Localization length in the quasi one-dimensional disordered system revisited

• The localization length in quasi-one-dimensional disordered system is calculated.
• The hard wall and periodic boundary conditions are discussed.
• The expressions for localization lengths are in agreement with the numerical data.
• An arbitrary number of propagating and evanescent channels are considered.
• The presence of evanescent modes in a spectrum enhances the localization length.

We have provided a complete description of the electron localization length (LL) in quasi-one dimensional (Q1D) disordered quantum wire with hard wall and periodic boundary conditions. Presented analytical expressions for LL are in excellent agreement with numerical calculations, exact up to order W2 (W being the disorder strength), and valid for an arbitrary number of propagating and evanescent channels. We have calculated the average conductance in Q1D systems, establish relationship between various lengths and show that it basically differs from 1D case.