scholarly journals Mean-field expansion and meson effects in chiral condensate of analytically regularized Nambu-Jona-Lasinio model

Open Physics ◽  
2004 ◽  
Vol 2 (2) ◽  
Author(s):  
Rauf Jafarov ◽  
Vladimir Rochev
Keyword(s):  
Scalar Meson ◽  
Mean Field ◽  
Chiral Condensate ◽  
Quark Condensate ◽  
Pion Contribution ◽  
Sigma Meson ◽  
Parameter Values

AbstractScalar meson contributions in chiral quark condensate are calculated in the analytically regularized Nambu-Jona-Lasinio model using the framework of mean-field expansion in bilocal-source formalism. The sigma-meson contribution for physical values of the parameters is found to be small. Pion contribution is found to be significant and should be taken into account for the choice of the parameter values.

scholarly journals Hexagonal-Shaped Spin Crossover Nanoparticles Studied by Ising-Like Model Solved by Local Mean Field Approximation

2021 ◽  
Vol 7 (5) ◽  
pp. 69
Author(s):  
Catherine Cazelles ◽  
Jorge Linares ◽  
Mamadou Ndiaye ◽  
Pierre-Richard Dahoo ◽  
Kamel Boukheddaden
Keyword(s):  
Spin Crossover ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ligand Field ◽  
Order And Disorder ◽  
The Matrix ◽  
Local Mean ◽  
Parameter Values

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.

scholarly journals The sigma-meson exchange contribution to the muonic hydrogen Lamb shift

2019 ◽  
Vol 212 ◽  
pp. 07003 ◽  
Author(s):  
A.E. Dorokhov ◽  
A.P. Martynenko ◽  
F.A. Martynenko ◽  
A.E. Radzhabov
Keyword(s):  
Experimental Data ◽  
Lamb Shift ◽  
Scalar Meson ◽  
Muonic Hydrogen ◽  
Meson Exchange ◽  
Exchange Contribution ◽  
Meson Coupling ◽  
Decay Widths ◽  
Precise Experimental Data ◽  
Sigma Meson

The sigma(ξ)meson exchange contribution to the potential of the muon-proton interactionin muonichydrogen inducedbythe ξ-meson coupling to two photons is estimated. The transition form factor ξ → γγ is deduced from the quark model and experimental data on the decay widths Γσγγ. It is shown that scalar meson exchange contribution to the Lamb shift in muonic hydrogen, △ELs(2P−2S ),is rather large and relevant for a comparison with coming precise experimental data.

Hypernetwork models based on random hypergraphs

2019 ◽  
Vol 30 (08) ◽  
pp. 1950052
Author(s):  
Feng Hu ◽  
Jin-Li Guo ◽  
Fa-Xu Li ◽  
Hai-Xing Zhao
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
World Systems ◽  
Uniform Hypergraphs ◽  
Different Types ◽  
Powerful Means ◽  
Simulation Results ◽  
Parameter Values ◽  
Random Hypergraphs

Hypernetworks are ubiquitous in real-world systems. They provide a powerful means of accurately depicting networks of different types of entity and will attract more attention from researchers in the future. Most previous hypernetwork research has been focused on the application and modeling of uniform hypernetworks, which are based on uniform hypergraphs. However, random hypernetworks are generally more common, therefore, it is useful to investigate the evolution mechanisms of random hypernetworks. In this paper, we construct three dynamic evolutional models of hypernetworks, namely the equal-probability random hypernetwork model, the Poisson-probability random hypernetwork model and the certain-probability random hypernetwork model. Furthermore, we analyze the hyperdegree distributions of the three models with mean-field theory, and we simulate each model numerically with different parameter values. The simulation results agree well with the results of our theoretical analysis, and the findings indicate that our models could help understand the structure and evolution mechanisms of real systems.

Thermodynamic properties of light mesons and phase transition in an extended SU(2) NJL model

2019 ◽  
Vol 34 (13) ◽  
pp. 1950070
Author(s):  
J. R. Morones Ibarra ◽  
A. J. Garza Aguirre ◽  
Francisco V. Flores-Baez
Keyword(s):  
Chemical Potential ◽  
Pion Mass ◽  
Quark Condensate ◽  
The Other ◽  
Chiral Symmetry Restoration ◽  
Chiral Phase ◽  
Potential Dependence ◽  
Njl Model ◽  
The Masses ◽  
Sigma Meson

In this work, we study the temperature and chemical potential dependence of the masses of sigma and pion mesons as well as the quark condensate by using a SU(2) flavor version of the Nambu–Jona–Lassino model, introducing a prescription that mimics confinement. We have found that as the temperature increases, the mass of sigma shifts down, while the pion mass remains almost constant. On the other hand, the quark condensate decreases as the temperature and chemical potential increases. We have also analyzed the temperature and chemical potential dependence of the spectral function of the sigma meson, from which we observe at low values of T and [Formula: see text] an absence of a peak. Furthermore, as the Mott temperature is reached, its value increases abruptly and a distinct peak emerges, which is related with the dissociation of the sigma. For the case of [Formula: see text], the Mott dissociation is exhibited about the temperature of 189 MeV. We have also obtained the chiral phase diagram and the meson dissociation for different values of [Formula: see text]. From these results, we can state a relation between chiral symmetry restoration and Mott dissociation.

CHAOTIC MEAN FIELD DYNAMICS OF A BOOLEAN NETWORK WITH RANDOM CONNECTIVITY

2007 ◽  
Vol 18 (09) ◽  
pp. 1459-1473 ◽  
Author(s):  
MALIACKAL POULO JOY ◽  
DONALD E. INGBER ◽  
SUI HUANG
Keyword(s):  
Regulatory Networks ◽  
Boolean Network ◽  
Mean Field ◽  
Period Doubling ◽  
Structural Heterogeneity ◽  
Boolean Networks ◽  
Analytical Treatment ◽  
Random Boolean Networks ◽  
The Mean ◽  
Parameter Values

Random Boolean networks have been used as simple models of gene regulatory networks, enabling the study of the dynamic behavior of complex biological systems. However, analytical treatment has been difficult because of the structural heterogeneity and the vast state space of these networks. Here we used mean field approximations to analyze the dynamics of a class of Boolean networks in which nodes have random degree (connectivity) distributions, characterized by the mean degree k and variance D. To achieve this we generalized the simple cellular automata rule 126 and used it as the Boolean function for all nodes. The equation for the evolution of the density of the network state is presented as a one-dimensional map for various input degree distributions, with k and D as the control parameters. The mean field dynamics is compared with the data obtained from the simulations of the Boolean network. Bifurcation diagrams and Lyapunov exponents for different parameter values were computed for the map, showing period doubling route to chaos with increasing k. Onset of chaos was delayed (occurred at higher k) with the increase in variance D of the connectivity. Thus, the network tends to be less chaotic when the heterogeneity, as measured by the variance of connectivity, was higher.

scholarly journals Inhomogeneous chiral condensates in low-energy color-superconductivity models of QCD

2021 ◽  
Author(s):  
◽  
Philip Lakaschus
Keyword(s):  
Phase Diagram ◽  
Mean Field ◽  
Field Approximation ◽  
Chiral Condensate ◽  
Dispersion Relations ◽  
Mean Field Approximation ◽  
Color Superconductivity ◽  
Diquark Model ◽  
Coexistence Phase ◽  
The Mean

This thesis explores the phase diagrams of the Nambu--Jona-Lasinio (NJL) and quark-meson (QM) model in the mean-field approximation and beyond. The focus lies in the investigation of the interplay between inhomogeneous chiral condensates and two-flavor color superconductivity. In the first part of this thesis, we study the NJL model with 2SC diquarks in the mean-field approximation and determine the dispersion relations for quasiparticle excitations for generic spatial modulations of the chiral condensate in the presence of a homogeneous 2SC-diquark condensate, provided that the dispersion relations in the absence of color superconductivity are known. We then compare two different Ansätze for the chiral order parameter, the chiral density wave (CDW) and the real-kink crystal (RKC). For both Ansätze we find for specific diquark couplings a so-called coexistence phase where both the inhomogeneous chiral condensate and the diquark condensate coexist. Increasing the diquark coupling disfavors the coexistence phase in favor of a pure diquark phase. On the other hand, decreasing the diquark coupling favors the inhomogeneous phase over the coexistence phase. In the second part of this thesis the functional renormalization group is employed to study the phase diagram of the quark-meson-diquark model. We observe that the region of the phase diagram found in previous studies, where the entropy density takes on unphysical negative values, vanishes when including diquark degrees of freedom. Furthermore, we perform a stability analysis of the homogeneous phase and compare the results with those of previous studies. We find that an increasing diquark coupling leads to a smaller region of instability as the 2SC phase extends to a smaller chemical potential. We also find a region where simultaneously an instability occurs and a non-vanishing diquark condensate forms, which is an indication of the existence of a coexistence phase in accordance with the results of the first part of this work.

scholarly journals MONOPOLES FROM QUARK CONDENSATES IN QCD

2008 ◽  
Vol 23 (27n30) ◽  
pp. 2356-2359
Author(s):  
M. N. CHERNODUB
Keyword(s):  
Chiral Symmetry ◽  
Quark Gluon Plasma ◽  
Gluon Plasma ◽  
Chiral Condensate ◽  
Quark Condensate ◽  
Chiral Symmetry Restoration ◽  
Gauge Invariant ◽  
Different Temperatures

Chiral monopoles are hedgehoglike structures in local chiral condensates in QCD. These monopoles are (i) made of quark and gluon fields; (ii) explicitly gauge-invariant; (iii) they carry quantized and conserved chromomagnetic charge. We argue that the chiral condensate vanishes in a core of the chiral monopole while the density of these monopoles increases with temperature wiping out the quark condensate in quark-gluon plasma. We suggest that the chiral monopoles are responsible for the chiral symmetry restoration in QCD. We also argue that the chiral monopoles are unlikely to be responsible for confinement of color. Thus, phenomena of the chiral symmetry restoration and the color deconfinement in QCD are not necessarily related to each other and the corresponding transitions may happen at different temperatures.

scholarly journals Chiral Condensates in Quark and Nuclear Matter

2003 ◽  
Vol 18 (18) ◽  
pp. 3151-3174 ◽  
Author(s):  
G. X. Peng ◽  
H. C. Chiang ◽  
P. Z. Ning ◽  
U. Lombardo ◽  
M. Loewe
Keyword(s):  
Nuclear Matter ◽  
Quark Matter ◽  
Chiral Condensate ◽  
Quark Condensate ◽  
Model Parameters ◽  
Linear Extrapolation ◽  
Linear Behavior ◽  
Current Mass ◽  
Average Current ◽  
Model Independent

We present a novel treatment of calculating the in-medium quark condensates. The advantage of this approach is that one does not need to make further assumptions on the derivatives of model parameters with respect to the quark current mass. The normally accepted model-independent result in nuclear matter is naturally reproduced. The change of the quark condensate induced by interactions depends on the incompressibility of nuclear matter. When it is greater than 265 MeV, the density at which the condensate vanishes is higher than that from the linear extrapolation. For the chiral condensate in quark matter, a similar model-independent linear behavior is found at lower densities, which means that the decreasing speed of the condensate in quark matter is merely half of that in nuclear matter if the pion-nucleon sigma commutator is six times the average current mass of u and d quarks. The modification due to QCD-like interactions is found to slow the decreasing speed of the condensate, compared with the linear extrapolation.

ISOVECTOR COMPONENTS OF LIGHT SCALAR MESON AND NUCLEAR MATTER PROPERTIES

2007 ◽  
Vol 16 (09) ◽  
pp. 2867-2871 ◽  
Author(s):  
C. A. Z. VASCONCELLOS ◽  
E. LÜTZ ◽  
M. RAZEIRA ◽  
B. E. J. BODMANN ◽  
M. DILLIG ◽  
...  
Keyword(s):  
Nuclear Matter ◽  
Scalar Meson ◽  
Mean Field ◽  
Symmetry Transformation ◽  
Hadronic Matter ◽  
Meson Field ◽  
Field Approach ◽  
Relativistic Mean Field ◽  
Light Scalar ◽  
Scalar Meson Field

We have predicted (contribution to this issue) an isovector component of the light scalar meson sector by using the chiral symmetry transformation formalism. On the basis of this result, we study dense hadronic matter in a generalized relativistic mean field approach with σ, ω and ρ mesons as well as nonlinear self-couplings of the I = 1 component of a light scalar meson field and compare its predictions for neutron star properties with results from different models for nuclear matter found in the literature.

NEUTRON STARS WITH PARAMETRIZED MESON COUPLINGS

2000 ◽  
Vol 15 (29) ◽  
pp. 1789-1800 ◽  
Author(s):  
A. R. TAURINES ◽  
C. A. Z. VASCONCELLOS ◽  
M. MALHEIRO ◽  
M. CHIAPPARINI
Keyword(s):  
Neutron Stars ◽  
Nuclear Matter ◽  
Degrees Of Freedom ◽  
Scalar Meson ◽  
Mean Field Theory ◽  
Mean Field ◽  
Static Properties ◽  
Relativistic Mean Field ◽  
Specific Choice

We investigate static properties of nuclear and neutron star matter by using a relativistic mean field theory with parametrized couplings. With a suitable choice of mathematical parameters, the couplings allow one to reproduce results of current quantum hadrodynamics models. For other parametrizations, a better description of bulk properties of nuclear matter is obtained. The formalism is extended to include hyperon and lepton degrees of freedom, and an analysis on the effects of the phenomenological couplings in the fermion populations and mass of neutron stars is performed. The results show a strong similarity between the predictions of ZM-like models and those with exponential couplings. We have observed in particular an extreme sensibility of the predictions of these theories on the specific choice of the values of the binding energy of nuclear matter and saturation density. Additionally, the role of the very intense scalar meson mean field found in the interior of neutron stars in the screening of the nucleon mass is discussed.

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