We propose a realization of the one-dimensional random dimer model and certain N-leg generalizations using cold atoms in an optical lattice. We show that these models exhibit multiple delocalization energies that depend strongly on the symmetry prope
rties of the corresponding Hamiltonian and we provide analytical and numerical results for the localization length as a function of energy. We demonstrate that the N-leg systems possess similarities with their 1D ancestors but are demonstrably distinct. The existence of critical delocalization energies leads to dips in the momentum distribution which serve as a clear signal of the localization-delocalization transition. These momentum distributions are different for models with different group symmetries and are identical for those with the same symmetry.
We consider a clean two-dimensional interacting electron gas subject to a random perpendicular magnetic field, h({bf r}). The field is nonquantizing, in the sense, that {cal N}_h-a typical flux into the area lambda_{text{tiny F}}^2 in the units of th
e flux quantum (lambda_{text{tiny F}} is the de Broglie wavelength) is small, {cal N}_hll 1. If the spacial scale, xi, of change of h({bf r}) is much larger than lambda_{text{tiny F}}, the electrons move along semiclassical trajectories. We demonstrate that a weak field-induced curving of the trajectories affects the interaction-induced electron lifetime in a singular fashion: it gives rise to the correction to the lifetime with a very sharp energy dependence. The correction persists within the interval omega sim omega_0= E_{text{tiny F}}{cal N}_h^{2/3} much smaller than the Fermi energy, E_{text{tiny F}}. It emerges in the third order in the interaction strength; the underlying physics is that a small phase volume sim (omega/E_{text{tiny F}})^{1/2} for scattering processes, involving {em two} electron-hole pairs, is suppressed by curving. Even more surprising effect that we find is that {em disorder-averaged} interaction correction to the density of states, delta u(omega), exhibits {em oscillatory} behavior, periodic in bigl(omega/omega_0bigr)^{3/2}. In our calculations of interaction corrections random field is incorporated via the phases of the Green functions in the coordinate space. We discuss the relevance of the new low-energy scale for realizations of a smooth random field in composite fermions and in disordered phase of spin-fermion model of ferromagnetic quantum criticality.
We study the magnetoresistance, deltarho_{xx}(B)/rho_0, of a high-mobility 2D electron gas in the domain of magnetic fields, B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where deltarho_{xx}(B)/rho_0 is governe
d by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the {em second order} in the interaction parameter, $lambda$, a {em linear} B-dependence, deltarho_{xx}(B)/rho_0sim lambda^2omega_c/E_F with {em temperature-independent} slope emerges in this domain of B (here omega_c and E_F are the cyclotron frequency and the Fermi energy, respectively). Unlike previous mechanisms, the linear magnetoresistance is {em unrelated} to the electron executing the full Larmour circle, but rather originates from the impurity scattering via the B-dependence of the {em phase} of the impurity-induced Friedel oscillations.
Electron-electron interactions give rise to the correction, deltasigma^{int}(omega), to the ac magnetoconductivity, sigma(omega), of a clean 2D electron gas that is periodic in omega_c^{-1}, where omega_c is the cyclotron frequency. Unlike convention
al harmonics of the cyclotron resonance, which are periodic with omega, this correction is periodic with omega^{3/2}. Oscillations in deltasigma^{int}(omega) develop at low magnetic fields, omega_cllomega, when the conventional harmonics are suppressed by the disorder. Their origin is a {em double} backscattering of an electron from the impurity-induced Friedel oscillations. During the time simomega^{-1} between the two backscattering events the electron travels only a {em small portion} of the Larmour circle.
