Man'ko, and D.E. Nikonov, Phys. Lett. A162 (1992)359.]
基金supported by the National Natural Science Foundation of China(No.22033006,No.21833006,and No.21773191).
文摘The hierarchical stochastic Schrodinger equations(HSSE)are a kind of numerically exact wavefunction-based approaches suitable for the quantum dynamics simulations in a relatively large system coupled to a bosonic bath.Starting from the influence-functional description of open quantum systems,this review outlines the general theoretical framework of HSSEs and their concrete forms in different situations.The applicability and efficiency of HSSEs are exemplified by the simulations of ultrafast excitation energy transfer processes in large-scale systems.
文摘The numerical calculation of the energy distribution of electrons emitted by the tungsten, for a triangular barrier and given reflection images, has been carried out. It is shown that the numerical solution of Schrodinger equation is the most effective method of calculation of the transparency of potential barrier among those used in work. I-V characteristics, which were calculated by the application of this method under different conditions, match the experimental data the best. The application of the numerical solution of Schrodinger equation for the calculation of transparency of the potential barrier enables the in-depth analysis of the tunnels phenomena and allows forecasting the effects which can not be received by application of Wentzel-Kramers-Brillouin approximation.
基金Supported by National Natural Science Foundation of China under Grant No.10575028
文摘The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonie oscillator, due to diodes included in the circuit. In this paper, using the advanced quantum theory of mesoseopie circuits, which based on the fundamental fact that the electric charge takes discrete value, the diode included mesoscopic circuit is firstly studied. Schrodinger equation of the system is a four-order difference equation in p rep asentation. Using the extended perturbative method, the detail energy spectrum and wave functions axe obtained and verified, as an application of the results, the current quantum fluctuation in the ground state is calculated. Diode is a basis component in a circuit, its quantization would popularize the quantum theory of mesoscopie circuits. The methods to solve the high order difference equation are helpful to the application of mesoscopic quantum theory.
文摘The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.
基金Supported by the Ministry of Education,Science,and Technological Development of Serbia and the Flemish fund for Scientific Research(FWO Vlaanderen)
文摘We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schr¨odinger equation.The accuracy of the solution is explored as it varies with the range of the numerical domain.The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires.Also,the model of a linear harmonic oscillator is considered for comparison reasons.It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range,which is thus considered to be optimal.This range is found to depend on the number of mesh nodes N approximately as α_0 log_e^(α1)(α_2N),where the values of the constants α_0,α_1,and α_2are determined by fitting the numerical data.And the optimal range is found to be a weak function of the diffusion length.Moreover,it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schr¨odinger equation.
