scholarly journals The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions

2021 ◽  
pp. 109146
Author(s):  
Hoai-Minh Nguyen ◽  
Quoc-Hung Nguyen
Keyword(s):  
Transmission Eigenvalues ◽  
Weyl Law

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 A NEW UNIVERSALITY CLASS DESCRIBING THE INSULATING REGIME OF DISORDERED WIRES WITH STRONG SPIN-ORBIT SCATTERING

1996 ◽  
Vol 10 (15) ◽  
pp. 681-688 ◽  
Author(s):  
M. CASELLE
Keyword(s):  
Magnetic Field ◽  
Universality Class ◽  
Spin Orbit ◽  
Transmission Eigenvalues ◽  
Sutherland Model ◽  
Strong Spin

We discuss the distribution of transmission eigenvalues in the strongly localized regime in the presence of both a magnetic field and spin-orbit scattering. We show that, under suitable conditions, this distribution can be described by a new universality class labelled not only by the index β but also by a new index η. This result is obtained by mapping the problem into that of a suitable Calogero-Sutherland model.

Modified transmission eigenvalues in inverse scattering theory

2017 ◽  
Vol 33 (12) ◽  
pp. 125002 ◽  
Author(s):  
S Cogar ◽  
D Colton ◽  
S Meng ◽  
P Monk
Keyword(s):  
Inverse Scattering ◽  
Scattering Theory ◽  
Transmission Eigenvalues ◽  
Inverse Scattering Theory

scholarly journals Complex Transmission Eigenvalues in One Dimension

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yalin Zhang ◽  
Yanling Wang ◽  
Guoliang Shi ◽  
Shizhong Liao
Keyword(s):  
Index Of Refraction ◽  
One Dimension ◽  
Transmission Eigenvalues ◽  
One Dimensional ◽  
Complex Eigenvalues ◽  
Complex Transmission

We consider all of the transmission eigenvalues for one-dimensional media. We give some conditions under which complex eigenvalues exist. In the case when the index of refraction is constant, it is shown that all the transmission eigenvalues are real if and only if the index of refraction is an odd number or reciprocal of an odd number.

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