scholarly journals Low-Energy Theorems, Dispersion Relations, and Superconvergence Sum Rules for Compton Scattering

1968 ◽  
Vol 165 (5) ◽  
pp. 1594-1609 ◽  
Author(s):  
Henry D. I. Abarbanel ◽  
Marvin L. Goldberger
Keyword(s):  
Compton Scattering ◽  
Sum Rules ◽  
Dispersion Relations ◽  
Low Energy

Exact Sum Rules as Consequences of Low-Energy Theorems and Unsubtracted Dispersion Relations

1966 ◽  
Vol 152 (4) ◽  
pp. 1286-1290 ◽  
Author(s):  
Ken Kawarabayashi ◽  
Walter W. Wada
Keyword(s):  
Sum Rules ◽  
Dispersion Relations ◽  
Low Energy

scholarly journals Generalized Kramers–Kronig relations and sum rules for moments and powers of degenerate four wave mixing susceptibility

2021 ◽  
Author(s):  
Jarkko J. Saarinen
Keyword(s):  
Sum Rules ◽  
Terahertz Spectroscopy ◽  
Theoretical Models ◽  
Present Theory ◽  
Four Wave Mixing ◽  
Dispersion Relations ◽  
Nonlinear Susceptibility ◽  
Complex Frequency ◽  
Wave Mixing ◽  
Degenerate Four Wave Mixing

AbstractGeneralized Kramers–Kronig (K–K) type dispersion relations and sum rules are derived in the static limit for the moments of the degenerate four wave mixing susceptibility. The degenerate nonlinear susceptibility is different from a typical use of the conventional K–K dispersion relations, which assume absence of complex poles of a function in the upper half of complex frequency plane, whereas degenerate susceptibility has simultaneous poles in both half planes. In the derivation of the generalized K–K relations the poles and their order are taken into account by utilization of the theorem of residues. The conventional K–K relations can be used to estimate the real and imaginary parts of the second and higher powers of the susceptibility as the effect of the poles is reduced due to a faster convergence of the dispersion relations. The present theory is directly applicable to higher order susceptibilities and can be used in testing of theoretical models describing the degenerate four wave mixing susceptibility in nonlinear optical and terahertz spectroscopy.

Derivative sum rules and inconsistencies in the low-energy N scattering parameters

1969 ◽  
Vol 11 (1) ◽  
pp. 115-126 ◽  
Author(s):  
N.M. Queen ◽  
S. Leeman ◽  
F.E. Yeomans
Keyword(s):  
Sum Rules ◽  
Low Energy ◽  
Scattering Parameters
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