Asymptotic completeness of N-body wave operators II. A new proof for the short-range case and the asymptotic clustering for long-range systems

1993 ◽  
pp. 149-189 ◽  
Author(s):  
Hitoshi Kitada
Keyword(s):  
Long Range ◽  
Short Range ◽  
Body Wave ◽  
Asymptotic Completeness ◽  
Wave Operators

scholarly journals Spectral and scattering theory for Schrödinger operators on perturbed topological crystals

2018 ◽  
Vol 30 (04) ◽  
pp. 1850009 ◽  
Author(s):  
D. Parra ◽  
S. Richard
Keyword(s):  
Scattering Theory ◽  
Short Range ◽  
Schrödinger Operators ◽  
Multiplication Operator ◽  
Asymptotic Completeness ◽  
Schrodinger Operators ◽  
Wave Operators ◽  
Range Function ◽  
Range Type ◽  
Local Wave

In this paper, we investigate the spectral and the scattering theory of Schrödinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or a long-range function, or a short-range type modification of the measure defined on the vertices and on the edges of the graph. Mourre theory is used for describing the nature of the spectrum of the underlying operators. For short-range perturbations, existence and asymptotic completeness of local wave operators are also proved.

scholarly journals Structural basis of long-range to short-range synaptic transition in NHEJ

Nature ◽  
2021 ◽  
Author(s):  
Siyu Chen ◽  
Linda Lee ◽  
Tasmin Naila ◽  
Susan Fishbain ◽  
Annie Wang ◽  
...  
Keyword(s):  
Long Range ◽  
Short Range ◽  
Structural Basis

scholarly journals Comparison of short-range order in irradiated dysprosium titanates

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Roman Sherrod ◽  
Eric C. O’Quinn ◽  
Igor M. Gussev ◽  
Cale Overstreet ◽  
Joerg Neuefeind ◽  
...  
Keyword(s):  
Long Range ◽  
Short Range ◽  
Structural Model ◽  
Ion Irradiation ◽  
Function Analysis ◽  
Ion Beam ◽  
Structural Response ◽  
Heavy Ion ◽  
Range Order ◽  
Radiation Resistant

AbstractThe structural response of Dy2TiO5 oxide under swift heavy ion irradiation (2.2 GeV Au ions) was studied over a range of structural length scales utilizing neutron total scattering experiments. Refinement of diffraction data confirms that the long-range orthorhombic structure is susceptible to ion beam-induced amorphization with limited crystalline fraction remaining after irradiation to 8 × 1012 ions/cm2. In contrast, the local atomic arrangement, examined through pair distribution function analysis, shows only subtle changes after irradiation and is still described best by the original orthorhombic structural model. A comparison to Dy2Ti2O7 pyrochlore oxide under the same irradiation conditions reveals a different behavior: while the dysprosium titanate pyrochlore is more radiation resistant over the long-range with smaller degree of amorphization as compared to Dy2TiO5, the former involves more local atomic rearrangements, best described by a pyrochlore-to-weberite-type transformation. These results highlight the importance of short-range and medium-range order analysis for a comprehensive description of radiation behavior.

SHORT-RANGE AND LONG-RANGE ORDER OF TITANIUM IN Ti1+xS2

1977 ◽  
Vol 38 (C7) ◽  
pp. C7-202-C7-206 ◽  
Author(s):  
R. MORET ◽  
M. HUBER ◽  
R. COMÈS
Keyword(s):  
Long Range ◽  
Short Range ◽  
Range Order ◽  
Long Range Order

scholarly journals Short range smectic order driving long range nematic order: example of cuprates

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
R. S. Markiewicz ◽  
J. Lorenzana ◽  
G. Seibold ◽  
A. Bansil
Keyword(s):  
Long Range ◽  
Short Range ◽  
Nematic Order

ANDERSON LOCALIZATION FOR A MULTIDIMENSIONAL MODEL INCLUDING LONG RANGE POTENTIALS AND DISPLACEMENTS

2002 ◽  
Vol 14 (03) ◽  
pp. 273-302 ◽  
Author(s):  
HERIBERT ZENK
Keyword(s):  
Long Range ◽  
Anderson Model ◽  
Anderson Localization ◽  
Short Range ◽  
Energy Interval ◽  
Multidimensional Model ◽  
Short Summary

We give a short summary on how to combine and extend results of Combes and Hislop [2] (short range Anderson model with additional displacements), Kirsch, Stollmann and Stolz [13] and [14] (long range Anderson model without displacements) to get localization in an energy interval above the infimum of the almost sure spectrum for a continuous multidimensional Anderson model including long range potentials and displacements.

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