The Hamiltonian of a quantum rod with a boundary is presented after a coordinate transformation that changes the original ellipsoidal boundary into a spherical one. We then study the effect of temperature on the vibra...The Hamiltonian of a quantum rod with a boundary is presented after a coordinate transformation that changes the original ellipsoidal boundary into a spherical one. We then study the effect of temperature on the vibrational frequency and the ground state binding energy of the strong-coupling polaron in the rod. The two quantities are expressed as functions of the aspect ratio of the ellipsoid, the transverse and the longitudinal effective confinement lengths, the temperature and the electron-phonon coupling strength by linear combination operator and unitary transformation methods. It is found that the vibrational frequency and the ground state binding energy will increase rapidly with decreasing transverse and longitudinal effective confinement lengths. They are increasing functions of the electron- phonon coupling strength but become decreasing ones of the temperature and the aspect ratio.展开更多
The Hamiltonian of a quantum rod with an ellipsoidal boundary is given by using a coordinate transformation in which the ellipsoidal boundary is changed into a spherical one.Under the condition of strong electron-long...The Hamiltonian of a quantum rod with an ellipsoidal boundary is given by using a coordinate transformation in which the ellipsoidal boundary is changed into a spherical one.Under the condition of strong electron-longitudinal optical phonon coupling in the rod,we obtain both the electron eigenfunctions and the eigenenergies of the ground and first-excited state by using the Pekar-type variational method.This quantum rod system may be used as a two-level qubit.When the electron is in the superposition state of the ground and first-excited states,the probability density of the electron oscillates in the rod with a certain period.It is found that the oscillation period is an increasing function of the ellipsoid aspect ratio and the transverse and longitudinal effective confinement lengths of the quantum rod,whereas it is a decreasing function of the electron-phonon coupling strength.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.10964005)
文摘The Hamiltonian of a quantum rod with a boundary is presented after a coordinate transformation that changes the original ellipsoidal boundary into a spherical one. We then study the effect of temperature on the vibrational frequency and the ground state binding energy of the strong-coupling polaron in the rod. The two quantities are expressed as functions of the aspect ratio of the ellipsoid, the transverse and the longitudinal effective confinement lengths, the temperature and the electron-phonon coupling strength by linear combination operator and unitary transformation methods. It is found that the vibrational frequency and the ground state binding energy will increase rapidly with decreasing transverse and longitudinal effective confinement lengths. They are increasing functions of the electron- phonon coupling strength but become decreasing ones of the temperature and the aspect ratio.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10964005)
文摘The Hamiltonian of a quantum rod with an ellipsoidal boundary is given by using a coordinate transformation in which the ellipsoidal boundary is changed into a spherical one.Under the condition of strong electron-longitudinal optical phonon coupling in the rod,we obtain both the electron eigenfunctions and the eigenenergies of the ground and first-excited state by using the Pekar-type variational method.This quantum rod system may be used as a two-level qubit.When the electron is in the superposition state of the ground and first-excited states,the probability density of the electron oscillates in the rod with a certain period.It is found that the oscillation period is an increasing function of the ellipsoid aspect ratio and the transverse and longitudinal effective confinement lengths of the quantum rod,whereas it is a decreasing function of the electron-phonon coupling strength.
