A perturbation problem for transmission eigenvalues

2022 ◽  
Vol 9 (1) ◽  
Author(s):  
David M. Ambrose ◽  
Fioralba Cakoni ◽  
Shari Moskow
Keyword(s):  
Transmission Eigenvalues ◽  
Perturbation Problem

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

A Existence Theory for Positive Solutions to Superlinear Repulsive Singular Differential Equations with Impulse Effects

2010 ◽  
Vol 40-41 ◽  
pp. 149-155
Author(s):  
Zhang Xiao Ying ◽  
Guan Li Hong
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Singular Perturbation ◽  
Positive Solutions ◽  
Existence Theory ◽  
Singular Differential Equations ◽  
Perturbation Problem ◽  
Nonlinear Alternative

In this paper, we study positive solutions to the repulsive singular perturbation Hill equations with impulse effects. It is proved that such a perturbation problem has at least one positive impulsive periodic solution by a nonlinear alternative of Leray--Schauder.

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