417,106 research outputs found

### Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators

We study the bulk-edge correspondence in topological insulators by taking
Fu-Kane spin pumping model as an example. We show that the Kane-Mele invariant
in this model is Z2 invariant modulo the spectral flow of a single-parameter
family of 1+1-dimensional Dirac operators with a global boundary condition
induced by the Kramers degeneracy of the system. This spectral flow is defined
as an integer which counts the difference between the number of eigenvalues of
the Dirac operator family that flow from negative to non-negative and the
number of eigenvalues that flow from non-negative to negative. Since the bulk
states of the insulator are completely gapped and the ground state is assumed
being no more degenerate except the Kramers, they do not contribute to the
spectral flow and only edge states contribute to. The parity of the number of
the Kramers pairs of gapless edge states is exactly the same as that of the
spectral flow. This reveals the origin of the edge-bulk correspondence, i.e.,
why the edge states can be used to characterize the topological insulators.
Furthermore, the spectral flow is related to the reduced eta-invariant and thus
counts both the discrete ground state degeneracy and the continuous gapless
excitations, which distinguishes the topological insulator from the
conventional band insulator even if the edge states open a gap due to a strong
interaction between edge modes. We emphasize that these results are also valid
even for a weak disordered and/or weak interacting system. The higher spectral
flow to categorize the higher-dimensional topological insulators are expected.Comment: 9 page, accepted for publication in Nucl Phys

### Effects of Quantum Hall Edge Reconstruction on Momenum-Resolved Tunneling

During the reconstruction of the edge of a quantum Hall liquid, Coulomb
interaction energy is lowered through the change in the structure of the edge.
We use theory developed earlier by one of the authors [K. Yang, Phys. Rev.
Lett. 91, 036802 (2003)] to calculate the electron spectral functions of a
reconstructed edge, and study the consequences of the edge reconstruction for
the momentum-resolved tunneling into the edge. It is found that additional
excitation modes that appear after the reconstruction produce distinct features
in the energy and momentum dependence of the spectral function, which can be
used to detect the presence of edge reconstruction

### Electron Spectral Functions of Reconstructed Quantum Hall Edges

During the reconstruction of the edge of a quantum Hall liquid, Coulomb
interaction energy is lowered through the change in the structure of the edge.
We use theory developed earlier by one of the authors [K. Yang, Phys. Rev.
Lett. 91, 036802 (2003)] to calculate the electron spectral functions of a
reconstructed edge, and study the consequences of the edge reconstruction for
the momentum-resolved tunneling into the edge. It is found that additional
excitation modes that appear after the reconstruction produce distinct features
in the energy and momentum dependence of the spectral function, which can be
used to detect the presence of edge reconstruction.Comment: RevTeX, 5 pages, 4 figures; replaced with the published version;
journal reference adde

### Braess's paradox for the spectral gap in random graphs and delocalization of eigenvectors

We study how the spectral gap of the normalized Laplacian of a random graph
changes when an edge is added to or removed from the graph. There are known
examples of graphs where, perhaps counterintuitively, adding an edge can
decrease the spectral gap, a phenomenon that is analogous to Braess's paradox
in traffic networks. We show that this is often the case in random graphs in a
strong sense. More precisely, we show that for typical instances of
Erd\H{o}s-R\'enyi random graphs $G(n,p)$ with constant edge density $p \in
(0,1)$, the addition of a random edge will decrease the spectral gap with
positive probability, strictly bounded away from zero. To do this, we prove a
new delocalization result for eigenvectors of the Laplacian of $G(n,p)$, which
might be of independent interest.Comment: Version 2, minor change

### Magnetic edge states

Magnetic edge states are responsible for various phenomena of
magneto-transport. Their importance is due to the fact that, unlike the bulk of
the eigenstates in a magnetic system, they carry electric current along the
boundary of a confined domain. Edge states can exist both as interior (quantum
dot) and exterior (anti-dot) states. In the present report we develop a
consistent and practical spectral theory for the edge states encountered in
magnetic billiards. It provides an objective definition for the notion of edge
states, is applicable for interior and exterior problems, facilitates efficient
quantization schemes, and forms a convenient starting point for both the
semiclassical description and the statistical analysis. After elaborating these
topics we use the semiclassical spectral theory to uncover nontrivial spectral
correlations between the interior and the exterior edge states. We show that
they are the quantum manifestation of a classical duality between the
trajectories in an interior and an exterior magnetic billiard.Comment: 170 pages, 48 figures (high quality version available at
http://www.klaus-hornberger.de

### Spectral edge regularity of magnetic Hamiltonians

We analyse the spectral edge regularity of a large class of magnetic
Hamiltonians when the perturbation is generated by a globally bounded magnetic
field. We can prove Lipschitz regularity of spectral edges if the magnetic
field perturbation is either constant or slowly variable. We also recover an
older result by G. Nenciu who proved Lipschitz regularity up to a logarithmic
factor for general globally bounded magnetic field perturbations.Comment: 18 pages, submitte

### Assessment of AVIRIS data from vegetated sites in the Owens Valley, California

Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data were acquired from the Bishop, CA area, located at the northern end of the Owens Valley, on July 30, 1987. Radiometrically-corrected AVIRIS data were flat-field corrected, and spectral curves produced and analyzed for pixels taken from both native and cultivated vegetation sites, using the JPS SPAM software program and PC-based spreadsheet programs. Analyses focussed on the chlorophyll well and red edge portions of the spectral curves. Results include the following: AVIRIS spectral data are acquired at sufficient spectral resolution to allow detection of blue shifts of both the chlorophyll well and red edge in moisture-stressed vegetation when compared with non-stressed vegetation; a normalization of selected parameters (chlorophyll well and near infrared shoulder) may be used to emphasize the shift in red edge position; and the presence of the red edge in AVIRIS spectral curves may be useful in detecting small amounts (20 to 30 pct cover) of semi-arid and arid vegetation ground cover. A discussion of possible causes of AVIRIS red edge shifts in respsonse to stress is presented

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