438 research outputs found

### Comparing Methods for Interpolation to Improve Raster Digital Elevation Models

Digital elevation models (DEMs) are available as raster files at 100m, 30m, and 10m resolutions for the contiguous United States and are used in a variety of geographic analyses. Some projects may require a finer resolution. GIS software offers many options for interpolating data to higher resolutions. We compared ten interpolation methods using 10m sample data from the Ouachita Mountains in central Arkansas. We interpolated the 10m DEM to 5m, 2.5m, and 1m resolutions and compared the absolute mean difference (AMD) for each using surveyed control points. Overall, there was little difference in the accuracy between interpolation methods at the resolutions tested and minimal departure from the original 10m raster

### Spectrum and diffusion for a class of tight-binding models on hypercubes

We propose a class of exactly solvable anisotropic tight-binding models on an
infinite-dimensional hypercube. The energy spectrum is analytically computed
and is shown to be fractal and/or absolutely continuous according to the value
hopping parameters. In both cases, the spectral and diffusion exponents are
derived. The main result is that, even if the spectrum is absolutely
continuous, the diffusion exponent for the wave packet may be anything between
0 and 1 depending upon the class of models.Comment: 5 pages Late

### Analytical Results for Multifractal Properties of Spectra of Quasiperiodic Hamiltonians near the Periodic Chain

The multifractal properties of the electronic spectrum of a general
quasiperiodic chain are studied in first order in the quasiperiodic potential
strength. Analytical expressions for the generalized dimensions are found and
are in good agreement with numerical simulations. These first order results do
not depend on the irrational incommensurability.Comment: 10 Pages in RevTeX, 2 Postscript figure

### What determines the spreading of a wave packet?

The multifractal dimensions D2^mu and D2^psi of the energy spectrum and
eigenfunctions, resp., are shown to determine the asymptotic scaling of the
width of a spreading wave packet. For systems where the shape of the wave
packet is preserved the k-th moment increases as t^(k*beta) with
beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound.
Furthermore, we show that in d dimensions asymptotically in time the center of
any wave packet decreases spatially as a power law with exponent D_2^psi - d
and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure

### Stable Quantum Resonances in Atom Optics

A theory for stabilization of quantum resonances by a mechanism similar to
one leading to classical resonances in nonlinear systems is presented. It
explains recent surprising experimental results, obtained for cold Cesium atoms
when driven in the presence of gravity, and leads to further predictions. The
theory makes use of invariance properties of the system, that are similar to
those of solids, allowing for separation into independent kicked rotor
problems. The analysis relies on a fictitious classical limit where the small
parameter is {\em not} Planck's constant, but rather the detuning from the
frequency that is resonant in absence of gravity.Comment: 5 pages, 3 figure

### Dynamics of a quantum particle in low-dimensional disordered systems with extended states

We investigate the dynamics of a quantum particle in disordered tight-binding
models in one and two dimensions which are exceptions to the common wisdom on
Anderson localization, in the sense that the localization length diverges at
some special energies. We provide a consistent picture for two well-known
one-dimensional examples: the chain with off-diagonal disorder and the
random-dimer model. In both cases the quantum motion exhibits a peculiar kind
of anomalous diffusion which can be referred to as bi-fractality. The
disorder-averaged density profile of the particle becomes critical in the
long-time regime. The $q$-th moment of the position of the particle diverges
with time whenever $q$ exceeds some $q_0$. We obtain $q_0=2$ for off-diagonal
disorder on the chain (and conjecturally on two-dimensional bipartite lattices
as well). For the random-dimer model, our result $q_0=1/2$ corroborates known
rigorous results.Comment: 20 pages, 12 figures, 1 table. Note added on the recent work by Lepri
et a

### Quantum Diffusion in Separable d-Dimensional Quasiperiodic Tilings

We study the electronic transport in quasiperiodic separable tight-binding
models in one, two, and three dimensions. First, we investigate a
one-dimensional quasiperiodic chain, in which the atoms are coupled by weak and
strong bonds aligned according to the Fibonacci chain. The associated
d-dimensional quasiperiodic tilings are constructed from the product of d such
chains, which yields either the square/cubic Fibonacci tiling or the labyrinth
tiling. We study the scaling behavior of the mean square displacement and the
return probability of wave packets with respect to time. We also discuss
results of renormalization group approaches and lower bounds for the scaling
exponent of the width of the wave packet.Comment: 6 pages, 4 figures, conference proceedings Aperiodic 2012 (Cairns

### Field Theory Approach to Quantum Interference in Chaotic Systems

We consider the spectral correlations of clean globally hyperbolic (chaotic)
quantum systems. Field theoretical methods are applied to compute quantum
corrections to the leading (`diagonal') contribution to the spectral form
factor. Far-reaching structural parallels, as well as a number of differences,
to recent semiclassical approaches to the problem are discussed.Comment: 18 pages, 4 figures, revised version, accepted for publication in J.
Phys A (Math. Gen.

### Energy spectra, wavefunctions and quantum diffusion for quasiperiodic systems

We study energy spectra, eigenstates and quantum diffusion for one- and
two-dimensional quasiperiodic tight-binding models. As our one-dimensional
model system we choose the silver mean or `octonacci' chain. The
two-dimensional labyrinth tiling, which is related to the octagonal tiling, is
derived from a product of two octonacci chains. This makes it possible to treat
rather large systems numerically. For the octonacci chain, one finds singular
continuous energy spectra and critical eigenstates which is the typical
behaviour for one-dimensional Schr"odinger operators based on substitution
sequences. The energy spectra for the labyrinth tiling can, depending on the
strength of the quasiperiodic modulation, be either band-like or fractal-like.
However, the eigenstates are multifractal. The temporal spreading of a
wavepacket is described in terms of the autocorrelation function C(t) and the
mean square displacement d(t). In all cases, we observe power laws for C(t) and
d(t) with exponents -delta and beta, respectively. For the octonacci chain,
0<delta<1, whereas for the labyrinth tiling a crossover is observed from
delta=1 to 0<delta<1 with increasing modulation strength. Corresponding to the
multifractal eigenstates, we obtain anomalous diffusion with 0<beta<1 for both
systems. Moreover, we find that the behaviour of C(t) and d(t) is independent
of the shape and the location of the initial wavepacket. We use our results to
check several relations between the diffusion exponent beta and the fractal
dimensions of energy spectra and eigenstates that were proposed in the
literature.Comment: 24 pages, REVTeX, 10 PostScript figures included, major revision, new
results adde

### On the spacing distribution of the Riemann zeros: corrections to the asymptotic result

It has been conjectured that the statistical properties of zeros of the
Riemann zeta function near z = 1/2 + \ui E tend, as $E \to \infty$, to the
distribution of eigenvalues of large random matrices from the Unitary Ensemble.
At finite $E$ numerical results show that the nearest-neighbour spacing
distribution presents deviations with respect to the conjectured asymptotic
form. We give here arguments indicating that to leading order these deviations
are the same as those of unitary random matrices of finite dimension $N_{\rm
eff}=\log(E/2\pi)/\sqrt{12 \Lambda}$, where $\Lambda=1.57314 ...$ is a well
defined constant.Comment: 9 pages, 3 figure

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