Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems

Brouwer, Piet W.; Beenakker, C. W. J.

doi:10.1063/1.531667

Cited by 251 publications

(427 citation statements)

References 55 publications

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“…According to the diagrammatic rules of Ref. 29, the average is then done by connecting all dots by thin lines, summing over all possible ways of pairing up the dots. To leading order in 1/N ch , only planar diagrams contribute, i.e., the diagrams where the thin lines do not cross.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…To perform the average over S 0 , we use the diagrammatic technique of Ref. 29 and calculate G to leading order in 1/N ch . First, G is expanded in powers of S F S , G = S F S + S F S S N S F S + S F S S N S F S S N S F S + .…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…29. The results of that calculation is a self-consistent equation for G, analogous to the Dyson equation for the average Green function in a standard impurity average,…”

Section: B Chaotic Normal Layermentioning

confidence: 99%

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Magnetic exchange interaction induced by a Josephson current

2002

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We show that a Josephson current flowing through a ferromagnet-normal-metal-ferromagnet trilayer connected to two superconducting electrodes induces an equilibrium exchange interaction between the magnetic moments of the ferromagnetic layers. The sign and magnitude of the interaction can be controlled by the phase difference between the order parameters of the two superconductors. We present a general framework to calculate the Josephson current induced magnetic exchange interaction in terms of the scattering matrices of the different layers. The effect should be observable as the periodic switching of the relative orientation of the magnetic moments of the ferromagnetic layers in the ac Josephson effect.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Conclusion and Discussionmentioning

confidence: 99%

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Magnetic exchange interaction induced by a Josephson current

2002

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“…We assume now that the cavity is separated from the leads by tunnel barriers. Brouwer and Beenakker [101] were able to calculate the distribution function of transmission coefficients in this system for the symmetric case, when the number of channels supported by the left and the right lead are equal, N L = N R = N , and the transmission coefficientsT i in each channel i are same for the left and the right barriers. Assuming in addition NT i ≫ 1 for all channels, they found…”

Section: P(t)mentioning

confidence: 99%

Shot noise in mesoscopic conductors

2000

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Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron-electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and BoltzmannLangevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.

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“…However it can be shown that X c depends on the number of open channels, as X c ∼ √ N A general correlation function for QD can be derived in the case of a tunneling probability, Γ, smaller than one (all the above results assume Γ = 1). One finds [14], using the stub model [18],…”

Section: Ericson Fluctuationsmentioning

confidence: 99%

Chaotic behavior of the Compound Nucleus, open Quantum Dots and other nanostructures

Hussein

Ramos

2014

EPJ Web of Conferences

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Abstract. It is well established that physical systems exhibit both ordered and chaotic behavior. The chaotic behavior of nanostructures such as open quantum dots has been confirmed experimentally and discussed exhaustively theoretically. This is manifested through random fluctuations in the electronic conductance. What useful information can be extracted from this noise in the conductance? In this contribution we shall address this question. In particular, we will show that the average maxima density in the conductance is directly related to the correlation function whose characteristic width is a measure of the energy-or applied magnetic field-correlation length. The idea behind the above was originally discovered in the context of the atomic nucleus, a mesoscopic system. Our findings are directly applicable to graphene.

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Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems

Abstract: A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity ͑a ''quantum dot''͒ and through the interface between a normal metal and a superconductor.

Cited by 251 publications

References 55 publications

Magnetic exchange interaction induced by a Josephson current

Magnetic exchange interaction induced by a Josephson current

Shot noise in mesoscopic conductors

Chaotic behavior of the Compound Nucleus, open Quantum Dots and other nanostructures

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