Linewidths of collective excitations of the inhomogeneous electron gas: Application to two-dimensional quantum strips

It is well known that high-frequency collective excitations in electronic systems are not Landau damped, i.e., they cannot decay effectively into single particle-hole pairs. The leading damping mechanism in this regime is instead provided by dynamical exchange and correlation effects, such as multipair production. These effects are not captured by the widely used adiabatic local-density approximation (ALDA), which accounts for Landau damping only. In the recently developed time-dependent current density-functional formalism [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997)], exchange and correlation enter as viscoelastic stresses in the electron fluid, causing an additional damping that is not contained in the ALDA. We use this theory to derive an explicit formula for the linewidth of collective electronic excitations that are not Landau damped. The formula is then applied to calculate the linewidth of collective modes in two-dimensional (2D) quantum strips. In comparison with the corresponding modes in the homogeneous 2D electron gas, we find an order-of-magnitude enhancement of the linewidth due to the nonuniformity of the system.