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

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 occurs via ballistic single-mode point contacts, but becomes Gaussian if the coupling occurs via tunneling contacts.