The problem of quantum chaotic scattering with direct processes reduced to the one without

We show that the study of the statistical properties of the scattering matrix S for quantum chaotic scattering in the presence of direct processes (charaterized by a nonzero average S matrix ) can be reduced to the simpler case where direct processes are absent ( = 0). Our result is verified with a numerical simulation of the two-energy autocorrelation for two-dimensional S matrices. It is also used to extend Wigner's time delay distribution for one-dimensional S matrices, recently found for = 0, to the case not equal to zero; this extension is verified numerically. As a consequence of our result, future calculations can be restricted to the simpler case of no direct processes.Comment: 9 pages (Latex) and 1 EPS figure. Submitted to Europhysics Letters. The conjecture proposed in the previous version is proved; thus the present version contains a more satisfactory presentation of the proble

Controlling conductance statistics of quantum wires by driving ac fields

We calculate the entire distribution of the conductance P(G) of a one-dimensional disordered system --quantum wire-- subject to a time-dependent field. Our calculations are based on Floquet theory and a scaling approach to localization. Effects of the applied ac field on the conductance statistics can be strong and in some cases dramatic, as in the high-frequency regime where the conductance distribution shows a sharp cut-off. In this frequency regime, the conductance is written as a product of a frequency-dependent term and a field independent term, the latter containing the information on the disorder in the wire. We thus use the solution of the Mel'nikov equation for time-independent transport to calculate P(G) at any degree of disorder. At lower frequencies, it is found that the conductance distribution and the correlations of the transmission Floquet modes are described by a solution of the Dorokhov-Mello-Pereyra-Kumar equation with an effective number of channels. In the regime of strong localization, induced by the disorder or the ac field, P(G) is a log-normal distribution. Our theoretical results are verified numerically using a single-band Anderson Hamiltonian.Comment: 6 pages, 4 figures. V2: a new reference added. Minor correction

Conductance fluctuations in disordered 2D topological insulator wires: From quantum spin-Hall to ordinary quantum phases

Impurities and defects are ubiquitous in topological insulators (TIs) and thus understanding the effects of disorder on electronic transport is important. We calculate the distribution of the random conductance fluctuations $P(G)$ of disordered 2D TI wires modeled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian with realistic parameters. As we show, the disorder drives the TIs into different regimes: metal (M), quantum spin-Hall insulator (QSHI), and ordinary insulator (OI). By varying the disorder strength and Fermi energy, we calculate analytically and numerically $P(G)$ across the entire phase diagram. The conductance fluctuations follow the statistics of the unitary universality class $\beta=2$. At strong disorder and high energy, however, the size of the fluctutations $\delta G$ reaches the universal value of the orthogonal symmetry class ($\beta=1$). At the QSHI-M and QSHI-OI crossovers, the interplay between edge and bulk states plays a key role in the statistical properties of the conductance.Comment: 17 pages, 5 figure

Universal and nonuniversal scaling of transmission in thin random layered media

The statistics of transmission through random 1D media are generally presumed to be universal and to depend only upon a single dimensionless parameter, the ratio of the sample length and the mean free path, s=L/l. For s much larger than unity, the probability distribution function of the logarithm of transmission, P(ln T) is Gaussian with average value -s and variance 2s. Here we show in numerical simulations and optical measurements that in random binary systems, and most prominently in systems for which s less than unity, the statistics of transmission are universal for transmission near an upper cutoff of unity and depend upon the character of the discrete disorder near a lower cutoff. The universal behavior of P(ln T) closely resembles a segment of a Gaussian and arises in random binary media with as few as three binary layers. Above the lower cutoff, but below the crossover to a universal expression, the shape of P(ln T) also depends upon the reflectivity of the interface between the layers. For a given value of s, P(ln T) evolves towards a universal distribution given by random matrix theory in the dense weak scattering limit as the numbers of layers increases. P(ln T) found in simulations is compared to results of random matrix calculations in the dense weak scattering limit but with an imposed minimum in transmission. Optical measurements in stacks of glass coverslips are compared to random matrix theory, and differences are ascribed to transverse disorder in the layers.Comment: 7 pages, 7 figure

Time delay in 1D disordered media with high transmission

We study the time delay of reflected and transmitted waves in 1D disordered media with high transmission. Highly transparent and translucent random media are found in nature or can be synthetically produced. We perform numerical simulations of microwaves propagating in disordered waveguides to show that reflection amplitudes are described by complex Gaussian random variables with the remarkable consequence that the time-delay statistics in reflection of 1D disordered media are described as in random media in the diffusive regime. For transmitted waves, we show numerically that the time delay is an additive quantity and its fluctuations thus follow a Gaussian distribution. Ultimately, the distributions of the time delay in reflection and transmission are physical illustrations of the central limit theorem at work

Photonic heterostructures with Levy-type disorder: statistics of coherent transmission

We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution --L\'evy-type distribution. Based on recent predictions made for 1D coherent transport with L\'evy-type disorder, we show numerically that for a system of length $L$ (i) the average $\propto L^\alpha$ for $0 \propto L$ for $1\le\alpha<2$, $\alpha$ being the exponent of the power-law decay of the layer-thickness probability distribution; and (ii) the transmission distribution $P(T)$ is independent of the angle of incidence and frequency of the electromagnetic wave, but it is fully determined by the values of $\alpha$ and $$.Comment: 4 pages, 4 figure

Conductance distributions of 1D-disordered wires at finite temperature and bias voltage

We calculate the distribution of the conductance G in a one-dimensional disordered wire at finite temperature T and bias voltage V in a independent-electron picture and assuming full coherent transport. At high enough temperature and bias voltage, where several resonances of the system contribute to the conductance, the distribution P(G(T,V)) can be represented with good accuracy by autoconvolutions of the distribution of the conductance at zero temperature and zero bias voltage. The number of convolutions depends on T and V. In the regime of very low T and V, where only one resonance is relevant to G(T,V), the conductance distribution is analyzed by a resonant tunneling conductance model. Strong effects of finite T and V on the conductance distribution are observed and well described by our theoretical analysis, as we verify by performing a number of numerical simulations of a one-dimensional disordered wire at different temperatures, voltages, and lengths of the wire. Analytical estimates for the first moments of P(G(T,V)) at high temperature and bias voltage are also provided.Comment: 9 pages, 7 figures, Submitted to PR