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

Disordered vortex arrays in a two-dimensional condensate

We suggest a method to create turbulence in a Bose-Einstein condensate. The method consists in, firstly, creating an ordered vortex array, and, secondly, imprinting a phase difference in different regions of the condensate. By solving numerically the two-dimensional Gross-Pitaevskii equation we show that the motion of the resulting positive and negative vortices is disordered.Comment: 14 pages, 18 figures, accepted by Geophysical and Astrophysical Fluid Dynamic

Semiclassical description of resonant tunneling

We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The calculations idealize an experimental situation where a strong magnetic field tilted with respect to an electric field is used. The resulting semiclassical expression is written as the sum over special periodic orbits which hit both walls of the quantum well and are perpendicular to the first wall.Comment: LaTeX, 8 page

Confined magnetic guiding orbit states

We show how snake-orbit states which run along a magnetic edge can be confined electrically. We consider a two-dimensional electron gas (2DEG) confined into a quantum wire, subjected to a strong perpendicular and steplike magnetic field $B/-B$. Close to this magnetic step new, spatially confined bound states arise as a result of the lateral confinement and the magnetic field step. The number of states, with energy below the first Landau level, increases as $B$ becomes stronger or as the wire width becomes larger. These bound states can be understood as an interference between two counter-propagating one-dimensional snake-orbit states.Comment: 4 pages, 4 figure