Random-phase reservoir and a quantum resistor: the Lloyd model

Abstract

We introduce phase disorder in a one-dimensional quantum resistor through the formal device of 'fake channels' distributed uniformly over its length such that the outcoupled wave amplitude is reinjected back into the system, but with a phase which is random. The associated scattering problem is treated via invariant embedding in the continuum limit, and the resulting transport equation is found to correspond exactly to the Lloyd model. The latter has been a subject of much interest in recent years. This conversion of the random phase into the random Cauchy potential is a notable feature of our work. It is further argued that our phase-randomizing reservoir, as distinct from the well-known phase-breaking reservoirs, induces no decoherence, but essentially destroys all interference effects other than the coherent backscattering.