Symmetry Dependence of Localization in Quasi- 1- dimensional Disordered Wires

The crossover in energy level statistics of a quasi-1-dimensional disordered wire as a function of its length L is used, in order to derive its averaged localization length, without magnetic field, in a magnetic field and for moderate spin orbit scattering strength. An analytical function of the magnetic field for the local level spacing is obtained, and found to be in excellent agreement with the magnetic field dependent activation energy, recently measured in low-mobility quasi-one-dimensional wires\cite{khavin}. This formula can be used to extract directly and accurately the localization length from magnetoresistance experiments. In general, the local level spacing is shown to be proportional to the excitation gap of a virtual particle, moving on a compact symmetric space.