Macroscopic Approach to Correlations in the Electronic Transmission and Reflection from Disordered Conductors

Abstract

Recently, a macroscopic theory of TV-channel disordered conductors treated the evolution (with the length L) of the probability distribution of the transfer matrix for the full conductor and allowed a theoretical description of the universal conductance fluctuations. Those results are used here to calculate the correlation function between transmission as well as reflection coefficients: In the case L^>W (width of the sample), the former essentially coincides with the one obtained from microscopic perturbative calculations. The latter, on the other hand, is a prediction of the present model. PACS numbers: 72.15.Cz, 02.50.+S Much effort has recently been devoted to the understanding of the intensity fluctuations of waves multiply scattered from disordered media. In quantum electronic transport, multiple scattering leads to anomalously large (the so-called "universal") conductance fluctuations 1 " 9 (UCF): The variance of the dimensionless conductance g (in units of e 2 /h) is of order unity and, to a large extent, does not depend on the size of the sample nor on the degree of disorder. Multiple scattering is equally important in light propagation through a random medium, where it is responsible for various effects in intensity statistics (the speckle pattern). 6 ' 10 " 19 It turns out, 6 ' 10 for instance, that the variance of the transmission coefficient Tb=H a T a b (towards the right, say, when a single mode b is excited on the left) is of the order //TVL, which is again much larger than what a naive statistical consideration would suggest. Here / is the (elastic) mean free path, L the length of the system, and TV the total number of channels.Another interesting fact was pointed out is Refs. 3 and 5: The naive assumption that (in the TV»1 limit) the various transmission factors T a b are statistically independent violates the notion of UCF. It was then suggested in Ref. 5 that lack of correlation between reflection factors R a b might be consistent with UCF. The correlation coefficient Cab,a'b' between T a b and T a 'b' was explicitly evaluated later, 6 by use of diagrammatic perturbation theory. As far as we know, there is no explicit evaluation of the correlation coefficient C §,,ab' between reflection factors.The standard theoretical description of the abovementioned problems, usually based on a perturbative treatment or on numerical simulations, is of a microscopic nature. In Refs. 3 and 7-9, on the other hand, the input to the analysis is the transfer matrix for the full conductor: The approach was thereby named macroscopic in Refs. 8 and 9. The theory of Ref. 8 is based on the properties of flux conservation, time-reversal invariance, and the appropriate combination law when two wires are put together. The distribution associated with systems of very small length is selected on the basis of a maximum-entropy criterion; the combination law then shows that the "evolution" of the distribution with the length L is governed by a Fokker-Planck or diffusion equation in TV dimensions. In Ref. 9 it was shown that ...

Spatial-Field Correlation: The Building Block of Mesoscopic Fluctuations

“…Defining a correlation length, δr, as the first zero of C 1 gives δr = π/k = λ/2. The intensity is correlated far beyond δr as a result of scattering within the medium [2,3,4,5,6,7] so that intensity values in remote speckle spots are not statistically independent. This gives rise to two additional contributions to C, which can therefore be expressed as, C = C 1 + C 2 + C 3 [3,8], and leads to greatly enhanced mesoscopic fluctuations [9].…”

Giant backscattering peak in angle-resolved Andreev reflection

“…(7). If W > L the isotropy assumption breaks down [5] and we expect the peak to broaden over W/L modes. Fig.…”

“…Following Mello, Akkermans, and Shapiro [5], we assume that u is uniformly distributed over the unitary group. This "isotropy assumption" is an approximation which ignores the finite time scale of transverse diffusion.…”

Continuous-wave spatial quantum correlations of light induced by multiple scattering

“…The average photon flux is defined as n b (t) = â † b (t)â b (t) while the variance in the photon fluctuations is n 2 2 , where · · · describes the quantum mechanical expectation value. In the following, we focus on the setting in which the light beam is incident onto the medium through a single direction, a, thus the average photon flux for all other input modes is equal to zero.…”

“…Mesoscopic intensity fluctuations that survive averaging over all configurations of disorder give rise to phenomena such as enhanced backscattering and Anderson localization of light [1]. To characterize such a disordered medium, it is essential to investigate spectral or temporal intensity correlations in the multiply scattered light [2][3][4]. In the diffusive regime, the light intensities of different spatial directions (i.e., independent speckles) are uncorrelated.…”