Dynamics of localization in a waveguide

Beenakker, C. W. J.

doi:10.1007/978-94-010-0738-2_34

Cited by 9 publications

(15 citation statements)

References 36 publications

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“…(A.3) 28 The relation between the dynamical problem (real ω) and the static problem with absorption (complex ω) was used in another context in Refs. [116,168,14,17,84]. leading to (187).…”

Section: T T a Tmentioning

confidence: 99%

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Wigner time delay and related concepts: Application to transport in coherent conductors

Texier

2016

Physica E: Low-dimensional Systems and Nanostructures

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The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems ; the case of disorder in 1D with a chiral symmetry is discussed and the relation with exponential functionals of the Brownian motion underlined. Another approach for the analysis of time delay statistics is the random matrix approach, from which we review few results. As a pratical illustration, we briefly outline a theory of non-linear transport and AC transport developed by Büttiker and coworkers, where the concept of Wigner-Smith time delay matrix is a central piece allowing to describe screening properties in out-of-equilibrium coherent conductors.The published version has been updated.

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Section: T T a Tmentioning

confidence: 99%

“…The most fundamental aspects of time delays have been reviewed by Carvalho and Nussenzveig [67]. Some other articles have reviewed more specific aspects : Beenakker has considered the case of wave guides in the localised regime [14]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Wigner time delay and related concepts: Application to transport in coherent conductors

Texier

2016

Physica E: Low-dimensional Systems and Nanostructures

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“…The set {τ n } of eigenvalues of the Wigner-Smith matrix Q, the so-called proper time delays, provide a set of characteristic times of the scattering problem. Their joint distribution was obtained by Brouwer and Beenakker (assuming a semi-infinite disordered region) [6,7], who showed that Q −1 belongs to the Laguerre ensemble : in appropriate units, the joint probability density for the rates λ i = 1/τ i is…”

Section: Wigner-smith Matrix and Wigner Time Delaymentioning

confidence: 99%

Distribution of spectral linear statistics on random matrices beyond the large deviation function—Wigner time delay in multichannel disordered wires

Grabsch¹,

Texier²

2016

J. Phys. A: Math. Theor.

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An invariant ensemble of N × N random matrices can be characterised by a joint distribution for eigenvalues P (λ 1 , · · · , λ N ). The study of the distribution of linear statistics, i.e. of quantities of the formis a given function, appears in many physical problems. In the N → ∞ limit, L scales as L ∼ N η , where the scaling exponent η depends on the ensemble and the function f (x). Its distribution can be written under the form Pis the Dyson index. The Coulomb gas technique naturally provides the large deviation function Φ(s), which can be efficiently obtained thanks to a "thermodynamic identity" introduced earlier. We conjecture the pre-exponential function A N,β (s). We check our conjecture on several well controlled cases within the Laguerre and the Jacobi ensembles. Then we apply our main result to a situation where the large deviation function has no minimum (and L has infinite moments) : this arises in the statistical analysis of the Wigner time delay for semi-infinite multichannel disordered wires (Laguerre ensemble). The statistical analysis of the Wigner time delay then crucially depends on the pre-exponential function A N,β (s), which ensures the decay of the distribution for large argument.

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“…Therefore, with the knowledge of � L (n; α) and the delay-time probability density for canonical disordered systems, p s (τ R ) , we write the probability density p α (τ R ) for Lévy disordered systems as The probability density p s (τ R ) in its full generality remains, however, an open problem. For semi-infinite disordered systems, assuming no transmission, the limit ( L → ∞ ) delay-time distribution p ∞ (τ R ) is given by 11,[41][42][43][44][45] :…”

Section: Resultsmentioning

confidence: 99%

“…where τ 0 is the absorption time which is assumed very large [45][46][47] . A key point is that this relationship establishes that fluctuations of R determine the statistics of τ R .…”

Section: Resultsmentioning

confidence: 99%

Delay time of waves performing Lévy walks in 1D random media

Fernández-Marín

Méndez-Bermúdez

et al. 2020

Sci Rep

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The time that waves spend inside 1D random media with the possibility of performing Lévy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered systems via the delay time. We show that a wide class of disorder—Lévy disorder—leads to strong random fluctuations of the delay time; nevertheless, some statistical properties such as the tail of the distribution and the average of the delay time are insensitive to Lévy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.

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Dynamics of localization in a waveguide

Cited by 9 publications

References 36 publications

Wigner time delay and related concepts: Application to transport in coherent conductors

Wigner time delay and related concepts: Application to transport in coherent conductors

Distribution of spectral linear statistics on random matrices beyond the large deviation function—Wigner time delay in multichannel disordered wires

Delay time of waves performing Lévy walks in 1D random media

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