Analytical expressions for the high-order Herman–Wallis coefficients of a diatomic molecule

1997 ◽  
Vol 75 (11) ◽  
pp. 795-804 ◽  
Author(s):  
M Korek
Keyword(s):  
Diatomic Molecule ◽  
High Order ◽  
Analytical Expressions

High-order expanded XAFS Debye–Waller factors of HCP crystals based on classical anharmonic correlated Einstein model

2014 ◽  
Vol 28 (21) ◽  
pp. 1450174 ◽  
Author(s):  
Nguyen Van Hung ◽  
Tong Sy Tien ◽  
Ngyen Ba Duc ◽  
Dinh Quoc Vuong
Keyword(s):  
Effective Potential ◽  
Interatomic Interaction ◽  
High Order ◽  
Cumulant Expansion ◽  
X Ray ◽  
Einstein Model ◽  
Atomic Vibrations ◽  
X Ray Absorption ◽  
Analytical Expressions ◽  
Good Agreement

In this paper, high-order expanded anharmonic effective potential and Debye–Waller factors in X-ray absorption fine structure (XAFS) of hcp crystals have been studied based on classical anharmonic correlated Einstein model. Here XAFS Debye–Waller factors are presented in terms of cumulant expansion up to the fourth order and their analytical expressions have been derived based on classical statistical theory. They contain the parameters of a derived high-order anharmonic effective potential that takes into account all nearest neighbors of absorber and backscattering atoms, where Morse potential is assumed to describe interatomic interaction included in this derived anharmonic effective potential. The dependence of the derived cumulants on atomic vibrations is described by their proportionality to the correlated Einstein frequency. This model avoids full lattice dynamical calculations yet provides good agreement of numerical results for Zn and Cd with experiment at several temperatures.

HIGH-ORDER PHOTON-NUMBER CORRELATIONS: A RESOURCE FOR CHARACTERIZATION AND APPLICATIONS OF QUANTUM STATES

2012 ◽  
Vol 10 (08) ◽  
pp. 1241003 ◽  
Author(s):  
ALESSIA ALLEVI ◽  
STEFANO OLIVARES ◽  
MARIA BONDANI
Keyword(s):  
Correlation Functions ◽  
Photon Number ◽  
High Order ◽  
Quantum States ◽  
Quantum Behavior ◽  
Twin Beam ◽  
High Order Correlation ◽  
Analytical Expressions ◽  
Good Agreement ◽  
Classical States

We measure high-order correlation functions of detected-photon numbers in the mesoscopic regime by means of hybrid photodetectors. The analytical expressions for correlations are evaluated in terms of quantities that can be experimentally accessed by a selfconsistent analysis of the detectors' outputs. We demonstrate that high-order correlations can be used to characterize the nature of the optical states, for instance by better discriminating between classical and quantum behavior even in critical situations, such as multimode twin-beam state. The results are in very good agreement with the theory, both for classical states and quantum states.

Ondes electromagnétiques de surface en géométrie cylindrique. Les modes de révolution d'ordre supérieur

1985 ◽  
Vol 63 (5) ◽  
pp. 567-573
Author(s):  
G. Zepp ◽  
A. Wick ◽  
G. Ritoux ◽  
G. Fabre ◽  
M. Billaud
Keyword(s):  
Surface Wave ◽  
Attenuation Factor ◽  
High Order ◽  
Cross Sectional ◽  
Electromagnetic Surface Wave ◽  
Metallic Cylinder ◽  
Analytical Expressions ◽  
Wave Modes ◽  
The Revolution

We have studied the revolution electromagnetic surface wave modes of high order (TM, TE) propagating at the surface of a circular cross-sectional metallic cylinder coated with two dielectrics. We have determined precise analytical expressions of attenuation factor and power localization ratio.

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