Exact results for one-dimensional disordered bosons with strong repulsion

We study one-dimensional incommensurate bosons with strong repulsive interactions and weak disorder. In analogy to the clean Tonks-Girardeau gas, a Bose-Fermi mapping expresses this problem in terms of disordered free fermions. Thereby many known results apply, in particular for the density-density correlations, the distribution function of the local density of states, and the complete spectral statistics. We also analyze the bosonic momentum distribution, and comment on the experimental observability of these predictions in ultracold atomic gases.Comment: 5 pages, 2 figures, published versio

Conductivity in quasi two-dimensional systems

The conductivity in quasi two-dimensional systems is calculated using the quantum kinetic equation. Linearizing the Lenard-Balescu collision integral with the extension to include external field dependences allows one to calculate the conductivity with diagrams beyond the GW approximation including maximally crossed lines. Consequently the weak localization correction as an interference effect appears here from the field dependence of the collision integral (the latter dependence sometimes called intra-collisional field effect). It is shown that this weak localization correction has the same origin as the Debye-Onsager relaxation effect in plasma physics. The approximation is applied to a system of quasi two-dimensional electrons in hetero-junctions which interact with charged and neutral impurities and the low temperature correction to the conductivity is calculated analytically. It turns out that the dynamical screening due to charged impurities leads to a linear temperature dependence, while the scattering from neutral impurities leads to the usual Fermi-liquid behavior. By considering an appropriate mass action law to determine the ratio of charged to neutral impurities we can describe the experimental metal-insulator transition at low temperatures as a Mott-Hubbard transition.Comment: 7 pages 7 pages appendix 11 figure

Anderson localization and nonlinearity in one-dimensional disordered photonic lattices

We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one-dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly measured. Nonlinear perturbations enhance localization in one type and induce delocalization in the other. In a complementary approach, we study the evolution on short time scales of delta-like wave packets in the presence of disorder. A transition from ballistic wave packet expansion to exponential (Anderson) localization is observed. We also find an intermediate regime in which the ballistic and localized components coexist while diffusive dynamics is absent. Evidence is found for a faster transition into localization under nonlinear conditions

Evolution of wave packets in quasi-1D and 1D random media: diffusion versus localization

We study numerically the evolution of wavepackets in quasi one-dimensional random systems described by a tight-binding Hamiltonian with long-range random interactions. Results are presented for the scaling properties of the width of packets in three time regimes: ballistic, diffusive and localized. Particular attention is given to the fluctuations of packet widths in both the diffusive and localized regime. Scaling properties of the steady-state distribution are also analyzed and compared with theoretical expression borrowed from one-dimensional Anderson theory. Analogies and differences with the kicked rotator model and the one-dimensional localization are discussed.Comment: 32 pages, LaTex, 11 PostScript figure