171 research outputs found
Metal-insulator transition in the Hartree-Fock phase diagram of the fully polarized homogeneous electron gas in two dimensions
We determine numerically the ground state of the two-dimensional, fully
polarized electron gas within the Hartree-Fock approximation without imposing
any particular symmetries on the solutions. At low electronic densities, the
Wigner crystal solution is stable, but for higher densities ( less than
) we obtain a ground state of different symmetry: the charge density
forms a triangular lattice with about 11% more sites than electrons. We prove
analytically that this conducting state with broken translational symmetry has
lower energy than the uniform Fermi gas state in the high density region giving
rise to a metal to insulator transition.Comment: 13 pages, 5 figures, rewrite of 0804.1025 and 0807.077
Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
We show that a mobility edge exists in 1D random potentials provided specific
long-range correlations. Our approach is based on the relation between binary
correlator of a site potential and the localization length. We give the
algorithm to construct numerically potentials with mobility edge at any given
energy inside allowed zone. Another natural way to generate such potentials is
to use chaotic trajectories of non-linear maps. Our numerical calculations for
few particular potentials demonstrate the presence of mobility edges in 1D
geometry.Comment: 4 pages in RevTex and 2 Postscript figures; revised version published
in Phys. Rev. Lett. 82 (1999) 406
Scattering Theory Approach to Random Schroedinger Operators in One Dimension
Methods from scattering theory are introduced to analyze random Schroedinger
operators in one dimension by applying a volume cutoff to the potential. The
key ingredient is the Lifshitz-Krein spectral shift function, which is related
to the scattering phase by the theorem of Birman and Krein. The spectral shift
density is defined as the "thermodynamic limit" of the spectral shift function
per unit length of the interaction region. This density is shown to be equal to
the difference of the densities of states for the free and the interacting
Hamiltonians. Based on this construction, we give a new proof of the Thouless
formula. We provide a prescription how to obtain the Lyapunov exponent from the
scattering matrix, which suggest a way how to extend this notion to the higher
dimensional case. This prescription also allows a characterization of those
energies which have vanishing Lyapunov exponent.Comment: 1 figur
Nonlinear Impurity Modes in Homogeneous and Periodic Media
We analyze the existence and stability of nonlinear localized waves described
by the Kronig-Penney model with a nonlinear impurity. We study the properties
of such waves in a homogeneous medium, and then analyze new effects introduced
by periodicity of the medium parameters. In particular, we demonstrate the
existence of a novel type of stable nonlinear band-gap localized states, and
also reveal an important physical mechanism of the oscillatory wave
instabilities associated with the band-gap wave resonances.Comment: 11 pages, 3 figures; To be published in: Proceedings of the NATO
Advanced Research Workshop "Nonlinearity and Disorder: Theory and
Applications" (Tashkent, 2-6 Oct, 2000) Editors: P.L. Christiansen and F.K.
Abdullaev (Kluwer, 2001
Exponential dynamical localization for the almost Mathieu operator
We prove that the exponential moments of the position operator stay bounded
for the supercritical almost Mathieu operator with Diophantine frequency
Diffusion in disordered systems under iterative measurement
We consider a sequence of idealized measurements of time-separation onto a discrete one-dimensional disordered system. A connection with Markov
chains is found. For a rapid sequence of measurements, a diffusive regime
occurs and the diffusion coefficient is analytically calculated. In a
general point of view, this result suggests the possibility to break the
Anderson localization due to decoherence effects. Quantum Zeno effect emerges
because the diffusion coefficient vanishes at the limit .Comment: 8 pages, 0 figures, LATEX. accepted in Phys.Rev.
On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials
We consider discrete one-dimensional random Schroedinger operators with
decaying matrix-valued, independent potentials. We show that if the l^2-norm of
this potential has finite expectation value with respect to the product measure
then almost surely the Schroedinger operator has an interval of purely
absolutely continuous (ac) spectrum. We apply this result to Schroedinger
operators on a strip. This work provides a new proof and generalizes a result
obtained by Delyon, Simon, and Souillard.Comment: (1 figure
Force Distribution in a Granular Medium
We report on systematic measurements of the distribution of normal forces
exerted by granular material under uniaxial compression onto the interior
surfaces of a confining vessel. Our experiments on three-dimensional, random
packings of monodisperse glass beads show that this distribution is nearly
uniform for forces below the mean force and decays exponentially for forces
greater than the mean. The shape of the distribution and the value of the
exponential decay constant are unaffected by changes in the system preparation
history or in the boundary conditions. An empirical functional form for the
distribution is proposed that provides an excellent fit over the whole force
range measured and is also consistent with recent computer simulation data.Comment: 6 pages. For more information, see http://mrsec.uchicago.edu/granula
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