Magnetolocalization in disordered quantum wires

Magnetic-field-dependent localization in a disordered quantum wire is considered nonperturbatively. An increase of an averaged localization length with the magnetic field is found, saturating at twice its value without magnetic field. The crossover behavior is shown to be governed both in the weak- and strong-localization regimes by the magnetic diffusion length $L_B.$ This function is derived analytically in closed form as a function of the ratio of the mean free path l, the wire thickness W, and the magnetic length $l_B$ for a two-dimensional wire with specular boundary conditions, as well as for a parabolic wire. The applicability of the analytical formulas to resistance measurements in the strong localization regime is discussed. A comparison with recent experimental results is included.