# Random-matrix theory of quantum transport

@article{Beenakker1997RandommatrixTO, title={Random-matrix theory of quantum transport}, author={C. W. J. Beenakker}, journal={Reviews of Modern Physics}, year={1997}, volume={69}, pages={731-808} }

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 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…

## Figures and Tables from this paper

figure 1 figure 10 figure 11 figure 12 figure 13 figure 14 figure 15 figure 16 figure 17 figure 18 figure 19 figure 2 figure 20 figure 21 figure 22 figure 23 figure 24 figure 25 figure 26 figure 27 figure 28 figure 29 figure 3 figure 30 figure 31 figure 32 figure 33 figure 34 figure 35 figure 36 figure 37 figure 38 figure 39 figure 40 figure 41 figure 42 figure 43 figure 44 figure 45 figure 46 figure 47 figure 48 figure 49 figure 5 figure 50 figure 51 figure 52 figure 6 figure 7 figure 8 figure 9 table I table II table III table IV

## 1,623 Citations

### Scattering matrix ensemble for time-dependent transport through a chaotic quantum dot

- Physics
- 2002

Random matrix theory can be used to describe the transport properties of a chaotic quantum dot coupled to leads. In such a description, two approaches have been taken in the literature, considering…

### Scaling theory for anomalous semiclassical quantum transport

- Physics
- 2015

Quantum transport through devices coupled to electron reservoirs can be described in terms of the full counting statistics (FCS) of charge transfer. Transport observables, such as conductance and…

### Interference phenomena in electronic transport through chaotic cavities: An information-theoretic approach

- Physics
- 1998

We develop a statistical theory describing quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a…

### Counting statistics and an anomalous metallic phase in a network of quantum dots

- Physics
- 2014

We report results relating to the transport properties of a quantum network formed by connecting chaotic quantum dots to each other and to electron reservoirs via barriers of arbitrary…

### Random Matrix Theory and Quantum Transport

- Physics
- 2013

Random matrix theory begins with the observation that, given some distribution of matrix elements, the correlations of eigenvalues and vectors of these matrices are independent of many of the details…

### Disordered Quantum Wires: Microscopic Origins of the DMPK Theory and Ohm’s Law

- Physics
- 2012

We study the electronic transport properties of the Anderson model on a strip, modeling a quasi one-dimensional disordered quantum wire. In the literature, the standard description of such wires is…

### Influence of normal metal-superconductor interface on the statistics of conductance and shot noise power in a non-ideal chaotic quantum dot

- Physics
- 2021

In this paper, we apply Andreev’s reflection to study the sub-gap coherent transport properties for a quantum dot attached to normal metal and superconductor reservoirs via non-ideal leads. We use…

### Entanglement Structure of Current-Driven Diffusive Fermion Systems

- PhysicsPhysical Review X
- 2019

When an extended system is coupled at its opposite boundaries to two reservoirs at different temperatures or chemical potentials, it cannot achieve a global thermal equilibrium and is instead driven…

### Spin Related Effects in Transport Properties of "Open" Quantum Dots

- Physics
- 2005

We study the interaction corrections to the transport coefficients in open quantum dots (i.e., dots connected to leads of large conductance $G⪢{e}^{2}∕\ensuremath{\pi}\ensuremath{\hbar}$), via a…

## References

SHOWING 1-10 OF 63 REFERENCES

### Introduction to mesoscopic physics

- Physics
- 1997

Preface Preface to the second edition List of symbols 1. Introduction and a brief review of experimental systems 2. Quantum transport, Anderson Localization 3. Dephasing by coupling with the…

### Quantum transport in semiconductor submicron structures

- Physics
- 1996

Preface. 1. Introduction. Quantum Transport in Nano- Structured Semiconductors: A Survey B. Kramer. 2. The Quantum Hall Effect. Quantum Hall Effect Experiments R.J. Haug. Incompressibilis Ergo Sum:…

### Quantum signatures of chaos

- Physics
- 1991

The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2,…

### Chaos in classical and quantum mechanics

- Physics
- 1990

Contents: Introduction.- The Mechanics of Lagrange.- The Mechanics of Hamilton and Jacobi.- Integrable Systems.- The Three-Body Problem: Moon-Earth-Sun.- Three Methods of Section.- Periodic Orbits.-…

### Products of random matrices in statistical physics

- Physics
- 1993

I Background.- 1. Why Study Random Matrices?.- 1.1 Statistics of the Eigenvalues of Random Matrices.- 1.1.1 Nuclear Physics.- 1.1.2 Stability of Large Ecosystems.- 1.1.3 Disordered Harmonic Solids.-…

### Supersymmetry in Disorder and Chaos

- Physics
- 1996

1. Introduction 2. Supermathematics 3. Diffusion modes 4. Nonlinear supermatrix sigma- model 5. Perturbation theory and renormalization group 6. Energy level statistics 7. Quantum size effects in…

### Quantum field theory

- Physics
- 1956

This book is a modern pedagogic introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian…

### Electronic transport in mesoscopic systems

- Physics
- 1995

1. Preliminary concepts 2. Conductance from transmission 3. Transmission function, S-matrix and Green's functions 4. Quantum Hall effect 5. Localisation and fluctuations 6. Double-barrier tunnelling…