SCATTERING THEORY FOR LATTICE OPERATORS IN DIMENSION d ≥ 3

This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed Hamiltonian. For dimension d ≥ 3, the wave operator is given by an explicit formula in terms of this dilation operator, the free resolvent and the perturbation. From this formula, the scattering and time delay operators can be read off. Using the index theorem approach, a Levinson theorem is proved which also holds in the presence of embedded eigenvalues and threshold singularities.

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Electronic Structure of Aluminum Surfaces. Results from Empirical Tight-Binding Scattering Theory

physica status solidi (b) ◽

10.1002/pssb.2221790215 ◽

1993 ◽

Vol 179 (2) ◽

pp. 399-410 ◽

Cited By ~ 3

Author(s):

K. Würde ◽

A. Mazur ◽

J. Pollmann

Keyword(s):

Electronic Structure ◽

Scattering Theory ◽

Tight Binding ◽

Aluminum Surfaces

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Levinson’s Theorem: An Index Theorem in Scattering Theory

Operator Theory: Advances and Applications - Spectral Theory and Mathematical Physics ◽

10.1007/978-3-319-29992-1_9 ◽

2016 ◽

pp. 149-203 ◽

Cited By ~ 2

Author(s):

S. Richard

Keyword(s):

Scattering Theory ◽

Index Theorem ◽

Levinson’S Theorem

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The Green Function Cellular Method and Its Relation to Multiple Scattering Theory

MRS Proceedings ◽

10.1557/proc-253-205 ◽

1991 ◽

Vol 253 ◽

Cited By ~ 3

Author(s):

W. H. Butler ◽

X.-G Zhang ◽

A. Gonis

Keyword(s):

Multiple Scattering ◽

Scattering Theory ◽

Nearest Neighbor ◽

Tight Binding ◽

Full Potential ◽

Multiple Scattering Theory ◽

Secular Matrix ◽

The Green Function ◽

Cellular Method ◽

Structure Calculations

ABSTRACTWe investigate techniques for solving the wave equation which are based on the idea of obtaining exact local solutions within each potential cell, which are then joined to form a global solution. We derive full potential multiple scattering theory (MST) from the Lippmann-Schwinger equation and show that it as well as a closely related cellular method are techniques of this type. This cellular method appears to have all of the advantages of MST and the added advantage of having a secular matrix with only nearest neighbor interactions. Since this cellular method is easily linearized one can rigorously reduce electronic structure calculations to the problem of solving a nearest neighbor tight-binding problem.

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An extension to the Morse energy gradient flow

Mean Curvature Flow ◽

10.1515/9783110618365-004 ◽

2020 ◽

pp. 67-70

Keyword(s):

Gradient Flow ◽

Energy Gradient

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Relation between tight-binding and scattering theory for overlapping potentials

Journal of Physics C Solid State Physics ◽

10.1088/0022-3719/12/15/006 ◽

1979 ◽

Vol 12 (15) ◽

pp. 2965-2975 ◽

Cited By ~ 3

Author(s):

C H Hodges

Keyword(s):

Scattering Theory ◽

Tight Binding

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Southern Hemisphere Seti Survey: Five Years of Project Meta II

International Astronomical Union Colloquium ◽

10.1017/s0252921100015153 ◽

1997 ◽

Vol 161 ◽

pp. 611-621

Author(s):

Guillermo A. Lemarchand ◽

Fernando R. Colomb ◽

E. Eduardo Hurrell ◽

Juan Carlos Olalde

Keyword(s):

Southern Hemisphere ◽

Scattering Theory ◽

Galactic Plane ◽

Narrow Band ◽

Neutral Hydrogen ◽

Sky Survey ◽

Inertial Frames ◽

Interstellar Scattering ◽

Extraterrestrial Origin ◽

Spectral Channels

AbstractProject META II, a full sky survey for artificial narrow-band signals, has been conducted from one of the two 30-m radiotelescopes of the Instituto Argentino de Radioastronomía (IAR). The search was performed near the 1420 Mhz line of neutral hydrogen, using a 8.4 million channels Fourier spectrometer of 0.05 Hz resolution and 400 kHz instantaneous bandwidth. The observing frequency was corrected both for motions with respect to three astronomical inertial frames, and for the effect of Earths rotation, which provides a characteristic changing signature for narrow-band signals of extraterrestrial origin. Among the 2 × 1013spectral channels analyzed, 29 extra-statistical narrow-band events were found, exceeding the average threshold of 1.7 × 10−23Wm−2. The strongest signals that survive culling for terrestrial interference lie in or near the galactic plane. A description of the project META II observing scheme and results is made as well as the possible interpretation of the results using the Cordes-Lazio-Sagan model based in interstellar scattering theory.

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Dynamical Scattering in Electron Diffraction of wet Protein Crystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s1431927600000167 ◽

1980 ◽

Vol 38 ◽

pp. 42-43

Author(s):

B. B. Chang ◽

D. F. Parsons

Keyword(s):

Electron Diffraction ◽

Scattering Theory ◽

Protein Crystals ◽

Electron Diffraction Data ◽

Specimen Thickness ◽

Major Question ◽

X Ray ◽

Scattering Effects ◽

Diffraction Patterns ◽

Acceleration Voltage

The significance of dynamical scattering effects remains the major question in the structural analysis by electron diffraction of protein crystals preserved in the hydrated state. In the few cases (single layers of purple membrane and 400-600 Å thick catalase crystals examined at 100 kV acceleration voltage) where electron-diffraction patterns were used quantitatively, dynamical scattering effects were considered unimportant on the basis of a comparison with x-ray intensities. The kinematical treatment is usually justified by the thinness of the crystal. A theoretical investigation by Ho et al. using Cowley-Moodie multislice formulation of dynamical scattering theory and cytochrome b5as the test object2 suggests that kinematical analysis of electron diffraction data with 100-keV electrons would not likely be valid for specimen thickness of 300 Å or more. We have chosen to work with electron diffraction patterns obtained from actual wet protein crystals (rat hemoglobin crystals of thickness range 1000 to 2500 Å) at 200 and 1000 kV and to analyze these for dynamical effects.

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