Coherence and Partial Coherence in Interacting Electron Systems

We study coherence of electron transport through interacting quantum dots and discuss the relation of the coherent part to the flux-sensitive conductance for three different types of Aharonov-Bohm interferometers. Contributions to transport in first and second order in the intrinsic line width of the dot levels are addressed in detail. We predict an asymmetry of the interference signal around resonance peaks as a consequence of incoherence associated with spin-flip processes. Furthermore, we show by strict calculation that first-order contributions can be partially or even fully coherent. This contrasts with the sequential-tunneling picture which describes first-order transport as a sequence of incoherent tunneling processes

Geometric characterization of intermittency in the parabolic Anderson model

We consider the parabolic Anderson problem $\partial_tu=\Delta u+\xi(x)u$ on $\mathbb{R}_+\times\mathbb{Z}^d$ with localized initial condition $u(0,x)=\delta_0(x)$ and random i.i.d. potential $\xi$. Under the assumption that the distribution of $\xi(0)$ has a double-exponential, or slightly heavier, tail, we prove the following geometric characterization of intermittency: with probability one, as $t\to\infty$, the overwhelming contribution to the total mass $\sum_xu(t,x)$ comes from a slowly increasing number of ``islands'' which are located far from each other. These ``islands'' are local regions of those high exceedances of the field $\xi$ in a box of side length $2t\log^2t$ for which the (local) principal Dirichlet eigenvalue of the random operator $\Delta+\xi$ is close to the top of the spectrum in the box. We also prove that the shape of $\xi$ in these regions is nonrandom and that $u(t,\cdot)$ is close to the corresponding positive eigenfunction. This is the geometric picture suggested by localization theory for the Anderson Hamiltonian.Comment: Published at http://dx.doi.org/10.1214/009117906000000764 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org