Voltage-probe and imaginary potential models for dephasing in a chaotic quantum dot

TL;DR

This paper compares two models of dephasing in chaotic quantum dots, clarifies their equivalence conditions, and analyzes how dephasing affects conductance distribution, explaining discrepancies in previous results.

Contribution

It identifies the conditions under which voltage-probe and imaginary potential models are equivalent and analyzes the conductance distribution under different coupling regimes.

Findings

Models are equivalent in a specific limit.

Conductance distribution remains non-Gaussian under strong dephasing with ballistic contacts.

Distribution becomes Gaussian with tunneling contacts.

Abstract

We compare two widely used models for dephasing in a chaotic quantum dot: The introduction of a fictitious voltage probe into the scattering matrix and the addition of an imaginary potential to the Hamiltonian. We identify the limit in which the two models are equivalent and compute the distribution of the conductance in that limit. Our analysis explains why previous treatments of dephasing gave different results. The distribution remains non-Gaussian for strong dephasing if the coupling of the quantum dot to the electron reservoirs is via ballistic single-mode point contacts, but becomes Gaussian if the coupling is via tunneling contacts.