Abstract:
We conduct a theoretical study on the properties of a bound polaron in a quantum well under an electric field using linear combination operator and unitary transformation methods,which are valid in the whole range of electron-LO phonon coupling.The changing relations between the ground-state energy of the bound polaron in the quantum well and the Coulomb bound potential,the electric field strength,and the well width are derived.The numerical results show that the ground-state energy increases with the increase of the electric field strength and the Coulomb bound potential and decreases as the well width increases.

Abstract:
The properties of a bound polaron in a parabolic quantum dot with weak electron-LO-phonon coupling under a Coulomb field are studied.The ground state energy of the bound polaron is derived by using a linear combination operator and the perturbation method.The influence of the interaction between phonons with different wave vectors in the recoil process on the ground state energy of the bound polaron is discussed.Numerical calculations are performed,and the results show that the ground state energy increases significantly as the effective confinement length of the quantum dot decreases,considering of the interaction between phonons.When l0>1.0,the influence of the interaction between phonons on the ground state energy cannot be ignored.

Abstract:
Within the effective-mass approximation, a variational method is adopted to investigate the polaron effect in a strained GaN/AlxGa1-xN cylindrical quantum dot. The electron couples with both branches of longitudinal optical-like (LO-like) and transverse optical-like (TO-like) phonons and the built-in electric field are taken into account. The numerical results show that the binding energy of the bound polaron is reduced obviously by the polaron effect on the impurity states. Furthermore, the contribution of LO-like phonons to the binding energy is dominant, and the anisotropic angle and Al content influence on the binding energy are small.

Abstract:
We calculated the binding energy of a polaron bound to a hydrogenic donor impurity located in a spherical quantum dot by means of a variational and numerical technique for finite potential models. The polaronic effect has been considered taking into account the ion-phonon coupling under the Lee Low Pines approach. The results show that the binding energies are drastically affected by the dot radius, the potential barrier height and the polaronic effects.

Abstract:
Theoretical predictions of impurity bound polaron effects on the third harmonic generation in rectangular quantum well wires are presented.The formula for the third harmonic generation along the wire is derived by desity matrix method.The numerical results are presented for a typical GaAs quantum well wire.

Abstract:
We study the quantum dynamics of small polaron formation and polaron transport through finite quantum structures in the framework of the one-dimensional Holstein model with site-dependent potentials and interactions. Combining Lanczos diagonalization with Chebyshev moment expansion of the time evolution operator, we determine how different initial states, representing stationary ground states or injected wave packets, after an electron-phonon interaction quench, develop in real space and time. Thereby, the full quantum nature and dynamics of electrons and phonons is preserved. We find that the decay out of the initial state sensitively depends on the energy and momentum of the incoming particle, the electron-phonon coupling strength, and the phonon frequency, whereupon bound polaron-phonon excited states may emerge in the strong-coupling regime. The tunneling of a Holstein polaron through a quantum wall/dot is generally accompanied by strong phonon number fluctuations due to phonon emission and re-absorption processes.

Abstract:
The binding energy of a bound polaron in a finite parabolic quantum well is studied theoretically by a fractional-dimensional variational method.The numerical results for the binding energies of the bound polaron and longitudinal-optical phonon contributions in GaAs/Al0.3Ga0.7As parabolic quantum well structures are obtained as functions of the well width.It is shown that the binding energies of the bound polaron are obviously reduced by the electron-phonon interaction and the phonon contribution is observable and cannot be neglected.

Abstract:
This paper reports that the ground-state energy of polaron was obtained with strong electron-LO-phonon coupling by using a variational method of the Pekar type in a parabolic quantum dot. Quantum transition is occurred in the quantum system due to the electron--phonon interaction and the influence of temperature. That is the polaron transit from the ground-state to the first-excited state after absorbing a LO-phonon and it causes the change of the polaron lifetime. Numerical calculations are performed and the results illustrate that the ground-state lifetime of the polaron will increase with increasing the ground-state energy of polaron and decrease with increasing the electron-LO-phonon coupling strength, the confinement length of the quantum dot and the temperature.

Abstract:
We have proposed the Hamiltonian of the single or double polaron bound to a helium-type donor impurity in semiconductor quantum wells (QWs) in the case of positively charged donor center and neutral donor center. The couplings of an electron with various phonon modes are considered; in particular, the interaction of the impurity with the various phonon modes is included. We have calculated the binding energy of a bound polaron in Al(xl)Ga1-(xl)As/GaAs/Al(xr)Ga1-(xr) As symmetric and asymmetric QWs. The results are obtained as a function of barrier height (or equivalently of Al concent ration x), well width, and the position of impurity in the QWs. Our numerical calculations show clearly that for a thin well the cumulative effects of the electron-phonon coupling and the impurity-phonon coupling can contribute appreciably to the donor binding energy. The enhancement of polaronic effect is also found in the case of ionized donor.

Abstract:
The ground-state energy and the average number of virtual phonons around the electron of a hydrogenic impurity confined in a parabolic quantum dot are calculated using the squeezed-state variational approach,which is based on two successive canonical transformations and uses a displaced-oscillator type unitary transformation to deal with the bilinear terms,which are usually neglected.Numerical calculations are carried out in order to study the relation between the ground-state energy and the average number of virtual phonons around the electron of a bound polaron in a parabolic quantum dot with the Coulomb binding parameter.The electron-phonon coupling constant and the confinement length are derived.