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arXiv:cond-mat/9911188

Charge fluctuations and dephasing in coulomb coupled conductors

Μ. Büttiker

Published Nov 12, 1999• 0 citations
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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in {\it Quantum Mesoscopic Phenomena and Mesoscopic Devices}, edited by I. O. Kulik and R. Ellialtioglu, (Kluwer, unpublished).

DOI
10.48550/arxiv.cond-mat/9911188

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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in {\it Quantum Mesoscopic Phenomena and Mesoscopic Devices}, edited by I. O. Kulik and R. Ellialtioglu, (Kluwer, unpublished).
The charge fluctuations of two nearby mesoscopic conductors coupled only via the long range Coulomb force are discussed and used to find the dephasing rate which one conductor exerts on the other. The discussion is based on a formulation of the scattering approach for charge densities and the density response to a fluctuating potential. Coupling to the Poisson equation results in an electrically self-consistent description of charge fluctuations. At equilibrium the low-frequency noise power can be expressed with the help of a charge relaxation resistance (which together with the capacitance determines the RC-time of the structure). In the presence of transport the low frequency charge noise power is determined by a resistance which reflects the presence of shot noise. We use these results to derive expressions for the dephasing rates of Coulomb coupled conductors and to find a self-consistent expression for the measurement time.
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