  The dynamics of interacting quantum systems in the presence of disorder is
studied and an exact representation for disorder-averaged quantities via Ito
stochastic calculus is obtained. The stochastic integral representation affords
many advantages, including amenability to analytic approximation, applicability
to interacting systems, and compatibility with existing tensor network methods.
The integral may be expanded to produce a series of approximations, the first
of which already includes all diffusive corrections and, further, is manifestly
completely positive. The addition of fluctuations leads to a convergent series
of systematic corrections. As examples, expressions for the density of states,
spectral form factor, and out-of-time-order correlators for the Anderson model
are obtained.
