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

TL;DR

This paper models a 1D quantum resistor with phase disorder using fake channels, linking it to the Lloyd model, and shows it destroys interference effects without causing decoherence.

Contribution

It introduces a novel phase-randomizing reservoir that preserves coherence but suppresses interference, connecting phase disorder to the Lloyd model.

Findings

The transport equation matches the Lloyd model.

Phase disorder destroys interference effects.

The reservoir does not induce decoherence.

Abstract

We introduce phase disorder in a 1D quantum resistor through the formal device of `fake channels' distributed uniformly over its length such that the out-coupled wave amplitude is re-injected back into the system, but with a phase which is random. The associated scattering problem is treated via invariant imbedding 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 back scattering.