Magnetic-Field Dependence of the Localization Length in Anderson Insulators

Using the conventional scaling approach as well as the renormalization group analysis in $d=2+\epsilon$ dimensions, we calculate the localization length $\xi(B)$ in the presence of a magnetic field $B$. For the quasi 1D case the results are consistent with a universal increase of $\xi(B)$ by a numerical factor when the magnetic field is in the range \ell\ll{\ell_{\!{_H}}}\alt\xi(0), $\ell$ is the mean free path, ${\ell_{\!{_H}}}$ is the magnetic length $\sqrt{\hbar c/eB}$. However, for $d\ge 2$ where the magnetic field does cause delocalization there is no universal relation between $\xi(B)$ and $\xi(0)$. The effect of spin-orbit interaction is briefly considered as well.Comment: 4 pages, revtex, no figures; to be published in Europhysics Letter

Localized to extended states transition for two interacting particles in a two-dimensional random potential

We show by a numerical procedure that a short-range interaction $u$ induces extended two-particle states in a two-dimensional random potential. Our procedure treats the interaction as a perturbation and solve Dyson's equation exactly in the subspace of doubly occupied sites. We consider long bars of several widths and extract the macroscopic localization and correlation lengths by an scaling analysis of the renormalized decay length of the bars. For $u=1$, the critical disorder found is $W_{\rm c}=9.3\pm 0.2$, and the critical exponent $\nu=2.4\pm 0.5$. For two non-interacting particles we do not find any transition and the localization length is roughly half the one-particle value, as expected.Comment: 4 two-column pages, 4 eps figures, Revtex, to be published in Europhys. Let

Rare decay \pi^0 \to e^+e^- as a Test of Standard Model

Experimental and theoretical progress concerning the rare decay \pi^0 \to e^+e^- is briefly reviewed. It includes the latest data from KTeV and a new model independent estimate of the decay branching which show the deviation between experiment and theory at the level of $3.3\sigma$. The predictions for \eta and \eta' decays into lepton pair are presented. We also comment on the impact on the pion rare decay estimate of the BABAR collaboration on the pion transition form factor at large momentum transfer.Comment: 11 pages, 2 figures, extended version of the talk given at "New Physics and Quantum Chromodynamics at External Conditions" conference, May 3-6, 2009, Dnipropetrovsk, Ukrain

How the recent BABAR data for P to \gamma\gamma* affect the Standard Model predictions for the rare decays P to l+l-

Measuring the lepton anomalous magnetic moments $(g-2)$ and the rare decays of light pseudoscalar mesons into lepton pairs $P\to l^{+}l^{-}$, serve as important tests of the Standard Model. To reduce the theoretical uncertainty in the standard model predictions, the data on the charge and transition form factors of the light pseudoscalar mesons play a significant role. Recently, new data on the behavior of the transition form factors $P\to\gamma\gamma*$ at large momentum transfer were supplied by the BABAR collaboration. There are several problems with the theoretical interpretation of these data: 1) An unexpectedly slow decrease of the pion transition form factor at high momenta, 2) the qualitative difference in the behavior of the pion form factor and the $\eta$ and $\eta^\prime$ form factors at high momenta, 3) the inconsistency of the measured ratio of the $\eta$ and $\eta^\prime$ form factors with the predicted one. We comment on the influence of the new BABAR data on the rare decay branchings.Comment: 11 pages, 3 figure

The Generalized Star Product and the Factorization of Scattering Matrices on Graphs

In this article we continue our analysis of Schr\"odinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for the scattering matrices. This composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs. We perform a detailed analysis of the generalized star product for arbitrary unitary matrices. The relation to the theory of transfer matrices is also discussed

Interaction-induced delocalization of two particles in a random potential: Scaling properties

The localization length $\xi_2$ for coherent propagation of two interacting particles in a random potential is studied using a novel and efficient numerical method. We find that the enhancement of $\xi_2$ over the one-particle localization length $\xi_1$ satisfies the scaling relation $\xi_2/\xi_1=f(u/\Delta_\xi)$, where $u$ is the interaction strength and $\Delta_{\xi}$ the level spacing of a wire of length $\xi_1$. The scaling function $f$ is linear over the investigated parameter range. This implies that $\xi_2$ increases faster with $u$ than previously predicted. We also study a novel mapping of the problem to a banded-random-matrix model.Comment: 5 pages and two figures in a uuencoded, compressed tar file; uses revtex and psfig.sty (included); substantial revision of a previous version of the paper including newly discovered scaling behavio

Statistical Scattering of Waves in Disordered Waveguides: from Microscopic Potentials to Limiting Macroscopic Statistics

We study the statistical properties of wave scattering in a disordered waveguide. The statistical properties of a "building block" of length (delta)L are derived from a potential model and used to find the evolution with length of the expectation value of physical quantities. In the potential model the scattering units consist of thin potential slices, idealized as delta slices, perpendicular to the longitudinal direction of the waveguide; the variation of the potential in the transverse direction may be arbitrary. The sets of parameters defining a given slice are taken to be statistically independent from those of any other slice and identically distributed. In the dense-weak-scattering limit, in which the potential slices are very weak and their linear density is very large, so that the resulting mean free paths are fixed, the corresponding statistical properties of the full waveguide depend only on the mean free paths and on no other property of the slice distribution. The universality that arises demonstrates the existence of a generalized central-limit theorem. Our final result is a diffusion equation in the space of transfer matrices of our system, which describes the evolution with the length L of the disordered waveguide of the transport properties of interest. In contrast to earlier publications, in the present analysis the energy of the incident particle is fully taken into account.Comment: 75 pages, 10 figures, submitted to Phys. Rev

Anderson localization of a weakly interacting one dimensional Bose gas

We consider the phase coherent transport of a quasi one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow identified in [T. Paul et al., Phys. Rev. Lett. 98, 210602 (2007)], we focus here on the supersonic stationary regime where Anderson localization exists. We generalize the diffusion formalism of Dorokhov-Mello-Pereyra-Kumar to include interaction effects. It is shown that interactions modify the localization length and also introduce a length scale L* for the disordered region, above which most of the realizations of the random potential lead to time dependent flows. A Fokker-Planck equation for the probability density of the transmission coefficient that takes this new effect into account is introduced and solved. The theoretical predictions are verified numerically for different types of disordered potentials. Experimental scenarios for observing our predictions are discussed.Comment: 20 pages, 13 figure

Delocalization of tightly bound excitons in disordered systems

The localization length of a low energy tightly bound electron-hole pair (excitons) is calculated by exact diagonalization for small interacting disordered systems. The exciton localization length (which corresponds to the thermal electronic conductance) is strongly enhanced by electron-electron interactions, while the localization length (pertaining to the charge conductance) is only slightly enhanced. This shows that the two particle delocalization mechanism widely discussed for the electron pair case is more efficient close to the Fermi energy for an electron-hole pair. The relevance to experiment is also discussed.Comment: 10 pages, 2 figures - old version was posted by mistak

Conductance Fluctuations in Disordered Wires with Perfectly Conducting Channels

We study conductance fluctuations in disordered quantum wires with unitary symmetry focusing on the case in which the number of conducting channels in one propagating direction is not equal to that in the opposite direction. We consider disordered wires with $N+m$ left-moving channels and $N$ right-moving channels. In this case, $m$ left-moving channels become perfectly conducting, and the dimensionless conductance $g$ for the left-moving channels behaves as $g \to m$ in the long-wire limit. We obtain the variance of $g$ in the diffusive regime by using the Dorokhov-Mello-Pereyra-Kumar equation for transmission eigenvalues. It is shown that the universality of conductance fluctuations breaks down for $m \neq 0$ unless $N$ is very large.Comment: 6 pages, 2 figure