LAUSR

The 1D Schrödinger equation for an electron with the potential energy defined as a pair of equal delta-wells is analyzed. If the distance between the wells exceeds a critical value, there exist two negative eigenenergies. We focused attention on the non-stationary motion when the electron alternates periodically its position in the left and right well. The delta-wells are considered as models of quantum dots (QDs) in a quantum wire embedded in a semiconductor structure. To apprehend the motion of an electron between the QDs at low temperatures (which is evidently a tunnelling phenomenon), we employ a density-matrix formalism. We derive the solution of the Liouville (von Neumann) equation in the approximation of a relaxation time. The solution suggests that the oscillatory motion of the electron between the QDs undergoes a damping. The main cause of this damping is the electron–phonon interaction. At very low temperatures, the damping, corroborating a decoherence process, can also be effected artificially when a voltage source with a noise component is employed.