arXiv:cond-mat/0501208

Noise in mesoscopic physics

Thierry Martin

Published Jan 10, 2005• 20 citations

Abstract

This is a course on noise which covers some of the scattering theory for normal metals, Hanbury Brown and Twiss analogs for noise correlations with electrons, noise correlations in superconducting/normal metal junctions. Entanglement in such NS systems is described with a criterion for violating Bell inegalities. The last section is devoted to the perturbative derivation of noise in a particular one dimensional correlated electron system (Luttinger liquid): edge states in the fractional quantum Hall effect, where the comparison of the quasiparticle tunneling current and noise allow to identidy the fractional charge of quasiparticles.

DOI: 10.48550/arxiv.cond-mat/0501208

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arXiv:cond-mat/0501208

Noise in mesoscopic physics

Thierry Martin

Published Jan 10, 2005• 20 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/0501208

Related papers

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Without abstract; see full text.

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ω

near 0), and the high-frequency Josephson noise (

ω

near

ω_J=e^*V/\hbar

). Within perturbation theory, an algebraic singularity is present (to all orders) at the Josephson frequency

ω_J=e^*V/\hbar

, whose position depends on the charge

e^*

of the tunneling particles, either electrons or fractionally charged quasiparticles. We show in a non-perturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current.

{\mathit{e}}^{\mathrm{*}}

V/\ensuremath{\Elzxh}). Within perturbation theory, an algebraic singularity is present at the Josephson frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$=

{\mathit{e}}^{\mathrm{*}}

V/\ensuremath{\Elzxh}, whose position depends on the charge

{\mathit{e}}^{\mathrm{*}}

of the tunneling particles, either electrons or fractionally charged quasiparticles. These two types of tunneling are related by a strong-weak--coupling duality transformation. We show in a nonperturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current. \textcopyright{} 1996 The American Physical Society.