Lifetime analysis of quasistationary states of an electron in open quantum wires*

The quasistationary states of an electron in a cylindrically N-layered open quantum wire are investigated. A complex eigen-solver is developed to determine both the resonant states E_R and the corresponding lifetimes τ of the system. Here, we solve the eigenvalue equations for the quasibound states of an electron in open quantum wires using the adaptive finite element method (FEM). We have carefully examined the convergence of this approach for the desired accuracy and efficiency. All the quasistationary states of the system can be determined via this eigen-solver. For illustration, the numerical calculations are carried out for the GaAs/Al_xGa_1-xAs/GaAs multi-layered open quantum wire. Both the energy levels and the lifetimes of the quasistationary states are found as functions of the geometric parameters of the system. The lifetime of an electron in such a system is very sensitive to the geometric characteristics. Figure 1 shows our preliminary results are in good agreement with a previous work done by M. Tkach et al. which analyzed the cases of the quasiparticle lifetimes using the S-matrix theory.