Two interacting particles in an effective 2-3d random potential

We study the effect of coherent propagation of two interacting particles in an effective 2-3-d disordered potential. Our numerical data demonstrate that in dimension $d > 2$, interaction can lead to two--particles delocalization below one--particle delocalization border. We also find that the distance between the two delocalized particles (pair size) grows logarithmically with time. As a result pair propagation is subdiffusive.Comment: 15 Latex pages, + 15 figures compressed with uufile

Localized Thermal States

It is believed that thermalization in closed systems of interacting particles can occur only when the eigenstates are fully delocalized and chaotic in the preferential (unperturbed) basis of the total Hamiltonian. Here we demonstrate that at variance with this common belief the typical situation in the systems with two-body inter-particle interaction is much more complicated and allows to treat as thermal even eigenstates that are not fully delocalized. Using a semi-analytical approach we establish the conditions for the emergence of such thermal states in a model of randomly interacting bosons. Our numerical data show an excellent correspondence with the predicted properties of {\it localized thermal eigenstates}.Comment: Proceedings of the 5th Conference on Nuclei and Mesoscopic Physics, NMP17, East Lansing (USA

Enhancement of localization length for two interacting kicked rotators

We study the effect of coherent propagation of two interacting particles in a disordered potential. The dependence of the enhancement factor for coherent localization length due to interaction is investigated numerically in the model of quantum chaos. The effect of interaction for two particles in many dimensions is also discussed.Comment: 17 pages in revtex, 9 figures (postscript obtained upon request via e-mail at [email protected]) submitted to Nonlinearit

Cantori and dynamical localization in the Bunimovich Stadium

Classical and quantum properties of the Bunimovich stadium in the diffusive regime are reviewed. In particular, the quantum properties are directly investigated using an approximate quantum map. Different localized regimes are found, namely, perturbative, quasi-integrable (due to classical Cantori), dynamical and ergodic.Comment: RevTeX, 8 pages, to be published in Physica

Shared Value in Emerging Markets: How Multinational Corporations Are Redefining Business Strategies to Reach Poor or Vulnerable Populations

This report illuminates the enormous opportunities in emerging markets for companies to drive competitive advantage and sustainable impact at scale. It identifies how over 30 companies across multiple sectors and geographies design and measure business strategies that also improve the lives of underserved individuals