X-ray-edge problem in metals. I. Universal scaling in alkali-alkali alloys

1985 ◽  
Vol 32 (2) ◽  
pp. 588-601 ◽  
Author(s):  
T.-H. Chiu ◽  
Doon Gibbs ◽  
J. E. Cunningham ◽  
C. P. Flynn
Keyword(s):  
X Ray ◽  
Universal Scaling ◽  
Edge Problem

Noncanonical-transformation approach to the x-ray-edge problem

1991 ◽  
Vol 44 (11) ◽  
pp. 5877-5880 ◽  
Author(s):  
Ilias E. Perakis ◽  
Yia-Chung Chang
Keyword(s):  
X Ray ◽  
Edge Problem ◽  
Transformation Approach

X-Ray Edge Problem with Finite Hole Mass

1971 ◽  
Vol 4 (12) ◽  
pp. 4315-4318 ◽  
Author(s):  
G. Yuval
Keyword(s):  
X Ray ◽  
Edge Problem

Fine-structure correction in the x-ray-edge problem

1974 ◽  
Vol 10 (2) ◽  
pp. 529-534 ◽  
Author(s):  
Pierre Longe
Keyword(s):  
Fine Structure ◽  
X Ray ◽  
Edge Problem

scholarly journals Fractal x-ray edge problem at the critical point of the Aubry-André model

2019 ◽  
Vol 100 (16) ◽  
Author(s):  
Ang-Kun Wu ◽  
Sarang Gopalakrishnan ◽  
J. H. Pixley
Keyword(s):  
Critical Point ◽  
X Ray ◽  
Edge Problem

scholarly journals Wiener–Hopf Method Applied to the X-ray Edge Problem

1997 ◽  
Vol 11 (29) ◽  
pp. 3433-3453 ◽  
Author(s):  
V. Janiš
Keyword(s):  
Integral Equations ◽  
Time Limit ◽  
Time Interval ◽  
Infinite Time ◽  
Effective Lifetime ◽  
X Ray ◽  
Edge Problem ◽  
Long Time ◽  
The Difference ◽  
Hopf Method

We apply the Wiener–Hopf method of solving convolutive integral equations on a semi-infinite interval to the X-ray edge problem. Dyson equations for basic Green functions from the X-ray problem are rewritten as convolutive integral equations on a time-interval [0,t] with t→∞. The long-time asymptotics of solutions to these equations is derived with the aid of the Wiener–Hopf method. Although the Wiener–Hopf long-time exponents differ by a factor of two from the solution of Nozières and De Dominicis we demonstrate how the latter and the critical exponents of measurable amplitudes from the X-ray problem can be derived from the former. We explain that the difference in the exponents arises due to different ways of performing the long-time limit in the two solutions. To enable the infinite-time limit in the defining equations a new infinite-time scale τ→∞, interpreted as an effective lifetime of the core-hole, must be introduced. The ratio t/τ decides about the resulting critical exponent. The physical relevance of the Nozières and De Dominicis as well as of the Wiener–Hopf exponents is discussed.

scholarly journals Many-Body Effects in the Mesoscopic x-Ray Edge Problem

2007 ◽  
Vol 166 ◽  
pp. 143-151 ◽  
Author(s):  
Martina Hentschel ◽  
Georg Röder ◽  
Denis Ullmo
Keyword(s):  
Many Body ◽  
X Ray ◽  
Edge Problem ◽  
Many Body Effects
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