scholarly journals Weak localization in arrays of metallic quantum dots: Combined scattering matrix formalism and nonlinearσmodel

2006 ◽  
Vol 74 (24) ◽  
Author(s):  
Dmitri S. Golubev ◽  
Andrei D. Zaikin
Keyword(s):  
Quantum Dots ◽  
Weak Localization ◽  
Scattering Matrix ◽  
Matrix Formalism

Condensed matter physics

2018 ◽  
Author(s):  
Yan Fyodorov ◽  
Dmitry Savin
Keyword(s):  
Quantum Dots ◽  
Shot Noise ◽  
Matrix Theory ◽  
Quantum Wires ◽  
Condensed Matter ◽  
Weak Localization ◽  
Scattering Matrix ◽  
Condensed Matter Physics ◽  
Conductance Fluctuations ◽  
Non Gaussian

This article discusses some applications of concepts from random matrix theory (RMT) to condensed matter physics, with emphasis on phenomena, predicted or explained by RMT, that have actually been observed in experiments on quantum wires and quantum dots. These observations range from universal conductance fluctuations (UCF) to weak localization, non-Gaussian thermopower distributions, and sub-Poissonian shot noise. The article first considers the UCF phenomenon, nonlogarithmic eigenvalue repulsion, and sub-Poissonian shot noise in quantum wires before analysing level and wave function statistics, scattering matrix ensembles, conductance distribution, and thermopower distribution in quantum dots. It also examines the effects (not yet observed) of superconductors on the statistics of the Hamiltonian and scattering matrix.

Weak localization in ballistic quantum dots

1999 ◽  
Vol 60 (4) ◽  
pp. 2680-2690 ◽  
Author(s):  
R. Akis ◽  
D. K. Ferry ◽  
J. P. Bird ◽  
D. Vasileska
Keyword(s):  
Quantum Dots ◽  
Weak Localization

The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space

2007 ◽  
Author(s):  
Wen-I Liao ◽  
Tsung-Jen Teng ◽  
Shiang-Jung Wang
Keyword(s):  
Half Space ◽  
Transition Matrix ◽  
Plane Waves ◽  
Three Dimensional ◽  
Scattering Matrix ◽  
Elastic Half Space ◽  
Basis Functions ◽  
Matrix Formalism ◽  
T Matrix ◽  
Singular Wave

This paper develops the transition matrix formalism for scattering from an three-dimensional alluvium on an elastic half-space. Betti’s third identity is employed to establish orthogonality conditions among basis functions that are Lamb’s singular wave functions. The total displacements and associated tractions exterior and interior to the surface are expanded in a Rayleigh series. The boundary conditions are applied and the T-matrix is derived. A linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T-matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T-matrix is symmetric. Typical numerical results obtained by incident plane waves for verification are presented.

scholarly journals Exceptional points in composite structures consisting of two dielectric diffraction gratings with Lorentzian line shape

2021 ◽  
Vol 2015 (1) ◽  
pp. 012049
Author(s):  
Nikita Golovastikov ◽  
Dmitry Bykov ◽  
Leonid Doskolovich
Keyword(s):  
Composite Structure ◽  
Composite Structures ◽  
Diffraction Gratings ◽  
Scattering Matrix ◽  
Matrix Formalism ◽  
Exceptional Points ◽  
Lorentzian Line ◽  
Analytical Approximations ◽  
Lorentzian Profile ◽  
Analytical Expressions

Abstract Using scattering matrix formalism we derive analytical expressions for the eigenmodes of a composite structure consisting of two dielectric diffraction gratings with Lorentzian profile in reflection. Analyzing these expressions we prove formation of two distinct pairs of exceptional points, provide analytical approximations for their coordinates and by rigorous simulation demonstrate eigenmodes interchange as a result of encircling said exceptional points.

Electronic states in antidot lattices: Scattering-matrix formalism

1996 ◽  
Vol 53 (20) ◽  
pp. 13613-13623 ◽  
Author(s):  
Seiji Uryu ◽  
Tsuneya Ando
Keyword(s):  
Electronic States ◽  
Scattering Matrix ◽  
Matrix Formalism
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