50,265 research outputs found
Maximally-localized generalized Wannier functions for composite energy bands
We discuss a method for determining the optimally-localized set of
generalized Wannier functions associated with a set of Bloch bands in a
crystalline solid. By ``generalized Wannier functions'' we mean a set of
localized orthonormal orbitals spanning the same space as the specified set of
Bloch bands. Although we minimize a functional that represents the total spread
sum_n [ _n - _n^2 ] of the Wannier functions in real space, our method
proceeds directly from the Bloch functions as represented on a mesh of
k-points, and carries out the minimization in a space of unitary matrices
U_mn^k describing the rotation among the Bloch bands at each k-point. The
method is thus suitable for use in connection with conventional
electronic-structure codes. The procedure also returns the total electric
polarization as well as the location of each Wannier center. Sample results for
Si, GaAs, molecular C2H4, and LiCl will be presented.Comment: 22 pages, two-column style with 4 postscript figures embedded. Uses
REVTEX and epsf macros. Also available at
http://www.physics.rutgers.edu/~dhv/preprints/index.html#nm_wan
Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians
Quantum recurrence and dynamic localization are investigated in a class of
ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in
the undriven case provides a paradigmatic Hamiltonian model that realizes
perfect quantum state transfer and mirror inversion. The equivalence between
the the ac-driven single-particle Krawtchouk Hamiltonian and the
non-interacting ac-driven bosonic junction Hamiltonian enables to determine in
a closed form the quasi energy spectrum of and the conditions for
exact wave packet reconstruction (dynamic localization). In particular, we show
that quantum recurrence, which is predicted by the general quantum recurrence
theorem, is {\it exact} for the Krawtchouk quantum chain in a dense range of
the driving amplitude. Exact quantum recurrence provides perfect wave packet
reconstruction at a frequency which is {\it fractional} than the driving
frequency, a phenomenon that can be referred to as fractional dynamic
localization.Comment: 4 figures, to appear in Annals of Physic
Holographic particle localization under multiple scattering
We introduce a novel framework that incorporates multiple scattering for
large-scale 3D particle-localization using single-shot in-line holography.
Traditional holographic techniques rely on single-scattering models which
become inaccurate under high particle-density. We demonstrate that by
exploiting multiple-scattering, localization is significantly improved. Both
forward and back-scattering are computed by our method under a tractable
recursive framework, in which each recursion estimates the next higher-order
field within the volume. The inverse scattering is presented as a nonlinear
optimization that promotes sparsity, and can be implemented efficiently. We
experimentally reconstruct 100 million object voxels from a single 1-megapixel
hologram. Our work promises utilization of multiple scattering for versatile
large-scale applications
Non-equilibrium delocalization-localization transition of photons in circuit QED
We show that photons in two tunnel-coupled microwave resonators each
containing a single superconduct- ing qubit undergo a sharp non-equilibrium
delocalization-localization (self-trapping) transition due to strong
photon-qubit coupling. We find that dissipation favors the self-trapped regime
and leads to the possibility of observing the transition as a function of time
without tuning any parameter of the system. Furthermore, we find that
self-trapping of photons in one of the resonators (spatial localization) forces
the qubit in the opposite resonator to remain in its initial state (energetic
localization). This allows for an easy experimental observation of the
transition by local read-out of the qubit state.Comment: 4 pages, 5 figure
Shear band dynamics from a mesoscopic modeling of plasticity
The ubiquitous appearance of regions of localized deformation (shear bands)
in different kinds of disordered materials under shear is studied in the
context of a mesoscopic model of plasticity. The model may or may not include
relaxational (aging) effects. In the absence of relaxational effects the model
displays a monotonously increasing dependence of stress on strain-rate, and
stationary shear bands do not occur. However, in start up experiments transient
(although long lived) shear bands occur, that widen without bound in time. I
investigate this transient effect in detail, reproducing and explaining a t^1/2
law for the thickness increase of the shear band that has been obtained in
atomistic numerical simulations. Relaxation produces a negative sloped region
in the stress vs. strain-rate curve that stabilizes the formation of shear
bands of a well defined width, which is a function of strain-rate. Simulations
at very low strain-rates reveal a non-trivial stick-slip dynamics of very thin
shear bands that has relevance in the study of seismic phenomena. In addition,
other non-stationary processes, such as stop-and-go, or strain-rate inversion
situations display a phenomenology that matches very well the results of recent
experimental studies.Comment: 10 pages, 10 figure
Observation of surface states with algebraic localization
We introduce and experimentally demonstrate a class of surface bound states
with algebraic decay in a one-dimensional tight-binding lattice. Such states
have an energy embedded in the spectrum of scattered states and are
structurally stable against perturbations of lattice parameters. Experimental
demonstration of surface states with algebraic localization is presented in an
array of evanescently-coupled optical waveguides with tailored coupling rates.Comment: revised version with Supplemental Material, to appear in Phys. Rev.
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Identification of high-permeability subsurface structures with multiple point geostatistics and normal score ensemble Kalman filter
Alluvial aquifers are often characterized by the presence of braided high-permeable paleo-riverbeds, which constitute an interconnected preferential flow network whose localization is of fundamental importance to predict flow and transport dynamics. Classic geostatistical approaches based on two-point correlation (i.e., the variogram) cannot describe such particular shapes. In contrast, multiple point geostatistics can describe almost any kind of shape using the empirical probability distribution derived from a training image. However, even with a correct training image the exact positions of the channels are uncertain. State information like groundwater levels can constrain the channel positions using inverse modeling or data assimilation, but the method should be able to handle non-Gaussianity of the parameter distribution. Here the normal score ensemble Kalman filter (NS-EnKF) was chosen as the inverse conditioning algorithm to tackle this issue. Multiple point geostatistics and NS-EnKF have already been tested in synthetic examples, but in this study they are used for the first time in a real-world casestudy. The test site is an alluvial unconfined aquifer in northeastern Italy with an extension of approximately 3 km2. A satellite training image showing the braid shapes of the nearby river and electrical resistivity tomography (ERT) images were used as conditioning data to provide information on channel shape, size, and position. Measured groundwater levels were assimilated with the NS-EnKF to update the spatially distributed groundwater parameters (hydraulic conductivity and storage coefficients). Results from the study show that the inversion based on multiple point geostatistics does not outperform the one with a multiGaussian model and that the information from the ERT images did not improve site characterization. These results were further evaluated with a synthetic study that mimics the experimental site. The synthetic results showed that only for a much larger number of conditioning piezometric heads, multiple point geostatistics and ERT could improve aquifer characterization. This shows that state of the art stochastic methods need to be supported by abundant and high-quality subsurface data
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