Random magnetic flux problem in a quantum wire

Abstract

The random magnetic-flux problem on a lattice in a quasi-one-dimensional (wire) geometry is studied both analytically and numerically. The first two moments of the conductance are obtained analytically. Numerical simulations for the average and variance of the conductance agree with the theory. We find that the center of the band $\varepsilon =0\mathrm{}$ plays a special role. Away from $\varepsilon =0,$ transport properties are those of a disordered quantum wire in the standard unitary symmetry class. At the band center $\varepsilon =0,$ the dependence on the wire length of the conductance departs from the standard unitary symmetry class and is governed by a different universality class, the chiral unitary symmetry class. The most remarkable property of this universality class is the existence of an even-odd effect in the localized regime: Exponential decay of the average conductance for an even number of channels is replaced by algebraic decay for an odd number of channels.