Diagrammatic theory of random scattering matrices for normal-metal–superconducting mesoscopic junctions

Argaman, Nathan; Zee, A.

doi:10.1103/physrevb.54.7406

Cited by 17 publications

(20 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here we collect a few results we will need repeatedly. For more extensive treatments we refer to Creutz (1978), Samuel (1980), Mello (1990), Argaman and Zee (1996), and Brouwer and Beenakker (1996a). Let U be an N × N matrix which is uniformly distributed over the group U(N ) of N × N unitary matrices.…”

Section: Appendix B: Integration Over the Unitary Groupmentioning

confidence: 99%

Random-matrix theory of quantum transport

1997

View full text Add to dashboard Cite

This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined region with a chaotic classical dynamics, which is coupled to two electron reservoirs via point contacts. The disordered wire also connects to two reservoirs, either directly, or via a point contact or tunnel barrier. One of the two reservoirs may be in the superconducting state, in which case conduction involves Andreev reflection at the interface with the superconductor. In the case of the quantum dot, the distribution of the scattering matrix is Dyson's circular ensemble for ballistic point contacts, or the Poisson kernel for point contacts containing a tunnel barrier. In the case of the disordered wire, the distribution of the scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation. The equivalence is discussed with the non-linear σ model, which is a supersymmetric field theory of localization. The distribution of scattering matrices is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction. To be published in Rev. Mod. Phys. (1997).

show abstract

Section: Appendix B: Integration Over the Unitary Groupmentioning

confidence: 99%

Random-matrix theory of quantum transport

1997

View full text Add to dashboard Cite

show abstract

“…To apply Eq. (5), we redraw this periodic circuit as a (counter-clockwise) oriented circle Following t'Hooft [10,31,32], it turns out that keeping track of the factors of N associated to each diagram is greatly facilitated by using double line or ribbon notation, in which all bulk lines must run in pairs which do not separate. It is clear that this is possible when the relative permutation τ −1 σ = 1 is trivial, as this implies that the solid (τ ) and dashed Drawing the diagrams using these rules allows us to interpret each diagram in O p as an oriented surface with boundary given by the circle.…”

Section: A Diagrammatic Averaging Over Unitary Groupmentioning

confidence: 99%

Many-body systems with random spatially local interactions

Morampudi

Laumann

2019

Phys. Rev. B

View full text Add to dashboard Cite

We extend random matrix theory to consider randomly interacting spin systems with spatial locality. We develop several methods by which arbitrary correlators may be systematically evaluated in a limit where the local Hilbert space dimension N is large. First, the correlators are given by sums over stacked planar diagrams which are completely determined by the spectra of the individual interactions and a dependency graph encoding the locality in the system. We then introduce heap freeness as a generalization of free independence, leading to a second practical method to evaluate the correlators. Finally, we generalize the cumulant expansion to a sum over dependency partitions, providing the third and most succinct of our methods. Our results provide tools to study dynamics and correlations within extended quantum many-body systems which conserve energy. We further apply the formalism to show that quantum satisfiability at large-N is determined by the evaluation of the independence polynomial on a wide class of graphs. arXiv:1808.08674v1 [cond-mat.stat-mech] 27 Aug 2018 1 The Hilbert space has dimension N n . The generalization to varying qudit dimensions Nq is straightforward, so we use Nq = N throughout to simplify the presentation. 2 We use superscripts i, j to label interactions and Greek subscripts α, β, µ, ν to label states in Hilbert space. 3 With suitable treatment of e −βH and/or e −iHt , such trace moments include finite temperature and/or dynamical correlators.

show abstract

“…where the expectation is over the channel matrix G. To make progress, one could expand the quantity inside the expectation in (39) in terms of products of the matrices U and U † and then average the resulting products over the unitary group. These averages are however quite complicated and in most cases can only be treated in an asymptotic fashion 25,26 . Instead here we employ a different approach first introduced by Balantekin 27 .…”

Section: A Character Expansions In Communicationsmentioning

confidence: 99%

Modern telecommunications: a playground for physicists?

Moustakas¹

2017

Stochastic Processes and Random Matrices

View full text Add to dashboard Cite

Data traffic in wireless networks has been increasing exponentially for a long time and is expected to continue this trend. The emerging data-hungry applications, such as video-on-demand and cloud computing, as well as the exploding number of smart user devices demand the introduction of disruptive technologies. An analogous situation appears in the case of wireline (mostly fiber-optical) traffic, where the currently deployed infrastructure is expected to soon reach its limits, leading to the so-called capacity crunch. The aim of this chapter is to introduce the physics and mathematics community to a number of relevant problems in communications research and the types of solutions that have been used to tackle them. In the process, interested readers may be able to further acquaint themselves with research in engineering bibliography cited herein.

show abstract

Diagrammatic theory of random scattering matrices for normal-metal–superconducting mesoscopic junctions

Cited by 17 publications

References 30 publications

Random-matrix theory of quantum transport

Random-matrix theory of quantum transport

Many-body systems with random spatially local interactions

Modern telecommunications: a playground for physicists?

Contact Info

Product

Resources

About