scholarly journals Comment on the accuracy of Rabitz’ effective potential approximation for rotational excitation by collisions

1975 ◽  
Vol 62 (9) ◽  
pp. 3568 ◽  
Author(s):  
Sheldon Green
Keyword(s):  
Effective Potential ◽  
Rotational Excitation ◽  
Potential Approximation ◽  
Effective Potential Approximation

Diffusion-Controlled Reactions in Micellar Systems

1994 ◽  
Vol 366 ◽  
Author(s):  
Masanori Tachiya ◽  
Alexander V. Barzykin
Keyword(s):  
Reaction Kinetics ◽  
Stochastic Theory ◽  
Micellar Solutions ◽  
Dynamic Information ◽  
Potential Approximation ◽  
Guest Molecules ◽  
Micellar Systems ◽  
Diffusion Controlled ◽  
Effective Potential Approximation ◽  
General Method

ABSTRACTReaction kinetics in micellar solutions are studied theoretically with an emphasis on diffusioncontrolled luminescence quenching. Different spatial arrangements of reactants within individual micelles are analyzed and a general method for treating diffusion-controlled reactions in a finite volume employing an effective potential approximation is developed. Several models are considered for the exchange of reactants between micelles including migration mediated by the bulk phase and successive multiparticle hopping through transient channels connecting micelles during their sticky collisions. These results are combined in a general stochastic theory of reaction kinetics in micellar solutions with exchange. The theory is further extended to reactions in clusters of micelles using a continuous time random walk approach. Once the principal features of micellar kinetics are understood, one can extract important structural and dynamic information on the aggregates and their guest molecules by analyzing suitably designed experiments.

scholarly journals ONSET OF SYMMETRY BREAKING BY THE FUNCTIONAL RG METHOD

2011 ◽  
Vol 26 (07n08) ◽  
pp. 1327-1345 ◽  
Author(s):  
V. PANGON ◽  
S. NAGY ◽  
J. POLONYI ◽  
K. SAILER
Keyword(s):  
Symmetry Breaking ◽  
Field Dependence ◽  
Numerical Algorithm ◽  
Effective Potential ◽  
Local Potential ◽  
Potential Approximation ◽  
Numerical Accuracy ◽  
Singular Field ◽  
Local Potential Approximation

A numerical algorithm is used to solve the bare and the effective potential for the scalar ϕ4 model in the local potential approximation. An approximate dynamical Maxwell-cut is found which reveals itself in the degeneracy of the action for modes at some scale. This result indicates that the potential develop singular field dependence as far as one can see it by an algorithm of limited numerical accuracy.

scholarly journals A COMPARED ANALYSIS OF THE SUSCEPTIBILITY IN THE O(N) THEORY

2013 ◽  
Vol 28 (17) ◽  
pp. 1350078 ◽  
Author(s):  
VINCENZO BRANCHINA ◽  
EMANUELE MESSINA ◽  
DARIO ZAPPALÀ
Keyword(s):  
Renormalization Group ◽  
Numerical Analysis ◽  
Effective Potential ◽  
Renormalization Group Flow ◽  
Potential Approximation ◽  
Functional Renormalization Group ◽  
Flow Equations ◽  
Large N ◽  
Local Potential Approximation ◽  
Group Flow

The longitudinal susceptibility χL of the O(N) theory in the broken phase is analyzed by means of three different approaches, namely the leading contribution of the 1/N expansion, the Functional Renormalization Group flow in the Local Potential approximation and the improved effective potential via the Callan–Symanzik equations, properly extended to d = 4 dimensions through the expansion in powers of ϵ = 4-d. The findings of the three approaches are compared and their agreement in the large N limit is shown. The numerical analysis of the Functional Renormalization Group flow equations at small N supports the vanishing of [Formula: see text] in d = 3 and d = 3.5 but is not conclusive in d = 4, where we have to resort to the Callan–Smanzik approach. At finite N as well as in the limit N→∞, we find that [Formula: see text] vanishes with J as Jϵ/2 for ϵ> 0 and as ( ln (J))-1 in d = 4.

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