AN APPLICATION OF THIRD FORMALISM OF QUANTUM STATISTICS AND A DIAGONALIZATION THEOREM IN ASYMPTOTIC EXACT THEORY OF SUPERCONDUCTIVITY

2005 ◽  
Vol 19 (01n03) ◽  
pp. 13-15
Author(s):  
LEI SUN ◽  
JIPING YE ◽  
XIANXI DAI ◽  
JIXIN DAI
Keyword(s):  
Perturbation Theory ◽  
Finite Order ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Coupling Parameter ◽  
Quantum Statistics ◽  
Variation Method ◽  
The Third ◽  
Theory Of Superconductivity ◽  
Good Agreement

Starting from an electron-phonon interacting model, by means of the third formalism of quantum statistics, and with the aid of a diagonalization theorem, the Tc of superconductors from weak coupling to strong coupling cases are studied in a unified way. Our results are comparable with those of McMillan's theory, (which is valid up to the electron-phonon (e-ph) coupling parameter λ~1, a good agreement is shown for λ<1.3) and the Allen and Dynes's theory. Especially our results are very close to those of Hg spectrum with λ~2.0 and some strong coupling compounds. The theory is exact in the thermodynamic limit, without introducing variation method, the compensation of the dangerous diagrams in finite order in perturbation theory, abnormal green's function etc.

scholarly journals The strong coupling from $e^+e^-\to$~hadrons

2019 ◽  
Author(s):  
Diogo Boito ◽  
Maarten Golterman ◽  
Alex Keshavarzi ◽  
Kim Maltman ◽  
Daiskuke Nomura ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Strong Coupling ◽  
Sum Rules ◽  
Finite Energy ◽  
Order Perturbation ◽  
Decay Data ◽  
Systematic Effects ◽  
Fixed Order ◽  
Charm Mass ◽  
Good Agreement

We use a new compilation of the hadronic RR-ratio from available data for the process e^+e^-\toe+e−→ hadrons below the charm mass to determine the strong coupling \alpha_sαs, using finite-energy sum rules. Quoting our results at the \tauτ mass to facilitate comparison to the results obtained from similar analyses of hadronic \tauτ-decay data, we find \alpha_s(m_\tau^2)=0.298\pm 0.016\pm 0.006αs(mτ2)=0.298±0.016±0.006 in fixed-order perturbation theory, and \alpha_s(m_\tau^2)=0.304\pm 0.018\pm 0.006αs(mτ2)=0.304±0.018±0.006 in contour-improved perturbation theory, where the first error is statistical, and the second error combines various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic \tauτ decays. We briefly compare the R(s)R(s)-based analysis with the \tauτ-based analysis.

THE OPTICAL POLARON IN A TUNABLE POTENTIAL WELL

2011 ◽  
Vol 25 (20) ◽  
pp. 1713-1724
Author(s):  
B. SAQQA ◽  
M. T. AL-MOKAYED ◽  
M. A. RADWAN ◽  
F. M. ABOU EL-ELA
Keyword(s):  
Quantum Well ◽  
Strong Coupling ◽  
Ground State ◽  
Weak Coupling ◽  
State Energy ◽  
Potential Well ◽  
Variational Technique ◽  
Coupling Strengths ◽  
Good Agreement

The optical polaron confined to quantum well with tunable dimensions is investigated within the framework of a variational technique intending to give a unified characterization of problem for all the coupling strengths. The ground state energy and the number of phonons around the electron are studied as a function of the degree of confinement of the quantum well to interpolate between all possible confinement geometries. A comparison is made with the pure strong-coupling and the pure weak-coupling theories and a good agreement is obtained.

scholarly journals DIMENSIONAL CONTINUATION WITHOUT PERTURBATION THEORY

1995 ◽  
Vol 10 (17) ◽  
pp. 1195-1199
Author(s):  
VIPUL PERIWAL
Keyword(s):  
Perturbation Theory ◽  
Strong Coupling ◽  
Correlation Functions ◽  
Weak Coupling ◽  
Strong Coupling Expansion ◽  
Weighted Sums ◽  
Arbitrary Integer ◽  
Correct Dimension

A formula is proposed for continuing physical correlation functions to noninteger numbers of dimensions, expressing them as infinite weighted sums over the same correlation functions in arbitrary integer dimensions. The formula is motivated by studying the strong coupling expansion, but the end result makes no reference to any perturbation theory. It is shown that the formula leads to the correct dimension dependence in weak coupling perturbation theory at one-loop.

scholarly journals Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Cesar Ayala ◽  
Xabier Lobregat ◽  
Antonio Pineda
Keyword(s):  
Perturbation Theory ◽  
Energy Range ◽  
Short Distance ◽  
Weak Coupling ◽  
Strong Consistency ◽  
Lattice Data ◽  
Static Potential ◽  
Static Energy ◽  
Static Quark

Abstract We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $$ {Z}_3^F $$ Z 3 F (nf = 3) = $$ 2{Z}_3^V $$ 2 Z 3 V (nf = 3) = 0.37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $$ {\Lambda}_{\overline{\mathrm{MS}}} $$ Λ MS ¯ when fitting to short-distance lattice data of the static energy. We obtain $$ {\Lambda}_{\overline{\mathrm{MS}}}^{\left({n}_f=3\right)} $$ Λ MS ¯ n f = 3 = 338(12) MeV and α(Mz) = 0.1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

THE RELATION BETWEEN CHIRAL SYMMETRY SPONTANEOUSLY BREAKING AND CONFINEMENT IN QED

2001 ◽  
Vol 16 (12) ◽  
pp. 2253-2266
Author(s):  
KOU SU-PENG
Keyword(s):  
Strong Coupling ◽  
Chiral Symmetry ◽  
Dimensional Reduction ◽  
Weak Coupling ◽  
Coupling Phase ◽  
Fermion Pairs ◽  
Two Phases

In this paper, we use Parisi and Sourlas dimensional reduction to show that QED has two phases, the strong coupling phase and weak coupling phase. Because chiral symmetry is spontaneously broken, particles with fractional charges are confined in the strong coupling phase by the condensation of topological configurations, and particles with integer charges are screened by fermion pairs.

Weak Coupling Strategy for Multi-Physics CFD Simulation in Engineering Problems

2011 ◽  
Author(s):  
Makoto Yamamoto ◽  
Masaya Suzuki
Keyword(s):  
Strong Coupling ◽  
Time Scale ◽  
Weak Coupling ◽  
Particle Deposition ◽  
Cfd Simulation ◽  
The Other ◽  
Cfd Simulations ◽  
Sand Erosion ◽  
Coupling Strategy ◽  
The Difference

Multi-Physics CFD Simulation will be one of key technologies in various engineering fields. There are two strategies to simulate a multi-physics phenomenon. One is “Strong Coupling”, and the other is “Weak Coupling”. Each can be employed, based on time-scales of physics embedded in a problem. That is, when a time-scale of one physics is nearly same as that of the other physics, we have to use Strong Coupling to take into account the interaction between two physics. On the other hand, when one time-scale is quite different from the other one, Weak Coupling can be applied. Considering the present computer performance, Strong Coupling is difficult to be used in engineering design processes now. Therefore, we are focusing on Weak Coupling, and it has been applied to a number of multi-physics CFD simulations in engineering. We have successfully simulated sand erosion, ice accretion, particle deposition, electro-chemical machining and so on, with using Weak Coupling method. In the present study, the difference between strong and weak couplings is briefly described, and two examples of our multi-physics CFD simulations are expressed. The numerical results indicate that Weak Coupling strategy is promising in a lot of multi-physics CFD simulations.

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