Vibrational frequency of a strong-coupling polaron in a quantum rod at finite temperatures

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 electronphonon coupling strength but become decreasing ones of the temperature and the aspect ratio.