Universal Conductance Fluctuations, Random Matrix Theory and the Scaling Theory of Localization

1988 ◽  
pp. 315-322 ◽  
Author(s):  
A. D. Stone ◽  
K. A. Muttalib ◽  
J.-L. Pichard
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Scaling Theory ◽  
Universal Conductance Fluctuations ◽  
Conductance Fluctuations ◽  
Universal Conductance

scholarly journals EXACTLY SOLVABLE SCALING THEORY OF CONDUCTION IN DISORDERED WIRES

1994 ◽  
Vol 08 (08n09) ◽  
pp. 469-478 ◽  
Author(s):  
C. W. J. Beenakker
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Scaling Theory ◽  
Transmission Eigenvalues ◽  
Conductance Fluctuations ◽  
Recent Developments ◽  
Log Normal ◽  
Universal Conductance ◽  
Conductance Distribution

Recent developments in the scaling theory of phase-coherent conduction through a disordered wire are reviewed. The Dorokhov–Mello–Pereyra–Kumar equation for the distribution of transmission eigenvalues has been solved exactly, in the absence of time-reversal symmetry. Comparison with the previous prediction of random-matrix theory shows that this prediction was highly accurate but not exact: the repulsion of the smallest eigenvalues was overestimated by a factor of two. This factor of two resolves several disturbing discrepancies between random-matrix theory and microscopic calculations, notably in the magnitude of the universal conductance fluctuations in the metallic regime, and in the width of the log-normal conductance distribution in the insulating regime.

scholarly journals Random matrix theory for the analysis of the performance of an analog computer: a scaling theory

2004 ◽  
Vol 323 (3-4) ◽  
pp. 204-209 ◽  
Author(s):  
Asa Ben-Hur ◽  
Joshua Feinberg ◽  
Shmuel Fishman ◽  
Hava T. Siegelmann
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Analog Computer ◽  
Scaling Theory

SSA, Random Matrix Theory, and Noise-Reduced Correlations

2016 ◽  
Author(s):  
Jan W Dash ◽  
Xipei Yang ◽  
Mario Bondioli ◽  
Harvey J. Stein
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory

History—an overview

2018 ◽  
Author(s):  
Oriol Bohigas ◽  
Hans A. Weidenmüller
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Rapid Development ◽  
The Past ◽  
History Of ◽  
And Mathematics

An overview of the history of random matrix theory (RMT) is provided in this chapter. Starting from its inception, the authors sketch the history of RMT until about 1990, focusing their attention on the first four decades of RMT. Later developments are partially covered. In the past 20 years RMT has experienced rapid development and has expanded into a number of areas of physics and mathematics.

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