On the condition of electric-LO phonon strong coupling in a parabolic quantum dot,we obtain theeigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method ofPekar ty...On the condition of electric-LO phonon strong coupling in a parabolic quantum dot,we obtain theeigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method ofPekar type.This system in a quantum dot may be employed as a two-level quantum system-qubit.When the electronis in the superposition state of the ground state and the first-excited state,we obtain the time evolution of the electrondensity.The relations of the probability density of electron on the temperature and the electron-LO-phonon couplingconstant and the relations of the period of oscillation on the temperature,the electron-LO-phonon coupling constant,the Coulomb binding parameter and the confinement length are derived.The results show that the probability densityof electron oscillates with a period when the electron is in the superposition state of the ground and the first-excitedstate,and show that there are different laws that the probability density of electron and the period of oscillation changewith the temperature and the electron-LO-phonon coupling constant when the temperature is lower or higher.Andit is obtained that the period of oscillation decreases with increasing the Coulomb bound potential and increases withincreasing the confinement length not only at lower temperatures but also at higher temperatures.展开更多
By using the random phase approximation (RPA) in many-body perturbation theory,we calculate thepolarization function of the electron gas in graphene at finite temperature.Based on this,we calculate the temperaturedepe...By using the random phase approximation (RPA) in many-body perturbation theory,we calculate thepolarization function of the electron gas in graphene at finite temperature.Based on this,we calculate the temperaturedependent dielectric function ∈(q).The thermal effect on ∈(q) in various q regions is discussed.The temperaturedependence is found to be quadratic.We also investigate the plasmon dispersion relation at finite temperature,with thezero-temperature relation as a special case.The result is in good agreement with recent experimental data.展开更多
The fully consistent relativistic continuum random phase approximation (RCRPA) has been constructed in the momentum representation in the first part of this paper. In this part we describe the numerical details for ...The fully consistent relativistic continuum random phase approximation (RCRPA) has been constructed in the momentum representation in the first part of this paper. In this part we describe the numerical details for solving the Bethe-Salpeter equation. The numerical results are checked by the inverse energy weighted sum rules in the isoscalar giant monopole resonance, which are obtained from the constraint relativistic mean field theory and also calculated with the integration of the RCRPA strengths. Good agreement between them is achieved. We study the effects of the self-consistency violation, particularly the currents and Coulomb interaction to various collective multipole excitations. Using the fully consistent RCRPA method, we investigate the properties of isoscalar and isovector collective multipole excitations for some stable and exotic from light to heavy nuclei. The properties of the resonances, such as the centroid energies and strength distributions are compared with the experimental data as well as with results calculated in other models.展开更多
The single particle energies obtained in a Kohn-Sham density functional theory(DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport,tunneling an...The single particle energies obtained in a Kohn-Sham density functional theory(DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport,tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The G_0W_0 approximation is a widely used technique in which the self energy is expressed as the convolution of a noninteracting Green's function(G_0) and a screened Coulomb interaction(W_0) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating W_0 at multiple frequencies. In this paper, we discuss how the cost of G_0W_0 calculation can be reduced by constructing a low rank approximation to the frequency dependent part of W_0. In particular, we examine the effect of such a low rank approximation on the accuracy of the G_0W_0 approximation. We also discuss how the numerical convolution of G_0 and W_0 can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.10747002Research Funds from Qufu Normal University under Grant No.XJZ200839
文摘On the condition of electric-LO phonon strong coupling in a parabolic quantum dot,we obtain theeigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method ofPekar type.This system in a quantum dot may be employed as a two-level quantum system-qubit.When the electronis in the superposition state of the ground state and the first-excited state,we obtain the time evolution of the electrondensity.The relations of the probability density of electron on the temperature and the electron-LO-phonon couplingconstant and the relations of the period of oscillation on the temperature,the electron-LO-phonon coupling constant,the Coulomb binding parameter and the confinement length are derived.The results show that the probability densityof electron oscillates with a period when the electron is in the superposition state of the ground and the first-excitedstate,and show that there are different laws that the probability density of electron and the period of oscillation changewith the temperature and the electron-LO-phonon coupling constant when the temperature is lower or higher.Andit is obtained that the period of oscillation decreases with increasing the Coulomb bound potential and increases withincreasing the confinement length not only at lower temperatures but also at higher temperatures.
基金Supported by National Natural Science Foundation of China under Grant No.10474001
文摘By using the random phase approximation (RPA) in many-body perturbation theory,we calculate thepolarization function of the electron gas in graphene at finite temperature.Based on this,we calculate the temperaturedependent dielectric function ∈(q).The thermal effect on ∈(q) in various q regions is discussed.The temperaturedependence is found to be quadratic.We also investigate the plasmon dispersion relation at finite temperature,with thezero-temperature relation as a special case.The result is in good agreement with recent experimental data.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10875150, 10775183, 10535010Major State Basic Research Development Programme of China Under Contract Number 2007CB815000
文摘The fully consistent relativistic continuum random phase approximation (RCRPA) has been constructed in the momentum representation in the first part of this paper. In this part we describe the numerical details for solving the Bethe-Salpeter equation. The numerical results are checked by the inverse energy weighted sum rules in the isoscalar giant monopole resonance, which are obtained from the constraint relativistic mean field theory and also calculated with the integration of the RCRPA strengths. Good agreement between them is achieved. We study the effects of the self-consistency violation, particularly the currents and Coulomb interaction to various collective multipole excitations. Using the fully consistent RCRPA method, we investigate the properties of isoscalar and isovector collective multipole excitations for some stable and exotic from light to heavy nuclei. The properties of the resonances, such as the centroid energies and strength distributions are compared with the experimental data as well as with results calculated in other models.
基金supported by the SciD AC Program on Excited State Phenomena in Energy Materials funded by the US Department of Energy,Office of Basic Energy Sciences and of Advanced Scientific Computing Research at Lawrence Berkeley National Laboratory(Grant No.DE-AC02-05CH11231)the Center for Applied Mathematics for Energy Research Applications funded by US Department of Energy,Office of Science,Advanced Scientific Computing Research and Basic Energy Sciences,the Alfred P.Sloan FellowshipNational Natural Science Foundation of China(Grant No.11171232)
文摘The single particle energies obtained in a Kohn-Sham density functional theory(DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport,tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The G_0W_0 approximation is a widely used technique in which the self energy is expressed as the convolution of a noninteracting Green's function(G_0) and a screened Coulomb interaction(W_0) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating W_0 at multiple frequencies. In this paper, we discuss how the cost of G_0W_0 calculation can be reduced by constructing a low rank approximation to the frequency dependent part of W_0. In particular, we examine the effect of such a low rank approximation on the accuracy of the G_0W_0 approximation. We also discuss how the numerical convolution of G_0 and W_0 can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.