On the distribution of transmission eigenvalues in disordered wires

Abstract

We solve the Dorokhov-Mello-Pereyra-Kumar equation which describes the evolution of an ensamble of disordered wires of increasing length in the three cases $\beta =1,2,4$. The solution is obtained by mapping the problem in that of a suitable Calogero-Sutherland model. In the $\beta =2$ case our solution is in complete agreement with that recently found by Beenakker and Rejaei.

arXiv comment4 pages, Revtex, few comments added at the end of the paper

References in corpus (1)

• Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory

Cited by in corpus (52)

• Random-Matrix Theory of Quantum Transport
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Random matrix theory and symmetric spaces
• Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
• Quantum Transport in Disordered Wires: Equivalence of One-Dimensional Sigma Model and Dorokhov-Mello-Pereyra-Kumar Equation
• Random matrices beyond the Cartan classification
• DIFFUSION IN ONE DIMENSIONAL RANDOM MEDIUM AND HYPERBOLIC BROWNIAN MOTION
• Inequivalent Quantizations of the Rational Calogero Model
• Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
• Multicomponent Calogero Model of $B_N$-Type Confined in Harmonic Potential
• From Wires to Cosmology
• Generalized Fokker-Planck Equation For Multichannel Disordered Quantum Conductors
• Integrable $1/r^2$ Spin Chain with Reflecting End
• Nonuniversality in quantum wires with off-diagonal disorder: a geometric point of view
• Conductance distribution in strongly disordered mesoscopic systems in three dimensions
• Conductance distribution in quasi-one-dimensional disordered quantum wires
• Exactly solvable D_N-type quantum spin models with long-range interaction
• Fluctuations and correlations of transmission eigenchannels in diffusive media
• Localization-delocalization transition in the quasi-one-dimensional ladder chain with correlated disorder
• Quantization and Conformal Properties of a Generalized Calogero Model
• The Lyapunov Spectrum of a Continuous Product of Random Matrices
• Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systems
• The $W_{1+\infty }$ effective theory of the Calogero- Sutherland model and Luttinger systems.
• A proposed signature of Anderson localization and correlation-induced delocalization in an N-leg optical lattice
• Spectral properties of supersymmetric Polychronakos spin chain associated with A_{N-1} root system
• The spin Sutherland model of D_N type and its associated spin chain
• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• Distribution of conductance for Anderson Insulators: A theory with a single parameter
• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• From the Anderson model on a strip to the DMPK equation and random matrix theory
• Critical Properties of the Calogero-Sutherland Model with Boundaries
• DMPK Equation for the Edge Transport of Quantum Spin Hall Insulator
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Superconformal Quantum Mechanics from M2-branes
• Random ballistic growth and diffusion in symmetric spaces
• Fokker-Planck description of the transfer matrix limiting distribution in the scattering approach to quantum transport
• Calogero-Sutherland techniques in the physics of disorderd wires
• Symmetric space description of carbon nanotubes
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
• Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• A novel class of translationally invariant spin chains with long-range interactions
• Statistical analysis of the transmission based on the DMPK equation: An application to Pb nano-contacts
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Generalized para-Bose states
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• Disordered quantum wires: microscopic origins of the DMPK theory and Ohm's law
• Path Integral Approach to the Scattering Theory of Quantum Transport
• A Generalization of Random Matrix Ensemble I: General Theory
• Waiting time fluctuations in quasi-one-dimensional disordered conductors