Symmetry-adapted correlation function for semiclassical quantization

2005 ◽  
Vol 122 (17) ◽  
pp. 174108 ◽  
Author(s):  
Koji Hotta ◽  
Kazuo Takatsuka
Keyword(s):  
Correlation Function ◽  
Semiclassical Quantization

Rate Constants, Reactive Flux

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Correlation Function ◽  
Rate Constant ◽  
Cross Sections ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Exact Expression ◽  
Reaction Cross ◽  
Dividing Surface ◽  
Definition Of ◽  
Reactive Flux

This chapter discusses a direct approach to the calculation of the rate constant k(T) that bypasses the detailed state-to-state reaction cross-sections. The method is based on the calculation of the reactive flux across a dividing surface on the potential energy surface. Versions based on classical as well as quantum mechanics are described. The classical version and its relation to Wigner’s variational theorem and recrossings of the dividing surface is discussed. Neglecting recrossings, an approximate result based on the calculation of the classical one-way flux from reactants to products is considered. Recrossings can subsequently be included via a transmission coefficient. An alternative exact expression is formulated based on a canonical average of the flux time-correlation function. It concludes with the quantum mechanical definition of the flux operator and the derivation of a relation between the rate constant and a flux correlation function.

scholarly journals Investigation of local maxima of the modified modular correlation function

2020 ◽  
Vol 1515 ◽  
pp. 042105
Author(s):  
D M Malinichev ◽  
E A Melnikova ◽  
Y V Prus
Keyword(s):  
Correlation Function ◽  
Local Maxima

A Rheo-optical Investigation into the Viscoelastic Moduli of Acidified Milk Gel

1999 ◽  
Vol 9 (6) ◽  
pp. 246-253 ◽  
Author(s):  
E. O. Arikainen ◽  
J. C. Earnshaw ◽  
A. Wehling ◽  
E. Waghorne
Keyword(s):  
Correlation Function ◽  
Mean Square Displacement ◽  
Slow Motion ◽  
Casein Micelle ◽  
Optical Investigation ◽  
Viscoelastic Moduli ◽  
Decay Times ◽  
Delay Times ◽  
Intensity Correlation Function ◽  
Viscoelastic Modulus

Abstract Diffusing wave spectroscopy (DWS) in the backscattering geometry was employed to observe the evolution of the intensity correlation function during the acidification of skimmed milk by gluconic-δ-lactone (GDL). At the stage when the formation of casein particle gel is largely complete the correlation function at shorter decay times reveals the local structural arrest of the casein micelles, whereas at longer delay times it illustrates the hindered slow motion of casein micelle aggregates. We use the principles of the approach suggested by Mason, Gang and Weitz, linking the optically measured mean square displacement, <Δr2(t)>, of the microscopic particles in a dense colloid to its viscoelastic properties, to provide an estimate of the frequency dependent viscoelastic modulus of the acidified milk gel (AMG). We compare the viscoelastic moduli measured by the conventional mechanical rheometry with the optically measured ones. The results of the two different experimental methods are found to be in reasonable agreement.

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