Polaron effects and boundary conditions in cylindrical wires

In this work we show that the polaron effects in cylindrical quantum wires are function of the cylinder radius R-0 through the boundary conditions for both the ionic and the electronic motion and through the size dependence of the static and high frequency dielectric constants. We find that the dielectric constants are increasing functions of R-0. This fact and the different boundary conditions for the ions and the electrons have the final consequence that polaron self-energy can either be an increasing or a decreasing function of R-0.