Engineering Quantum States, Nonlinear Measurements, and Anomalous Diffusion by Imaging

We show that well-separated quantum superposition states, measurements of strongly nonlinear observables, and quantum dynamics driven by anomalous diffusion can all be achieved for single atoms or molecules by imaging spontaneous photons that they emit via resonance florescence. To generate anomalous diffusion we introduce continuous measurements driven by L\'evy processes, and prove a number of results regarding their properties. In particular we present strong evidence that the only stable L\'evy density that can realize a strictly continuous measurement is the Gaussian.Comment: revtex4-1, 17 pages, 7 eps figure

Random Diffusion Model with Structure Corrections

The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to one with a more natural large-wavenumber cutoff. We investigate whether the features seen previously -- namely a slowing down of the system and the development of a prepeak in the dynamic structure factor at a wavenumber below the first structure peak -- survive in this model. A method for extracting information about a hidden prepeak in experimental data is presented.Comment: 13 pages, 8 figure

Strain-Dependence of Surface Diffusion: Ag on Ag(111) and Pt(111)

Using density-functional theory with the local-density approximation and the generalized gradient approximation we compute the energy barriers for surface diffusion for Ag on Pt(111), Ag on one monolayer of Ag on Pt(111), and Ag on Ag(111). The diffusion barrier for Ag on Ag(111) is found to increase linearly with increasing lattice constant. We also discuss the reconstruction that has been found experimentally when two Ag layers are deposited on Pt(111). Our calculations explain why this strain driven reconstruction occurs only after two Ag layers have been deposited.Comment: 4 pages, 3 figures, Phys. Rev. B 55 (1997), in pres

Density Driven Diffusion

In this work we derive a novel density driven diffusion scheme for image enhancement. Our approach, called D3, is a semi-local method that uses an initial structure-preserving oversegmentation step of the input image.  Because of this, each segment will approximately conform to a homogeneous region in the image, allowing us to easily estimate parameters of the underlying stochastic process thus achieving adaptive non-linear filtering. Our method is capable of producing competitive results when compared to state-of-the-art methods such as non-local means, BM3D and tensor driven diffusion on both color and grayscale images.VIDIGARNICSBILDLA

Fast Domain Growth through Density-Dependent Diffusion in a Driven Lattice Gas

We study electromigration in a driven diffusive lattice gas (DDLG) whose continuous Monte Carlo dynamics generate higher particle mobility in areas with lower particle density. At low vacancy concentrations and low temperatures, vacancy domains tend to be faceted: the external driving force causes large domains to move much more quickly than small ones, producing exponential domain growth. At higher vacancy concentrations and temperatures, even small domains have rough boundaries: velocity differences between domains are smaller, and modest simulation times produce an average domain length scale which roughly follows $L \sim t^{\zeta}$, where $\zeta$ varies from near .55 at 50% filling to near .75 at 70% filling. This growth is faster than the $t^{1/3}$ behavior of a standard conserved order parameter Ising model. Some runs may be approaching a scaling regime. At low fields and early times, fast growth is delayed until the characteristic domain size reaches a crossover length which follows $L_{cross} \propto E^{-\beta}$. Rough numerical estimates give $\beta= >.37$ and simple theoretical arguments give $\beta= 1/3$. Our conclusion that small driving forces can significantly enhance coarsening may be relevant to the YB$_2$Cu$_3$O$_{7- \delta}$ electromigration experiments of Moeckly {\it et al.}(Appl. Phys. Let., {\bf 64}, 1427 (1994)).Comment: 18 pages, RevTex3.

Diffusion-driven flows in a non-linear stratified fluid layer

Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates diffusion-driven flow within a nonlinearly density-stratified fluid confined between two tilted parallel walls. We introduce a novel asymptotic expansion inspired by the center manifold theory, where quantities are expanded in terms of derivatives of the cross-sectional averaged density field. This technique provides accurate approximations for velocity, density, and pressure fields. Furthermore, we derive an evolution equation describing the cross-sectional averaged density field. This equation takes the form of the traditional diffusion equation but replaces the constant diffusion coefficient with a positive-definite function dependent on the solution's derivative. Numerical simulations validate the accuracy of our approximations. Our investigation of the effective equation reveals that the density profile depends on a non-dimensional parameter denoted as $\gamma$ which is related to the flow strength. In the large $\gamma$ limit, the system emulates a diffusion process with an augmented diffusion coefficient of $1+\cot^{2}\theta$, where $\theta$ signifies the inclination angle of the channel domain. This parameter regime is where diffusion-driven flow exhibits its strongest mixing ability. Conversely, in the small $\gamma$ regime, the density field behaves akin to pure diffusion with distorted isopycnals. Lastly, we show that the classical thin film equation aligns with the results obtained using the novel expansion in the small $\gamma$ regime but fails to accurately describe the dynamics of the density field for large $\gamma$

Supersonic strain front driven by a dense electron-hole plasma

We study coherent strain in (001) Ge generated by an ultrafast laser-initiated high density electron-hole plasma. The resultant coherent pulse is probed by time-resolved x-ray diffraction through changes in the anomalous transmission. The acoustic pulse front is driven by ambipolar diffusion of the electron-hole plasma and propagates into the crystal at supersonic speeds. Simulations of the strain including electron-phonon coupling, modified by carrier diffusion and Auger recombination, are in good agreement with the observed dynamics.Comment: 4 pages, 6 figure