Charge fluctuations and dephasing in coulomb coupled conductors

TL;DR

This paper demonstrates that charge relaxation resistances govern dephasing rates in Coulomb-coupled mesoscopic structures, linking charge fluctuations, RC-time, and voltage noise spectra through a self-consistent theoretical framework.

Contribution

It introduces a self-consistent method to calculate charge relaxation resistance and dephasing rates using a generalized Wigner-Smith delay-time matrix, applicable to various geometries.

Findings

Dephasing rate is determined by charge relaxation resistance.

Charge relaxation resistance influences voltage fluctuation spectrum.

Theoretical expressions connect resistance, capacitance, and dephasing in mesoscopic systems.

Abstract

It is shown that the dephasing rate in Coulomb coupled mesoscopic structures is determined by charge relaxation resistances. The charge relaxation resistance together with the capacitance determines the RC-time of the mesoscopic structure and at small frequencies determines the voltage fluctuation spectrum. Self-consistent expressions are presented which give the charge relaxation resistance and consequently the dephasing rate in terms of the diagonal and off-diagonal elements of a generalized Wigner-Smith delay-time matrix. Dephasing rates are discussed both for the equilibrium state and in the transport state in which charge fluctuations are generated by shot noise. A number of different geometries are discussed. This article is to appear in {\it Quantum Mesoscopic Phenomena and Mesoscopic Devices}, edited by I. O. Kulik and R. Ellialtioglu, (Kluwer, unpublished).