Statistics of Wigner delay time in Anderson disordered systems

Xu, Fuming; Wang, Jian

doi:10.1103/physrevb.84.024205

Cited by 17 publications

(15 citation statements)

References 45 publications

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“…A long τ −2 tail in the distribution of the delay times in the localised regime was previously found analytically for 1d and quasi-1d systems [7,18]. In the numerical simulations for the 2d Anderson model both power-laws τ − 3 2 and τ −2 , which follow from our result, were identified [19]. The localisation length can be estimated as…”

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confidence: 82%

Scattering Approach to Anderson Localization

Ossipov

2018

Phys. Rev. Lett.

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We develop a novel approach to the Anderson localization problem in a d-dimensional disordered sample of dimension L×M^{d-1}. Attaching a perfect lead with the cross section M^{d-1} to one side of the sample, we derive evolution equations for the scattering matrix and the Wigner-Smith time delay matrix as a function of L. Using them one obtains the Fokker-Planck equation for the distribution of the proper delay times and the evolution equation for their density at weak disorder. The latter can be mapped onto a nonlinear partial differential equation of the Burgers type, for which a complete analytical solution for arbitrary L is constructed. Analyzing the solution for a cubic sample with M=L in the limit L→∞, we find that for d<2 the solution tends to the localized fixed point, while for d>2 to the metallic fixed point, and provide explicit results for the density of the delay times in these two limits.

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confidence: 82%

Scattering Approach to Anderson Localization

Ossipov

2018

Phys. Rev. Lett.

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“…The localised regime was studied by numerical simulations in Ref. [211]. (iii) A study of time delay at a critical point like the metal-insulator transition was performed in Ref.…”

Section: Higher Dimensionsmentioning

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 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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“…Their fundamental characters and statistical consequences to the transmission are widely studied 12,[14][15][16][17] . Recently, it is demonstrated that the NSs have evident contribution to the short-time transport of wave package [19][20][21][22] and the dynamics of fluctuations of localized waves 23 . More profoundly, the number of NS can increase dramatically as approaching the Anderson transition point, which strongly supports a modes-coupling induced quantum percolation scenario for the Anderson localization-delocalization transition 24,25 .…”

Section: Introductionmentioning

confidence: 99%

Characterization of short necklace states in the logarithmic transmission spectra of localized systems

Chen

Jiang

2013

J. Phys.: Condens. Matter

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High transmission plateaus exist widely in the logarithmic transmission spectra of localized systems. Their physical origins are short chains of coupled-localized-states embedded inside the localized system, which are dubbed as "short necklace states". In this work, we define the essential quantities and then, based on these quantities, we investigate the short necklace states' properties statistically and quantitatively. Two different approaches are utilized and the results from them agree with each other very well. In the first approach, the typical plateau-width and the typical order of short necklace states are obtained from the correlation function of logarithmic transmission. In the second approach, we investigate statistical distributions of the peak/plateau-width measured in logarithmic transmission spectra. A novel distribution is found, which can be exactly fitted by the summation of two Gaussian distributions. These two distributions are the results of sharp peaks of localized states and the high plateaus of short necklace states. The center of the second distribution also tells us the typical plateau-width of short necklace states. With increasing the system length, the scaling property of typical plateau-width is very special since it almost does not decrease. The methods and the quantities defined in this work can be widely used on Anderson localization studies.

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Statistics of Wigner delay time in Anderson disordered systems

Cited by 17 publications

References 45 publications

Scattering Approach to Anderson Localization

Scattering Approach to Anderson Localization

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

Characterization of short necklace states in the logarithmic transmission spectra of localized systems

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