Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential

We present calculations of the localisation length, $\lambda_{2}$, for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength $U$ and system size. $\lambda_{2}(U)$ is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates $\xi_{2}(U)$ are obtained by finite-size scaling. For U=0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for finite $U$, we find that $\xi_{2}(U) \sim \xi_2(0)^{\beta(U)}$ with $\beta(U)$ varying between $\beta(0)=1$ and $\beta(1) \approx 1.5$. We test the validity of various other proposed fit functions and also study the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs. As a check of our method and data, we also reproduce well-known results for the two-dimensional Anderson model without interaction.Comment: 34 RevTeX 3.0 pages with 16 figures include

L\'{e}vy flights in quantum transport in quasi-ballistic wires

Conductance fluctuations, localization and statistics of Lyapunov exponents are studied numerically in pure metallic wires with rough boundaries (quasi-ballistic wires). We find that the correlation energy of conductance fluctuations scales anomalously with the sample dimensions, indicating the role of L\'{e}vy flights. Application of a magnetic field deflects the L\'{e}vy flights which reduces the localization length. This deflection also breaks the geometrical flux cancellation and restores the usual Aharonov-Bohm type magneto-conductance fluctuations.Comment: Available also at http://roberto.fis.uniroma3.it/leadbeat/pub.htm

Non-linear conductivity and quantum interference in disordered metals

We report on a novel non-linear electric field effect in the conductivity of disordered conductors. We find that an electric field gives rise to dephasing in the particle-hole channel, which depresses the interference effects due to disorder and interaction and leads to a non-linear conductivity. This non-linear effect introduces a field dependent temperature scale $T_E$ and provides a microscopic mechanism for electric field scaling at the metal-insulator transition. We also study the magnetic field dependence of the non-linear conductivity and suggest possible ways to experimentally verify our predictions. These effects offer a new probe to test the role of quantum interference at the metal-insulator transition in disordered conductors.Comment: 5 pages, 3 figure