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Barabanenkov, Yu. N.; Barabanenkov, M. Yu.

doi:10.1088/0959-7174/7/4/007

Cited by 4 publications

(8 citation statements)

References 23 publications

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“…33 Instead the proof follows the derivation of a similar Ward identity in the case of wave propagation in disordered media. 36 Starting from the equations of motion of the single particle Green's function before impurity averaging…”

Section: Renormalized Perturbation Theory Of Quantum Transport In Dismentioning

confidence: 99%

Self-Consistent Theory of Anderson Localization: General Formalism and Applications

Wölfle¹,

Vollhardt²

2010

50 Years of Anderson Localization

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The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered solids, the regimes of weak and strong localization are discussed. Then the scaling theory of the Anderson localization transition is reviewed. The renormalization group theory is introduced and results and consequences are presented. It is shown how scale-dependent terms in the renormalized perturbation theory of the inverse diffusion coefficient lead in a natural way to a self-consistent equation for the diffusion coefficient. The latter accounts quantitatively for the static and dynamic transport properties except for a region near the critical point. Several recent applications and extensions of the self-consistent theory, in particular for classical waves, are discussed.Here c(r) is the wave velocity at position r in an inhomogeneous medium, assumed to be a randomly fluctuating quantity. The main difference between the Schrödinger

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Section: Renormalized Perturbation Theory Of Quantum Transport In Dismentioning

confidence: 99%

Self-Consistent Theory of Anderson Localization: General Formalism and Applications

Wölfle¹,

Vollhardt²

2010

50 Years of Anderson Localization

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“…Here T ¼ ð0Þ ðr, r 0 Þ is the electric field T-scattering tensor (dyadic) operator of a single particle satisfying the Lippmann-Schwinger (LS) integral equation with a scattering potential VðrÞ, [28] G ¼ ð0Þ ðrÞ is the electric field dyadic Green function in the background given by…”

Section: Em Excitation Transfer Along Finite Chain Of Particlesmentioning

confidence: 99%

“…The current excited in the first irradiated particle is dependent on currents in other particles because of wave coupling between them. A system of equations for self‐consistent currents excited inside particles by an incident EM wave field has the form [ 25,28 ]

{boldJ}^{(j)} (r) = {boldJ}_{(1)}^{(j)} (r) + \int d {boldr}^{'} \int boldr ″ {\overset{=}{T}}^{(0)} (r - {boldr}_{j}, {boldr}^{'} - {boldr}_{j}) {\overset{=}{G}}^{(0)} ({boldr}^{'} - boldr ″) \sum_{j \neq j^{'} = 1}^{N} {boldJ}^{(j^{'})} (boldr ″)

{boldJ}_{(1)}^{(j)} (r) = \int d {boldr}^{'} {\overset{=}{T}}^{(0)} (r - {boldr}_{j}, {boldr}^{'} - {boldr}_{j}) {boldE}^{(0)} ({boldr}^{'})

Here

{\overset{=}{T}}^{(0)} (r, {boldr}^{'})

is the electric field T‐scattering tensor (dyadic) operator of a single particle satisfying the Lippmann–Schwinger (LS) integral equation with a scattering potential

V (r)

, [ 28 ]

...

…”

Section: Em Excitation Transfer Along Finite Chain Of Particlesmentioning

confidence: 99%

“…In the Equation (3), the total electric conductive and polarization current density JðrÞ excited inside N particles of a chain reads [25,28] JðrÞ ¼ VðrÞEðrÞ ¼ X N j¼1 J ð jÞ ðrÞ,…”

Section: Em Excitation Transfer Along Finite Chain Of Particlesmentioning

confidence: 99%

“…In the Equation (3), the total electric conductive and polarization current density

J (r)

excited inside N particles of a chain reads [ 25,28 ]

J (r) = V (r) E (r) = \sum_{j = 1}^{N} {boldJ}^{(j)} (r), V (r) = - \frac{ω^{2}}{c^{2}} [\overset{falseˆ}{ε} (r) - ε_{0}]

where

{boldJ}^{(j)} (r)

are self‐consistent currents excited inside coupled particles. The quantity

V (r)

stands in the Equation (5) for an effective scattering potential of particles; the inhomogeneous complex permittivity

\overset{falseˆ}{ε} (r)

is equal to a complex value ε inside a dielectric or a metallic particle [ 29 ] and is equal to

ε_{0}

outside the particles.…”

Section: Em Excitation Transfer Along Finite Chain Of Particlesmentioning

confidence: 99%

See 2 more Smart Citations

Comparative Study of Light Guiding by Freestanding Linear Chains of Spherical Au and Si Nanoparticles

Barabanenkov

Italyantsev

Sapegin

2020

Physica Status Solidi (b)

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Electromagnetic energy guiding by free‐standing straight finite chains of Au and Si spherical nanoparticles is comparatively studied on the basis of a system of integral equations for self‐consistent currents excited inside particles. Self‐consistent currents are given in terms of an electric field T‐scattering tensor (dyadic) operator of a single particle of any shape. Simplifying the T‐scattering operator, the equations system is resolved analytically in the nearest‐neighbor coupling approximation. Interactions beyond the nearest neighbors are accounted for by the perturbative theory. It is shown that electromagnetic excitation propagates along a chain of coupled particles without radiation losses in the form of a dark mode. The resonant conditions for the coupling parameter yield the frequency of the dark mode and the corresponding radius of the particles. As a result, unlike Au chains, no long‐range electromagnetic energy transfer was revealed along the Si chains. Physically, in both cases of Au and Si spheres, the resonant frequencies fall within the bands of the corresponding electric dipole Mie resonances. However, the positive value of the real part of the Si refraction index at the resonant frequency causes exponential excitation currents decreasing with the particle number.

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Introduction to radiative transfer of seismic waves

Margerin

2005

Geophysical Monograph Series

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Untitled

Cited by 4 publications

References 23 publications

Self-Consistent Theory of Anderson Localization: General Formalism and Applications

Self-Consistent Theory of Anderson Localization: General Formalism and Applications

Comparative Study of Light Guiding by Freestanding Linear Chains of Spherical Au and Si Nanoparticles

Introduction to radiative transfer of seismic waves

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