Anomalous coalescence from a nonlinear Schroedinger equation with a quintic term: interpretation through Thompson's approach

Nassif, Cláudio; Silva, P.R.

doi:10.1016/j.physa.2003.11.019

Cited by 4 publications

(13 citation statements)

References 19 publications

(48 reference statements)

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“…According to a previous paper [2], an e ective action to describe A + A → A(0) coalescence with anomalous di usion condition was proposed by the present author, namely…”

Section: The Critical Exponents In the Stationary Regime For A + A → A(0) Anomalous Coalescencementioning

confidence: 92%

“…In a previous paper [2], we took n as being the density of particles A to represent bubbles (or domain) concentration [1], which behaves like n ∼ t −d= , according to (8).…”

Section: Critical Exponents For Jr's Anomalous Coalescence: Scaling Relations Among Such New Exponentsmentioning

confidence: 99%

“…was considered to be a free parameter. However, it was assumed that must be a function of the dimensionality ( (d)), through the following ansatz [2], namely:…”

Section: Critical Exponents For Jr's Anomalous Coalescence: Scaling Relations Among Such New Exponentsmentioning

confidence: 99%

“…So in order to do that, we must take into account the ansatz (21). Thus by introducing ( 21) into ( 17), ( 20) and (18) ( = 1, for d ¿ 2 [2]), we ÿnally obtain the following special exponents:…”

Section: Critical Exponents For Jr's Anomalous Coalescence: Scaling Relations Among Such New Exponentsmentioning

confidence: 99%

“…On the other hand, motivated by Josserand and Rica's work (hereafter, JR) [1] and also by a more recent paper [2], where droplet and bubble anomalous coalescence in 1-d was well explained through Thompson's scaling approach [4], we must be able to pick up anomalous exponents which depend on parameter for anomalous di usion condition [5]. We also have to consider depending on dimensionality ( (d)) [2].…”

Section: Introductionmentioning

confidence: 99%

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Anomalous coalescence phenomena under stationary regime condition through Thompson's method

Nassif

2004

Physica A: Statistical Mechanics and its Applications

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“…According to a previous paper [2], an e ective action to describe A + A → A(0) coalescence with anomalous di usion condition was proposed by the present author, namely…”

Section: The Critical Exponents In the Stationary Regime For A + A → A(0) Anomalous Coalescencementioning

confidence: 92%

“…In a previous paper [2], we took n as being the density of particles A to represent bubbles (or domain) concentration [1], which behaves like n ∼ t −d= , according to (8).…”

Section: Critical Exponents For Jr's Anomalous Coalescence: Scaling Relations Among Such New Exponentsmentioning

confidence: 99%

“…was considered to be a free parameter. However, it was assumed that must be a function of the dimensionality ( (d)), through the following ansatz [2], namely:…”

Section: Critical Exponents For Jr's Anomalous Coalescence: Scaling Relations Among Such New Exponentsmentioning

confidence: 99%

Section: Critical Exponents For Jr's Anomalous Coalescence: Scaling Relations Among Such New Exponentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anomalous coalescence phenomena under stationary regime condition through Thompson's method

Nassif

2004

Physica A: Statistical Mechanics and its Applications

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Asymptotic freedom and quarks confinement treated through Thompson’s approach

2016

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In this work, we first use Thompson's renormalization group method to treat QCDvacuum behavior close to the regime of asymptotic freedom. QCD-vacuum behaves effectively like a "paramagnetic system" of a classical theory in the sense that virtual color charges (gluons) emerge in it as spin effect of a paramagnetic material when a magnetic field aligns their microscopic magnetic dipoles. Making a classical analogy with the paramagnetism of Landau's theory, we are able to introduce a kind of Landau effective action without temperature and phase transition for just representing QCD-vacuum behavior at higher energies as being magnetization of a paramagnetic material in the presence of a magnetic field H. This reasoning allows us to use Thompson's heuristic approach in order to obtain an "effective susceptibility" (χ > 0) of the QCD-vacuum. It depends on logarithmic of energy scale u to investigate hadronic matter. Consequently, we are able to get an "effective magnetic permeability" (µ > 1) of such a "paramagnetic vacuum". As QCD-vacuum must obey Lorentz invariance, the attainment of µ > 1 must simply require that the "effective electrical permissivity" is ǫ < 1 in such a way that µǫ = 1 (c 2 = 1). This leads to the anti-screening effect, where the asymptotic freedom takes place. On the other hand, quarks confinement, a subject which is not treatable by perturbative calculations, is worked by the present approach. We apply the method to study this issue for obtaining the string constant, which is in agreement with the experiments.

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Quantum Electrodynamics and Chromodynamics Treated Through Thompson's Approach

Nassif

Silva

2006

Int. J. Mod. Phys. A

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In this work we apply Thompson's method (of the dimensions and scales) to study some features of the Quantum Electrodynamics and Chromodynamics. This heuristic method can be considered as a simple and alternative way to the Renormalization Group approach and when applied to QED-Lagrangian is able to obtain in a first approximation both the running coupling constant behavior of α(μ) and the mass m(μ). The calculations are evaluated only at dc = 4, where dc is the upper critical dimension of the problem, so that we obtain the logarithmic behavior both for the coupling α and the excess of mass Δm on the energy scale μ. Although our results are well known in the vast literature of field theories, the advantage of Thompson's method, beyond its simplicity is that it is able to extract directly from QED-Lagrangian the physical (finite) behavior of α(μ) and m(μ), bypassing hard problems of divergences which normally appear in the conventional renormalization schemes applied to field theories like QED. Quantum Chromodynamics (QCD) is also treated by the present method in order to obtain the quark condensate value. Besides this, the method is also able to evaluate the vacuum pressure at the boundary of the nucleon. This is done by assumming a step function behavior for the running coupling constant of the QCD, which fits nicely to some quantities related to the strong interaction evaluated through the MIT-bag model.

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Anomalous coalescence from a nonlinear Schroedinger equation with a quintic term: interpretation through Thompson's approach

Cited by 4 publications

References 19 publications

Anomalous coalescence phenomena under stationary regime condition through Thompson's method

Anomalous coalescence phenomena under stationary regime condition through Thompson's method

Asymptotic freedom and quarks confinement treated through Thompson’s approach

Quantum Electrodynamics and Chromodynamics Treated Through Thompson's Approach

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