Nonuniversal dynamic conductance fluctuations in disordered systems (original) (raw)
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Physical Review B Condensed Matter and Materials Physics, 2006
We have studied numerically the fluctuations of the conductance, g, in two-dimensional, threedimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of ln g varies with the lateral sample size as L 2/5 in three-dimensional systems, and as a logarithm in four-dimensional systems. The precise knowledge of the dependence of this variance with system size allows us to test the single-parameter scaling hypothesis in three-dimensional systems. We have also calculated the third cumulant of the distribution of ln g in two-and threedimensional systems, and have found that in both cases it diverges with the exponent of the variance times 3/2, remaining relevant in the large size limit.
Sample-to-sample fluctuations in the conductivity of a disordered medium
Journal of Statistical Physics, 1992
We investigate the sample-to-sample fluctuations in the conductivity of a random resistor network--equivalently, in the diffusivity of a disordered medium with symmetric hopping rates. We argue that whenever the effective conductivity ~* is strictly positive, then the fluctuations are normal, i.e., proportional to (volume) -1/2. If the local conductivities are allowed to be zero, then a* vanishes when approaching the percolation threshold Pc. Close to Pc the fluctuations are anomalous. From the renormalization group on hierarchical lattices we find that at Pc fluctuations and mean scale in the same fashion, i.e., there is no independent scaling exponent for the fluctuations.
On the Relation between Electrical Noise Spectra and AC Conductivity in Disordered Systems
2007
We show that the low frequency, f, spectra of current fluctuations, S(f), and complex AC conductivity sigma(f)=sigma'(f)+isigma''(f), are linked by the relationship following from the fluctuation-dissipation, FD, theorem, sigma'(f)/S(f)~f2. We measured sigma(f) and S(f) in impurity conduction in lightly doped semiconductors, where at sufficiently low temperatures, sigma'(f) and sigma''(f), follow a power function of f. At higher temperatures, in a mixed, hopping and extended state transport regime, noise becomes very strong and S(f)~1/f2, with a flat sigma(f), implied by the FD theorem.
Spectrum of universal conductance fluctuations
Physical review letters, 1987
The spectra of conductance fluctuations caused by fluctuating interference terms in the scattering of disordered materials at low temperature are calculated. When the net magnitude of the temporal fluctuation approaches the "universal" value, the form of the spectrum is found to change from that obtained from the bare spectrum of the time-varying scatterers. Anomalous fluctuation statistics occur in the same regime. Remnants of such effects for high-temperature 1/f noise are discussed.
Conductance fluctuations and distribution in disordered chains in the presence of an electric field
Physica A: Statistical Mechanics and its Applications, 1996
A simple Kronig-Peiiney model for ID mesoscopic systems with disordered 6-peak and finite width potentials under an electric field is used to study the conductance fluctuations and distributions in different phase states. The electr ic field allows us to obtain the insulating, transition and metallic regimes. In the superlocalized electron states found previously near the Briltouin zone edges of the corresponding periodic system the conductance fluctuations are smaller than those of the insulating regime corresponding to tin. vanishing field, but. the conductance probability distribution has a similar behaviour.
Fluctuations of Transmission Distribution in Disordered Conductors
Physical Review Letters, 1996
We developed a microscopic approach to calculate the sample-to-sample uctuations of transmission distribution in disordered conductors. This bridges between Green's function and random matrix theories of quantum transport. The results obtained show that the correlations of transmission eigenvalues obey universal Dyson statistics at small separations between eigenvalues being non-universal otherwise. The results facilitate an easy computation of di erent physical quantities and impose important constrains on a future imaginable theory of quantum transport.
Conductivity in disordered systems
Physical review. B, Condensed matter, 1985
By combining numerical results on wires of finite cross section with the coherent-potential approximation and the potential-well analogy, a formula for the conductivity of a three-dimensional disordered system is obtained which interpolates between the weak-scattering limit and the mobility edge.
Conductance fluctuations in the localized regime
2006
We have studied numerically the fluctuations of the conductance, ggg, in two-dimensional, three-dimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of lng\ln glng varies with the lateral sample size as L2/5L^{2/5}L2/5 in three-dimensional systems, and as a logarithm in four-dimensional systems. The precise knowledge of the dependence of this variance with system size allows us to test the single-parameter scaling hypothesis in three-dimensional systems. We have also calculated the third cumulant of the distribution of lng\ln glng in two- and three-dimensional systems, and have found that in both cases it diverges with the exponent of the variance times 3/2, remaining relevant in the large size limit.
Physical Review Letters, 1988
Recently, a macroscopic theory of N-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 ยป 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.