Quantum evolution with random phase scattering

Abstract

We consider the quantum evolution of a fermion-hole pair in a d-dimensional gas of non-interacting fermions in the presence of
random phase scattering. This system is mapped onto an effective Ising model, which enables us to show rigorously that the
probability of recombining the fermion and the hole decays exponentially with the distance of their initial spatial separation. 
In contrast, without
random phase scattering the recombination probability decays like a power law, which is reflected by an infinite
mean square displacement. The effective Ising model is studied within a saddle point approximation and yields a finite
mean square displacement that depends on the evolution time and on the spectral properties of the deterministic part of
the evolution operator.