Asymptotic behaviour of nonlocal effective potentials in two-cluster atomic scattering

1985 ◽  
Vol 63 (10) ◽  
pp. 1353-1356
Author(s):  
T. F. Treml
Keyword(s):  
Asymptotic Behaviour ◽  
Effective Potential ◽  
Nonlocal Potential ◽  
Effective Potentials ◽  
Cluster Threshold ◽  
Atomic Scattering ◽  
Coulomb Potentials

Dilation and boost transformations are used to study the nonlocal effective potentials in two-cluster atomic scattering below the lowest three-cluster threshold, where the particles interact via two-body Coulomb potentials and at least one cluster is neutral. Boost analyticity is used to express the rotated potential in a form that displays explicitly its behaviour for large values of the cluster separation. When one cluster is neutral, the nonlocal effective potential falls off, in some sense, as r−4 for large values of r, where r is the distance between the centres of mass of the two clusters. When both clusters are neutral, the nonlocal potential can be shown to fall off as r−5 for large values of r.

Existence of partial-wave two-cluster atomic scattering amplitudes

1979 ◽  
Vol 57 (3) ◽  
pp. 449-456 ◽  
Author(s):  
J. Nuttall ◽  
S. R. Singh
Keyword(s):  
Scattering Amplitudes ◽  
Partial Wave ◽  
Scattering Problem ◽  
Potential Scattering ◽  
Atomic Systems ◽  
Almost Everywhere ◽  
Cluster Threshold ◽  
Channel Potential ◽  
Atomic Scattering ◽  
Coupled Channel

It is shown, with some restrictions, that two-cluster partial wave scattering amplitudes for atomic systems whose particles interact via two-body Coulomb potentials exist almost everywhere in the energy range below any three-cluster threshold. The method of proof is to reduce the problem to a coupled channel potential scattering problem with pseudo-local potentials. Boost analyticity is used to derive the pseudo-locality.

scholarly journals Self-interaction-corrected Kohn–Sham effective potentials using the density-consistent effective potential method

2021 ◽  
Vol 155 (6) ◽  
pp. 064109
Author(s):  
Carlos M. Diaz ◽  
Luis Basurto ◽  
Santosh Adhikari ◽  
Yoh Yamamoto ◽  
Adrienn Ruzsinszky ◽  
...  
Keyword(s):  
Effective Potential ◽  
Potential Method ◽  
Effective Potentials

scholarly journals Influence of the Effective Potential on the Crossover Width in the Two Flavor Polyakov-Nambu-Jona-Lasinio Model

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
E. Valbuena-Ordóñez ◽  
N. B. Mata-Carrizal ◽  
A. J. Garza-Aguirre ◽  
J. R. Morones-Ibarra
Keyword(s):  
Phase Diagram ◽  
Phase Diagrams ◽  
Effective Potential ◽  
Crossover Region ◽  
Effective Potentials ◽  
End Point ◽  
Strongly Interacting ◽  
Njl Model ◽  
Matter Phase

We study the strongly interacting matter phase diagram on the T−μ plane through the two flavor Polyakov extended NJL model. We compare the phase diagrams obtained from three different effective potentials, focusing on the behavior of the width of the crossover region and the critical end point for each case. We describe various susceptibilities to obtain the chiral crossover and the color deconfinement crossover.

scholarly journals Field statistics in nonlinear composites. I. Theory

2006 ◽  
Vol 463 (2077) ◽  
pp. 183-202 ◽  
Author(s):  
Martín I Idiart ◽  
Pedro Ponte Castañeda
Keyword(s):  
Effective Potential ◽  
Second Order ◽  
Local Fields ◽  
Two Phase ◽  
Effective Potentials ◽  
Second Moments ◽  
Local Potentials ◽  
Homogenization Methods ◽  
Derivatives Of ◽  
Nonlinear Composites

This work presents a means for extracting the statistics of the local fields in nonlinear composites from the effective potential of suitably perturbed composites. The idea is to introduce a parameter in the local potentials, generally a tensor, such that differentiation of the corresponding effective potential with respect to the parameter yields the volume average of the desired quantity. In particular, this provides a generalization to the nonlinear case of well-known formulas in the context of linear composites, which express phase averages and second moments of the local fields in terms of derivatives of the effective potential. Such expressions are useful since they allow the generation of estimates for the field statistics in nonlinear composites, directly from homogenization estimates for appropriately defined effective potentials. Here, use is made of these expressions in the context of the ‘variational’, ‘tangent second-order’ and ‘second-order’ homogenization methods, to obtain rigorous estimates for the first and second moments of the fields in nonlinear composites. While the variational estimates for these quantities are found to be identical to those proposed in previous works, the tangent second-order and second-order estimates are found be different. In particular, the new estimates for the first moments given in this work are found to be entirely consistent with the corresponding estimates for the macroscopic behaviour. Sample results for two-phase, power-law composites are provided in part II of this work.

scholarly journals Minima of classically scale-invariant potentials

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Kristjan Kannike ◽  
Kaius Loos ◽  
Luca Marzola
Keyword(s):  
Standard Model ◽  
Effective Potential ◽  
Stationary Point ◽  
Mass Matrix ◽  
Tensor Algebra ◽  
Scale Invariant ◽  
New Formalism ◽  
Effective Potentials ◽  
Point Equation ◽  
Carry Over

Abstract We propose a new formalism to analyse the extremum structure of scale-invariant effective potentials. The problem is stated in a compact matrix form, used to derive general expressions for the stationary point equation and the mass matrix of a multi-field RG-improved effective potential. Our method improves on (but is not limited to) the Gildener-Weinberg approximation and identifies a set of conditions that signal the presence of a radiative minimum. When the conditions are satisfied at different scales, or in different subspaces of the field space, the effective potential has more than one radiative minimum. We illustrate the method through simple examples and study in detail a Standard-Model-like scenario where the potential admits two radiative minima. Whereas we mostly concentrate on biquadratic potentials, our results carry over to the general case by using tensor algebra.

EFFECTIVE POTENTIALS FOR ϕ4-THEORY IN 2+1 DIMENSIONS

1994 ◽  
Vol 09 (28) ◽  
pp. 2623-2635 ◽  
Author(s):  
R.A. OLSEN ◽  
F. RAVNDAL
Keyword(s):  
Transition Temperature ◽  
Symmetry Breaking ◽  
Effective Potential ◽  
Gaussian Approximation ◽  
Critical Value ◽  
Zero Temperature ◽  
Coupling Constant ◽  
Effective Potentials ◽  
Bare Coupling Constant ◽  
Symmetric Phase

Spontaneous symmetry breaking in ϕ4-theory in 2+1 dimensions is investigated using the Gaussian approximation. The theory stays in the symmetric phase at zero temperature as long as the bare coupling constant is below a critical value λc. When λ>λc the symmetric phase is again stable when the temperature is above a transition temperature T(λ). The obtained results are compared with the predictions of the standard one-loop effective potential.

RG IMPROVEMENT OF THE EFFECTIVE POTENTIAL AT FINITE TEMPERATURE

1996 ◽  
Vol 11 (28) ◽  
pp. 2259-2269 ◽  
Author(s):  
HISAO NAKKAGAWA ◽  
HIROSHI YOKOTA
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Finite Temperature ◽  
Renormalization Group Equation ◽  
Effective Procedure ◽  
Coefficient Function ◽  
Group Equation ◽  
Leading Order ◽  
Effective Potentials ◽  
The One

We present a simple and effective procedure to improve the finite temperature effective potential so as to satisfy the renormalization group equation (RGE). With the L-loop knowledge of the effective potential and of the RGE coefficient function, this procedure carries out a systematic resummation of large-T as well as large-log terms up to the Lth-to-leading order, giving an improved effective potential which satisfies the RGE and is exact up to the Lth-to-leading T and log terms. Applications to the one- and two-loop effective potentials are explicitly performed.

scholarly journals SELF-INTERACTING SCALAR FIELDS ON SPACE-TIME WITH COMPACT HYPERBOLIC SPATIAL PART

1993 ◽  
Vol 08 (21) ◽  
pp. 2011-2021 ◽  
Author(s):  
ANDREI BYTSENKO ◽  
KLAUS KIRSTEN ◽  
SERGEI ODINTSOV
Keyword(s):  
Phase Transitions ◽  
Scalar Field ◽  
Effective Potential ◽  
Discrete Group ◽  
Scalar Fields ◽  
Space Time ◽  
Selberg Trace Formula ◽  
Effective Potentials ◽  
Spatial Part ◽  
The One

We calculate the one-loop effective potential of a self-interacting scalar field on the space-time of the form ℝ2×H2/Γ. The Selberg trace formula associated with a co-compact discrete group Γ in PSL(2, ℝ) (hyperbolic and elliptic elements only) is used. The closed form for the one-loop unrenormalized and renormalized effective potentials is given. The influence of non-trivial topology on curvature induced phase transitions is also discussed.

scholarly journals A new way of calculating the effective potential for a light radion

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
J.M. Lizana ◽  
M. Olechowski ◽  
S. Pokorski
Keyword(s):  
Critical Temperature ◽  
Effective Potential ◽  
Effective Action ◽  
Equations Of Motion ◽  
Field Method ◽  
The Other ◽  
Back Reaction ◽  
Stabilization Mechanism ◽  
Numerical Examples ◽  
Effective Potentials

Abstract We address again the old problem of calculating the radion effective potential in Randall-Sundrum scenarios, with the Goldberger-Wise stabilization mechanism. Various prescriptions have been used in the literature, most of them based on heuristic derivations and then applied in some approximations. We define rigorously a light radion 4D effective action by using the interpolating field method. For a given choice of the interpolating field, defined as a functional of 5D fields, the radion effective action is uniquely defined by the procedure of integrating out the other fields, with the constrained 5D equations of motion always satisfied with help of the Lagrange multipliers. Thus, for a given choice of the interpolating fields we obtain a precise prescription for calculating the effective potential. Different choices of the interpolating fields give different prescriptions but in most cases very similar effective potentials. We confirm the correctness of one prescription used so far on a more heuristic basis and also find several new, much more economical, ways of calculating the radion effective potential. Our general considerations are illustrated by several numerical examples. It is shown that in some cases the old methods, especially in models with strong back-reaction, give results which are off even by orders of magnitude. Thus, our results are important e.g. for estimation of critical temperature in phase transitions.

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