  Systems with bond disorder are defined through lattice Hamiltonians that are
of pure nearest neighbour hopping type, i.e. do not contain on-site
contributions. Previous analyses based on the Dorokhov-Mello-Pereyra-Kumar
(DMPK) transfer matrix technique have shown that both spectral and transport
properties of quasi one-dimensional systems belonging to this category are
highly unusual. Notably, regimes with absence of exponential Anderson
localization are observed, the single particle density of states exhibits
singular structure in the vicinity of the band centre, and the manifestation of
these phenomena depends in an apparently topological manner on the even- or
oddness of the channel number. In this paper we re-consider the problem from
the complementary perspective of the non-linear sigma-model. Relying on the
standard analogy between one-dimensional statistical field theories and
zero-dimensional quantum mechanics, we will relate the problem to the behaviour
of a quantum point particle subject to an Aharonov-Bohm flux. We will re-derive
previous DMPK results, identify a new class of even/odd staggering phenomena
and trace back the anomalous behaviour of the bond disordered system to a
simple physical mechanism, viz. the flux periodicity of the quantum
Aharonov-Bohm system. We will also touch upon connections to the low energy
physics of other lattice systems, notably disordered chiral systems in 0 and 2
dimensions and antiferromagnetic spin chains.
