Delta isobars in relativistic mean-field models with $\\sigma$-scaled hadron masses and couplings
Kolomeitsev, E E; Voskresensky, D N
2016-01-01
We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar $\\sigma$ field, studied previously to incorporate $\\Delta(1232)$ baryons. Available empirical information is analyzed to put constraints on the couplings of $\\Delta$s with meson fields. Conditions for the appearance of $\\Delta$s are studied. We demonstrate that with inclusion of the $\\Delta$s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urca and the gravitational-baryon mass ratio constraints.
Maslov, K A; Voskresensky, D N
2016-01-01
Knowledge of the equation of state of the baryon matter plays a decisive role in the description of neutron stars. With an increase of the baryon density the filling of Fermi seas of hyperons and $\\Delta$ isobars becomes possible. Their inclusion into standard relativistic mean-field models results in a strong softening of the equation of state and a lowering of the maximum neutron star mass below the measured values. We extend a relativistic mean-field model with scaled hadron masses and coupling constants developed in our previous works and take into account now not only hyperons but also the $\\Delta$ isobars. We analyze available empirical information to put constraints on coupling constants of $\\Delta$s to mesonic mean fields. We show that the resulting equation of state satisfies majority of presently known experimental constraints.
Diabatic constrained relativistic mean field approach
L"u, H F; Meng, J
2005-01-01
A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean field model. The potential energy surfaces of $^{208}$Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. The diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to define the single particle orbits at very deformed region by their quantum numbers, and to obtain several well defined deformed excited states which can hardly be expected from the adiabatic PES's.
Relativistic mean field description of cluster radioactivity
Bhagwat, A.; Gambhir, Y. K.
2005-01-01
Comprehensive investigations of the observed cluster radioactivity are carried out. First, the relativistic mean field (RMF) theory is employed for the calculations of the ground-state properties of relevant nuclei. The calculations reproduce the experiment well. The calculated RMF point densities are folded with the density-dependent M3Y nucleon-nucleon interaction to obtain the cluster-daughter interaction potential. This, along with the calculated and experimental Q values, is used in the WKB approximation for estimating the half-lives of the parent nuclei against cluster decay. The calculations qualitatively agree with the experiment. Sensitive dependence of the half-lives on Q values is explicitly demonstrated.
Relativistic mean-field mass models
Peña-Arteaga, D.; Goriely, S.; Chamel, N.
2016-10-01
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented.
Relativistic mean-field mass models
Pena-Arteaga, D.; Goriely, S.; Chamel, N. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)
2016-10-15
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented. (orig.)
Relativistic Mean-Field Models and Nuclear Matter Constraints
Dutra, M; Carlson, B V; Delfino, A; Menezes, D P; Avancini, S S; Stone, J R; Providência, C; Typel, S
2013-01-01
This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear \\sigma^3+\\sigma^4 models, (iii) \\sigma^3+\\sigma^4+\\omega^4 models, (iv) models containing mixing terms in the fields \\sigma and \\omega, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the \\sigma (\\omega) field. The isospin dependence of the interaction is modeled by the \\rho meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.
Finite Size Corrected Relativistic Mean-Field Model and QCD Critical End Point
Uddin, Saeed; Ahmad, Jan Shabir
2012-01-01
The effect of finite size of hadrons on the QCD phase diagram is analyzed using relativistic mean field model for the hadronic phase and the Bag model for the QGP phase. The corrections to the EOS for hadronic phase are incorporated in a thermodynamic consistent manner for Van der Waals like interaction. It is found that the effect of finite size of baryons is to shift CEP to higher chemical potential values.
Relativistic mean-field models and nuclear matter constraints
Dutra, M.; Lourenco, O.; Carlson, B. V. [Departamento de Fisica, Instituto Tecnologico de Aeronautica-CTA, 12228-900, Sao Jose dos Campos, SP (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminense, 24210-150, Boa Viagem, Niteroi, RJ (Brazil); Menezes, D. P.; Avancini, S. S. [Departamento de Fisica, CFM, Universidade Federal de Santa Catarina, CP. 476, CEP 88.040-900, Florianopolis, SC (Brazil); Stone, J. R. [Oxford Physics, University of Oxford, OX1 3PU Oxford (United Kingdom) and Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996 (United States); Providencia, C. [Centro de Fisica Computacional, Department of Physics, University of Coimbra, P-3004-516 Coimbra (Portugal); Typel, S. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Theorie, Planckstrasse 1,D-64291 Darmstadt (Germany)
2013-05-06
This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear {sigma}{sup 3}+{sigma}{sup 4} models, (iii) {sigma}{sup 3}+{sigma}{sup 4}+{omega}{sup 4} models, (iv) models containing mixing terms in the fields {sigma} and {omega}, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the {sigma} ({omega}) field. The isospin dependence of the interaction is modeled by the {rho} meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.
Spurious Shell Closures in the Relativistic Mean Field Model
Geng, L S; Toki, H; Long, W H; Shen, G
2006-01-01
Following a systematic theoretical study of the ground-state properties of over 7000 nuclei from the proton drip line to the neutron drip line in the relativistic mean field model [Prog. Theor. Phys. 113 (2005) 785], which is in fair agreement with existing experimental data, we observe a few spurious shell closures, i.e. proton shell closures at Z=58 and Z=92. These spurious shell closures are found to persist in all the effective forces of the relativistic mean field model, e.g. TMA, NL3, PKDD and DD-ME2.
General Relativistic Mean Field Theory for rotating nuclei
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
Cranked Relativistic Mean Field Description of Superdeformed Rotational Bands
Afanasjev, A. V.; Lalazissis, G. A.; Ring, P.
1997-01-01
The cranked relativistic mean field theory is applied for a detailed investigation of eight superdeformed rotational bands observed in $^{151}$Tb. It is shown that this theory is able to reproduce reasonably well not only the dynamic moments of inertia $J^{(2)}$ of the observed bands but also the alignment properties of the single-particle orbitals.
Cluster decay in very heavy nuclei in Relativistic Mean Field
Bhattacharya, Madhubrata; Gangopadhyay, G.
2008-01-01
Exotic cluster decay of very heavy nuclei has been studied in the microscopic Super-Asymmetric Fission Model. Relativistic Mean Field model with the force FSU Gold has been employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction have been used in the double folding model to obtain the potential between the cluster and the daughter. Half life values have been ca...
Relativistic Mean Field Study on Halo Structures of Mirror Nuclei
LIANG Yu-Jie; LI Yan-Song; LIU Zu-Hua; ZHOU Hong-Yu
2009-01-01
Halo structures of some light mirror nuclei are investigated with the relativistic mean field (RMF) theory.The calculations show that the dispersion of the valence proton is larger than that of the valence neutron in its mirror nucleus,the difference between the root-mean-square (rms) radius of the valence nucleon in each pair of mirror nuclei becomes smailer with the increase of the mass number A,and all the ratios of the rms radius of the valence nucleon to that of the matter in each pair o~ mirror nuclei decrease almost linearly with the increase of the mass number A.
A New Parameter Set for the Relativistic Mean Field Theory
Nerlo-Pomorska, B; Nerlo-Pomorska, Bozena; Sykut, Joanna
2004-01-01
Subtracting the Strutinsky shell corrections from the selfconsistent energies obtained within the Relativistic Mean Field Theory (RMFT) we have got estimates for the macroscopic part of the binding energies of 142 spherical even-even nuclei. By minimizing their root mean square deviations from the values obtained with the Lublin-Srasbourg Drop (LSD) model with respect to the nine RMFT parameters we have found the optimal set (NL4). The new parameters reproduce also the radii of these nuclei with an accuracy comparable with that obtained with the NL1 and NL3 sets.
Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field
LI Yan-Song; LONG Gui-Lu
2004-01-01
We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shellmodel (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method.In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF)theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained.This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei 16O and 208Pb,the deformed nucleus 20Ne. Good agreement is obtained.
Cluster decay in very heavy nuclei in Relativistic Mean Field
Bhattacharya, Madhubrata
2008-01-01
Exotic cluster decay of very heavy nuclei has been studied in the microscopic Super-Asymmetric Fission Model. Relativistic Mean Field model with the force FSU Gold has been employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction have been used in the double folding model to obtain the potential between the cluster and the daughter. Half life values have been calculated in the WKB approximation and the spectroscopic factors have been extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions have been made for some possible decays.
Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter
ZHANG Qi-Ren; GAO Chun-Yuan
2011-01-01
We propose a quantization procedure for the nucleon-scalar meson system, in which an arbitrary mean scalar meson field Φ is introduced.The equivalence of this procedure with the usual one is proven for any given value of Φ.By use of this procedure, the scalar meson field in the Walecka's MFA and in Chin's RHA are quantized around the mean field.Its corrections on these theories are considered by perturbation up to the second order.The arbitrariness of Φ makes us free to fix it at any stage in the calculation.When we fix it in the way of Walecka's MFA, the quantum corrections are big, and the result does not converge.When we fix it in the way of Chin's RHA, the quantum correction is negligibly small, and the convergence is excellent.It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka's MFA does not.We suggest to fix the parameter Φ at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory (QRMFT) a variational method.
Green's function relativistic mean field theory for Λ hypernuclei
Ren, S.-H.; Sun, T.-T.; Zhang, W.
2017-05-01
The relativistic mean field theory with the Green's function method is extended to study Λ hypernuclei. Taking the hypernucleus Ca61Λ as an example, the single-particle resonant states for Λ hyperons are investigated by analyzing the density of states, and the corresponding energies and widths are given. Different behaviors are observed for the resonant states, i.e., the distributions of the very narrow 1 f5 /2 and 1 f7 /2 states are very similar to bound states while those of the wide 1 g7 /2 and 1 g9 /2 states are like scattering states. Besides, the impurity effect of Λ hyperons on the single-neutron resonant states is investigated. For most of the resonant states, both the energies and widths decrease with adding more Λ hyperons due to the attractive Λ N interaction. Finally, the energy level structure of Λ hyperons in the Ca hypernucleus isotopes with mass number A =53 -73 are studied; obvious shell structure and small spin-orbit splitting are found for the single-Λ spectrum.
Hadron resonance gas and mean-field nuclear matter for baryon number fluctuations
Fukushima, Kenji
2014-01-01
We give an estimate for the skewness and the kurtosis of the baryon number distribution in two representative models; i.e., models for a hadron resonance gas and relativistic mean-field nuclear matter. We emphasize formal similarity between these two descriptions. The hadron resonance gas leads to a deviation from the Skellam distribution if quantum statistical correlation is taken into account at high baryon density, but this effect is not strong enough to explain fluctuation data seen in the beam-energy scan at RHIC/STAR. In the calculation of mean-field nuclear matter the density correlation with the vector \\omega-field rather than the effective mass with the scalar \\sigma-field renders the kurtosis suppressed at higher baryon density so as to account for the observed behavior of the kurtosis. We finally discuss the difference between the baryon number and the proton number fluctuations from correlation effects in isospin space. Our numerical results suggest that such effects are only minor even in the cas...
COMPRESSIBILITY OF NUCLEI IN RELATIVISTIC MEAN FIELD-THEORY
BOERSMA, HF; MALFLIET, R; SCHOLTEN, O
1991-01-01
Using the relativistic Hartree approximation in the sigma-omega model we study the isoscalar giant monopole resonance. It is shown that the ISGMR of lighter nuclei has non-negligible anharmonic terms. The compressibility of nuclear matter is determined using a leptodermous expansion.
Hot and dense matter beyond relativistic mean field theory
Zhang, Xilin
2016-01-01
Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\\odot$ neutron star req...
Multiple chiral doublet candidate nucleus $^{105}$Rh in a relativistic mean-field approach
Li, Jian; Meng, J; 10.1103/PhysRevC.83.037301
2011-01-01
Following the reports of two pairs of chiral doublet bands observed in $^{105}$Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M$\\chi$D) phenomenon. The existence of M$\\chi$D phenomenon in $^{105}$Rh is highly expected.
Shape Coexistence for 179Hg in Relativistic Mean-Field Theory
WANG Nan; MENG Jie; ZHAO En-Guang
2005-01-01
The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.
One-Proton Halo in 31Cl with Relativistic Mean-Field Theory
蔡翔舟; 沈文庆; 任中洲; 蒋维洲; 方德清; 张虎勇; 钟晨; 魏义彬; 郭威; 马余刚; 朱志远
2002-01-01
We investigate proton-rich isotopes s1,32Cl using the nonlinear relativistic mean-field model. It is shown that this model can reproduce the properties of these nuclei well. A long tail appears in the calculated proton density distribution of 31 Cl. The results of relativistic density-dependent Hartree theory show a similar trend of tail density distribution. It is strongly suggested that there is a proton halo in 31Cl and it is indicated that there may be a proton skin in 32 Cl. The relation between the proton halo in 31Cl and the new proton magic number is discussed.
Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
Niksic, T; Vretenar, D; Prochniak, L; Meng, J; Ring, P
2008-01-01
The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A model is developed for the solution of the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The model is tested in a series of illustrative calculations of potential energy surfaces and the resulting collective excitation spectra and transition probabilities of the chain of even-even gadolinium isotopes.
Systematic nuclear structure studies using relativistic mean field theory in mass region A ˜ 130
Shukla, A.; Åberg, Sven; Bajpeyi, Awanish
2017-02-01
Nuclear structure studies for even-even nuclei in the mass region \\backsim 130, have been performed, with a special focus around N or Z = 64. On the onset of deformation and lying between two closed shell, these nuclei have attracted attention in a number of studies. A revisit to these experimentally accessible nuclei has been made via the relativistic mean field. The role of pairing and density depletion in the interior has been specially investigated. Qualitative analysis between two versions of relativistic mean field suggests that there is no significant difference between the two approaches. Moreover, the role of the filling {{{s}}}1/2 orbital in density depletion towards the centre has been found to be consistent with our earlier work on the subject Shukla and Åberg (2014 Phys. Rev. C 89 014329).
Proton rich nuclei at and beyond the proton drip line in the Relativistic Mean Field theory
Geng, L S; Meng, J
2003-01-01
The Relativistic Mean Field theory is applied to the analysis of ground-state properties of deformed proton-rich odd-Z nuclei in the region $55\\le Z \\le 73$ >. The model uses the TMA and NL3 effective interactions in the mean-field Lagrangian, and describes pairing correlations by the density-independent delta-function interaction. The model predicts the location of the proton drip line, the ground-state quadrupole deformation, one-proton separation energy at and beyond the proton drip line, the deformed single-particle orbital occupied by the odd valence proton and the corresponding spectroscopic factor. The results are in good agreement with the available experimental data except for some odd-odd nuclei in which the proton-neutron pairing may become important and are close to those of Relativistic Hartree-Bogoliubov model.
Description of $^{178}$Hf$^{m2}$ in the constrained relativistic mean field theory
Wei, Zhang; Shuang-Quan, Zhang
2009-01-01
The properties of the ground state of $^{178}$Hf and the isomeric state $^{178}$Hf$^{m2}$ are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of $^{178}$Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with $K^\\pi=16^+$ is found to be $\
Restoration of rotational symmetry in deformed relativistic mean-field theory
YAO Jiang-Ming; MENG Jie; Pena Arteaga Daniel; Ring Peter
2009-01-01
We report on a very recently developed three-dimensional angular momentum projected relativistic mean-field theory with point-coupling interaction (3DAMP+RMF-PC). Using this approach the same effective nucleon-nucleon interaction is adopted to describe both the single-particle and collective motions in nuclei.Collective states with good quantum angular momentum are built projecting out the intrinsic deformed meanfield states. Results for 24Mg are shown as an illustrative application.
Relativistic mean field study of the superdeformed rotational bands in the A {approx} 60 mass region
Madokoro, Hideki [Dept. of Physics, Kyushu Univ., Fukuoka (Japan); Matsuzaki, Masayuki
1999-03-01
The superdeformed rotational bands in {sup 62}Zn, which were recently discovered, are examined using Relativistic Mean Field model. The experimental dynamical moments of inertia and deformations are well reproduced, but the calculated bands which seem to correspond to the experimental data do not become yrast. This seems to be connected with the wrong position of the g{sup 9/2} single neutron orbit. (author)
Antimagnetic rotation in 108,110In with tilted axis cranking relativistic mean-field approach
Sun, Wu-Ji; Xu, Hai-Dan; Li, Jian; Liu, Yong-Hao; Ma, Ke-Yan; Yang, Dong; Lu, Jing-Bing; Ma, Ying-Jun
2016-08-01
Based on tilted axis cranking relativistic mean-field theory within point-coupling interaction PC-PK1, the rotational structure and the characteristic features of antimagnetic rotation for ΔI = 2 bands in 108,110In are studied. Tilted axis cranking relativistic mean-field calculations reproduce the experimental energy spectrum well and are in agreement with the experimental I ∼ ω plot, although the calculated spin overestimates the experimental values. In addition, the two-shears-like mechanism in candidate antimagnetic rotation bands is clearly illustrated and the contributions from two-shears-like orbits, neutron (gd) orbits above Z = 50 shell and Z = 50, N = 50 core are investigated microscopically. The predicted B(E2), dynamic moment of inertia ℑ(2), deformation parameters β and γ, and ℑ(2)/B(E2) ratios in tilted axis cranking relativistic mean-field calculations are discussed and the characteristic features of antimagnetic rotation for the bands before and after alignment are shown. Supported by National Natural Science Foundation of China (11205068, 11205069, 11405072, 11475072, 11547308) and China Postdoctoral Science Foundation (2012M520667)
Nuclear Matter in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S
1997-01-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the delta-meson [a_0(980)] is studied. While the delta-meson mean field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to delta-field to the nuclear symmetry energy is negative. To fit the empirical value, E_s=30 MeV, a stronger rho-meson coupling is required than in the absence of the delta-field. The energy per particle of neutron matter is then larger at high densities than the one with no delta-field included. Also, the proton fraction of beta-stable matter increases. Splitting of proton and neutron effective masses due to the delta-field can affect transport properties of neutron star matter.
Mean-field effects on flows in relativistic heavy-ion collisions
Isse, M.; Ohnishi, A. [Hokkaido Univ., Graduate School of Science, Sapporo, Hokkaido (Japan); Otuka, N. [Hokkaido Univ., Graduate School of Engineering, Sapporo, Hokkaido (Japan); Sahu, P.K. [Istituto Nazionale di Fisica Nucleare, Sezione di Catania (Italy); Nara, Y. [Brookhaven National Laboratory, RIKEN BNL Research Center, Upton, NY (United States)
2002-09-01
At RHIC experiments, started in 2000, the data obtained recently seem to exhibit QGP formation, but the conclusion is not drawn yet. Here, we pay out attention to the collective flows at hadronic freeze-out as an evidence of QGP formation. To discuss it, the mean-field effect on the flows is not negligible. It is dominant at SIS or AGS energy, and our conjecture is that it is negligible at SPS or RHIC energy. We formed a model to investigate our assumption, and some simulated results are shown. (author)
Neutron Stars in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S; Stachniewicz, S
1998-01-01
We study the equation of state of beta-stable dense matter and models of neutron stars in the relativistic mean field theory with the isovector scalar mean field corresponding to the delta-meson [a_0(980)]. A range of values of the delta-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E_s=30 MeV. We find that the quantity most sensitive to the delta-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the delta-field. The energy per baryon also increases but the effect is smaller. The equation of state becomes slightly stiffer and the maximum neutron star mass increases for stronger delta-meson coupling.
Three-dimensional angular momentum projection in relativistic mean-field theory
Yao, J M; Ring, P; Arteaga, D Pena
2009-01-01
Based on a relativistic mean-field theory with an effective point coupling between the nucleons, three-dimensional angular momentum projection is implemented for the first time to project out states with designed angular momentum from deformed intrinsic states generated by triaxial quadrupole constraints. The same effective parameter set PC-F1 of the effective interaction is used for deriving the mean field and the collective Hamiltonian. Pairing correlations are taken into account by the BCS method using both monopole forces and zero range d-forces with strength parameters adjusted to experimental even-odd mass differences. The method is applied successfully to the isotopes 24Mg, 30Mg, and 32Mg.
Relativistic heavy ion collisions with realistic non-equilibrium mean fields
Fuchs, C; Wolter, H H
1996-01-01
We study the influence of non-equilibrium phase space effects on the dynamics of heavy ion reactions within the relativistic BUU approach. We use realistic Dirac-Brueckner-Hartree-Fock (DBHF) mean fields determined for two-Fermi-ellipsoid configurations, i.e. for colliding nuclear matter, in a local phase space configuration approximation (LCA). We compare to DBHF mean fields in the local density approximation (LDA) and to the non-linear Walecka model. The results are further compared to flow data of the reaction Au on Au at 400 MeV per nucleon measured by the FOPI collaboration. We find that the DBHF fields reproduce the experiment if the configuration dependence is taken into account. This has also implications on the determination of the equation of state from heavy ion collisions.
Time-dependent Relativistic Mean-field Theory and Random Phase Approximation
P.Ring; D.Vretenar; A.Wandelt; NguyenVanGiai; MAZhong-yu; CAOLi-gang
2001-01-01
The relativistic random phase approximation (RRPA) is derived from the time-dependent relativistic mean field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also ah configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116Sn. It is shown that
Shell evolution at N=20 in the constrained relativistic mean field approach
无
2008-01-01
The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.
Fission Barrier for 240Pu in the Quadrupole Constrained Relativistic Mean Field Approach
L(U) Hong-Feng; GENG Li-Sheng; MENG Jie
2006-01-01
@@ The fission barrier for 240Pu is investigated beyond the second saddle point in the potential energy surface by the constrained relativistic mean field method with the newly proposed parameter set PK1. The microscopic correction for the centre-of-mass motion is essential to provide the correct potential energy surface. The shell effects that stabilize the nuclei against the fission is also investigated by the Strutinsky method. The shapes for the ground state, fission isomer and saddle-points, etc, are studied in detail.
Pasta phases in neutron star studied with extended relativistic mean field models
Gupta, Neha
2013-01-01
To explain several properties of finite nuclei, infinite matter, and neutron stars in a unified way within the relativistic mean field models, it is important to extend them either with higher order couplings or with density-dependent couplings. These extensions are known to have strong impact in the high-density regime. Here we explore their role on the equation of state at densities lower than the saturation density of finite nuclei which govern the phase transitions associated with pasta structures in the crust of neutron stars.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
无
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field(RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A = 139 where the neutron number is the magic number N = 82.It is also found that the octupole deformations may exist in the La isotopes with mass number A ～ 145-155.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
WANG Nan; GUO Lu
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field (RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A=139 where the neutron number is the magic number N=82.It is also found that the octupole deformations may exist in the La isotopes with mass number A～ 145-155.
Tidal deformability of neutron and hyperon star with relativistic mean field equations of state
Kumar, Bharat; Patra, S K
2016-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field (RMF) equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various love numbers kl (l=2, 3, 4), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through advanced LIGO detector from the final stages of inspiraling binary neutron star (BNS) merger.
Proton and neutron skins of light nuclei within the Relativistic Mean Field theory
Geng, L S; Ozawa, A; Meng, J
2004-01-01
The Relativistic Mean Field (RMF) theory is applied to the analysis of ground-state properties of Ne, Na, Cl and Ar isotopes. In particular, we study the recently established proton skin in Ar isotopes and neutron skin in Na isotopes as a function of the difference between the proton and the neutron separation energy. We take the TMA effective interaction in the RMF Lagrangian, and describe pairing correlation by the density-independent delta-function interaction. We calculate single neutron and proton separation energies, quadrupole deformations, nuclear matter radii, and differences in proton radii and neutron radii, and compare these results with the recent experimental data.
Tidal deformability of neutron and hyperon stars within relativistic mean field equations of state
Kumar, Bharat; Biswal, S. K.; Patra, S. K.
2017-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various Love numbers kl(l =2 ,3 ,4 ), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through an advanced LIGO detector from the final stages of an inspiraling binary neutron star merger.
Shell-model-like Approach (SLAP) for the Nuclear Properties in Relativistic Mean field Theory
MENG Jie; GUO Jian-you; LIU Lang; ZHANG Shuang-quan
2006-01-01
A Shell-model-like approach suggested to treat the pairing correlations in relativistic mean field theory is introduced,in which the occupancies thus obtained have been iterated back into the densities.The formalism and numerical techniques are given in detail.As examples,the ground state properties and low-lying excited states for Ne isotopes are studied.The results thus obtained are compared with the data available.The binding energies,the odd-even staggering,as well as the tendency for the change of the shapes in Ne isotopes are correctly reproduced.
Hadron production in heavy relativistic systems
Kuiper, R; Kuiper, Rolf; Wolschin, Georg
2007-01-01
We investigate particle production in heavy-ion collisions at RHIC energies as function of incident energy, and centrality in a three-sources Relativistic Diffusion Model. Pseudorapidity distributions of produced charged hadrons in Au + Au and Cu + Cu collisions at sqrt(s_NN) = 19.6 GeV, 62.4 GeV, 130 GeV and 200 GeV show an almost equilibrated midrapidity source that tends to increase in size towards higher incident energy, and more central collisions. It may indicate quark-gluon plasma formation prior to hadronization.
Description of Drip-Line Nuclei within Relativistic Mean-Field Plus BCS Approach
Yadav, H L; Toki, H
2004-01-01
Recently it has been demonstrated, considering Ni and Ca isotopes as prototypes, that the relativistic mean-field plus BCS (RMF+BCS) approach wherein the single particle continuum corresponding to the RMF is replaced by a set of discrete positive energy states for the calculation of pairing energy provides a good approximation to the full relativistic Hartree-Bogoliubov (RHB) description of the ground state properties of the drip-line neutron rich nuclei. The applicability of RMF+BCS is essentially due to the fact that the main contribution to the pairing correlations is provided by the low-lying resonant states. General validity of this approach is demonstrated by the detailed calculations for the ground state properties of the chains of isotopes of O, Ca, Ni, Zr, Sn and Pb nuclei. The TMA and NL-SH force parameter sets have been used for the effective mean-field Lagrangian. Comprehensive results for the two neutron separation energy, rms radii, single particle pairing gaps and pairing energies etc. are pres...
New parameterization of the effective field theory motivated relativistic mean field model
Kumar, Bharat; Singh, S. K.; Agrawal, B. K.; Patra, S. K.
2017-10-01
A new parameter set is generated for finite and infinite nuclear system within the effective field theory motivated relativistic mean field (ERMF) formalism. The isovector part of the ERMF model employed in the present study includes the coupling of nucleons to the δ and ρ mesons and the cross-coupling of ρ mesons to the σ and ω mesons. The results for the finite and infinite nuclear systems obtained using our parameter set are in harmony with the available experimental data. We find the maximum mass of the neutron star to be 2.03M⊙ and yet a relatively smaller radius at the canonical mass, 12.69 km, as required by the available data.
Hyperons in neutron star matter within relativistic mean-field models
Oertel, M; Gulminelli, F; Raduta, A R
2014-01-01
Since the discovery of neutron stars with masses around 2 solar masses the composition of matter in the central part of these massive stars has been intensively discussed. Within this paper we will (re)investigate the question of the appearance of hyperons. To that end we will perform an extensive parameter study within relativistic mean field models. We will show that it is possible to obtain high mass neutron stars (i) with a substantial amount of hyperons, (ii) radii of 12-13 km for the canonical mass of 1.4 solar masses, and (iii) a spinodal instability at the onset of hyperons. The results depend strongly on the interaction in the hyperon-hyperon channels, on which only very little information is available from terrestrial experiments up to now.
B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations
Pöschl, W
1997-01-01
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.
Ground State Properties of Ds Isotopes Within the Relativistic Mean Field Theory
张海飞; 张鸿飞; 李君清
2012-01-01
The ground state properties of Ds (Z=110) isotopes (N=151-195) are studied in the framework of the relativistic mean field (RMF) theory with the effective interaction NL-Z2.The pairing correlation is treated within the conventional BCS approximation.The calculated binding energies are consistent with the results from finite-range droplet model (FRDM) and Macroscopic-microscopic method (MMM).The quadrupole deformation,α-decay energy,α-decay half-live,charge radius,two-neutron separation energy and single-particle spectra are analyzed for Ds isotopes to find new characteristics of superheavy nuclei (SHN).Among the calculated results it is rather distinct that the isotopic shift appears evidently at neutron number N=184.
Description of 178 Hfm2 in the Constrained Relativistic Mean Field Theory
ZHANG Wei; PENG Jing; ZHANG Shuang-Quan
2009-01-01
Properties of the ground state of 178 Hf and the isomeric state 178Hfn2 are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of 178Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with Kπ = 16+ is found to be v(7/2- [514])-1 (9/2+ [624])1 π(7/2+ [404])-1 (9/2-[514])1. Its excitation energy calculated by the RMF theory with time-odd fields taken into account is equal to 2.801 MeV, i.e., close to the 178 Hfm2 experimental excitation energy 2.446 MeV. The self-consistent procedure accounting for the time-odd component of the meson fields is the most important aspect of the present calculation.
Cluster decay in very heavy nuclei in a relativistic mean field model
Bhattacharya, Madhubrata; Gangopadhyay, G.
2008-02-01
Exotic cluster decay of very heavy nuclei was studied in the microscopic Super-Asymmetric Fission Model. The Relativistic Mean Field model with the force FSU Gold was employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction were used in the double folding model to obtain the potential between the cluster and the daughter. Half-life values were calculated in the WKB approximation and the spectroscopic factors were extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions were made for some possible decays.
Study of reaction and decay using densities from relativistic mean field theory
Gangopadhyay, G
2012-01-01
Relativistic mean field calculations have been performed to obtain nuclear density pro- file. Microscopic interactions have been folded with the calculated densities of finite nuclei to obtain a semi-microscopic potential. Life time values for the emission of proton, alpha particles and complex clusters have been calculated in the WKB approach assum- ing a tunneling process through the potential barrier. Elastic scattering cross sections have been estimated for proton-nucleus scattering in light neutron rich nuclei. Low en- ergy proton reactions have been studied and their astrophysical implications have been discussed. The success of the semi-microscopic potentials obtained in the folding model with RMF densities in explaining nuclear decays and reactions has been emphasized.
Ground-State Properties of Z = 59 Nuclei in the Relativistic Mean-Field Theory
ZHOU Yong; MA Zhong-Yu; CHEN Bao-Qiu; LI Jun-Qing
2000-01-01
Ground-state properties of Pr isotopes are studied in a framework of the relativistic mean-field (RMF) theory using the recently proposed parameter set TM1. Bardeen-Cooper-Schrieffer (BCS) pproximation and blocking method is adopted to deal with pairing interaction and the odd nucleon, respectively. The pairing forces are taken to be isospin dependent. The domain of the validity of the BCS theory and the positions of neutron and proton drip lines are studied. It is shown that RMF theory has provided a good description of the binding energy,isotope shifts and deformation of nuclei over a large range of Pr isotopes, which are in good agreement with those obtained in the finite-range droplet model.
Investigation of A＋c- and Ab-Hypernuclei in Relativistic Mean-Field Model
TANYu-Hong; CAIChong-Hai; LILei; NINGPing-Zhi
2003-01-01
We investigate the properties of A+c- and Ab-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no A+c bound states can exist if the A+c potential well depth |UA+c| in nuclear matter is less than 10 MeV. If |UA+c|is less than 20 MeV, A+c cannot bind to the heavier nuclei with atomic number larger than 100. We suggest it is preferable to search the A+c-hypernuclei from medium-heavy nuclear systems in experiment. Very small spin-orbit splitting for the A+c in hypernuclei is a/so observed, and for the Ab it is nearly zero.
Magnetic moments of 33Mg in the time-odd relativistic mean field approach
无
2009-01-01
The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN self-consistently without introducing any parameter.The energy splittings of time reversal conjugate states,the neutron current,the energy contribution from the nuclear magnetic potential,and the effect of core polarization are discussed in detail.
K--nucleus relativistic mean field potentials consistent with kaonic atoms
Friedman, E.; Gal, A.; Mareš, J.; Cieplý, A.
1999-08-01
K- atomic data are used to test several models of the K- nucleus interaction. The t(ρ)ρ optical potential, due to coupled channel models incorporating the Λ(1405) dynamics, fails to reproduce these data. A standard relativistic mean field (RMF) potential, disregarding the Λ(1405) dynamics at low densities, also fails. The only successful model is a hybrid of a theoretically motivated RMF approach in the nuclear interior and a completely phenomenological density dependent potential, which respects the low density theorem in the nuclear surface region. This best-fit K- optical potential is found to be strongly attractive, with a depth of 180+/-20 MeV at the nuclear interior, in agreement with previous phenomenological analyses.
Madokoro, Hideki; Matsuzaki, Masayuki
1997-01-01
Relativistic Mean Field Theory is applied to the description of rotating nuclei. Since the previous formulation of Munich group was based on a special relativistic transformation property of the spinor fields, we reformulate in a fully covariant manner using tetrad formalism. The numerical calculations are performed for 3 zinc isotopes, including the newly discovered superdeformed band in $^{62}$Zn which is the first experimental observation in this mass region.
Madokoro, H.; Matsuzaki, M.
Relativistic Mean Field Theory is applied to the description of rotating nuclei. Since the previous formulation of Munich group was based on a special relativistic transformation property of the spinor fields, we reformulate in a fully covariant manner using tetrad formalism. The numerical calculations are performed for 3 zinc isotopes, including the newly discovered superdeformed band in $^{62}$Zn which is the first experimental observation in this mass region.
Pais, Helena
2016-01-01
The Vlasov formalism is extended to relativistic mean-field hadron models with non-linear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear $\\omega\\rho$ and $\\sigma\\rho$ coupling terms on the crust-core transition density and pressure, and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure, and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6$\\pm$0.3 km and a crust thickness of $1.36\\pm 0.06$km for a 1.4 $M_\\odot$ star.
A Study of Multi-Λ Hypernuclei Within Spherical Relativistic Mean-Field Approach
Rather, Asloob A.; Ikram, M.; Usmani, A. A.; Kumar, B.; Patra, S. K.
2017-09-01
This research article is a follow up of an earlier work by M. Ikram et al., reported in Int. J. Mod. Phys. E 25, 1650103 (2016) where we searched for Λ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (i.e., 16 O-208 P b) by injecting Λ's into them. In the present manuscript, working within the state of the art relativistic mean field theory with the inclusion of ΛN and ΛΛ interaction in addition to nucleon-meson NL 3∗ effective force, we extend the search of lambda magic numbers in multi- Λ hypernuclei using the predicted doubly magic nucleonic cores 292120, 304120, 360132, 370132, 336138, 396138 of the elusive superheavy mass regime. In analogy to well established signatures of magicity in conventional nuclear theory, the prediction of hypernuclear magicities is made on the basis of one-, two- Λ separation energy (S Λ,S 2Λ) and two lambda shell gaps (δ 2Λ) in multi- Λ hypernuclei. The calculations suggest that the Λ numbers 92, 106, 126, 138, 184, 198, 240, and 258 might be the Λ shell closures after introducing the Λ's in the elusive superheavy nucleonic cores. The appearance of new lambda shell closures apart from the nucleonic ones predicted by various relativistic and non-relativistic theoretical investigations can be attributed to the relatively weak strength of the spin-orbit coupling in hypernuclei compared to normal nuclei. Further, the predictions made in multi- Λ hypernuclei under study resembles closely the magic numbers in conventional nuclear theory suggested by various relativistic and non-relativistic theoretical models. Moreover, in support of the Λ shell closure, the investigation of Λ pairing energy and effective Λ pairing gap has been made. We noticed a very close agreement of the predicted Λ shell closures with the survey made on the pretext of S Λ, S 2Λ, and δ 2Λ except for the appearance of magic numbers corresponding to Λ = 156 which manifest in Λ effective
Nucleon Finite Volume Effect and Nuclear Matter Properties in a Relativistic Mean-Field Theory
R. Costa; A.J. Santiago; H. Rodrigues; J. Sa Borges
2006-01-01
Effects of excluded volume of nucleons on nuclear matter are studied, and the nuclear properties that follow from different relativistic mean-field model parametrizations are compared. We show that, for all tested parametrizations,the resulting volume energy a1 and the symmetry energy J are around the acceptable values of 16 MeV and 30 MeV,and the density symmetry L is around 100 Me V. On the other hand, models that consider only linear terms lead to incompressibility K0 much higher than expected. For most parameter sets there exists a critical point (ρc,δc), where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero. This critical point depends on the excluded volume parameter r. If this parameter is larger than 0.5 fm, there is no critical point and the pure neutron matter is predicted to be bound. The maximum value for neutron star mass is 1.85M⊙, which is in agreement with the mass of the heaviest observed neutron star 4U0900-40 and corresponds to r = 0.72 fm. We also show that the light neutron star mass (1.2M⊙) is obtained for r (≌) 0.9 fm.
A Second Relativistic Mean Field and Virial Equation of State for Astrophysical Simulations
Shen, G; O'Connor, E
2011-01-01
We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the Virial expansion of a non-ideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100,000 grid points in the temperature range $T$ = 0 to 80 MeV, the density range $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$, and the proton fraction range $Y_p$ = 0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3 ba...
Properties and structure of N=Z nuclei within relativistic mean field theory
GAO Yuan; DONG Jian-Min; ZHANG Hong-Fei; ZUO Wei; LI Jun-Qing
2009-01-01
The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.
Nuclear matter fourth-order symmetry energy in relativistic mean field models
Cai, Bao-Jun
2011-01-01
Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{4}(\\rho)$. Our results show that the value of $E_{4}(\\rho)$ at normal nuclear matter density $\\rho_{0}$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at $\\rho_{0}$. On the other hand, we find that the $E_{4}(\\rho)$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{4}(\\rho)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{\\mathrm{sat}}(\\delta)=K_{0}+K_{\\mathrm{{sat},2}}\\delta ^{2}+K_{\\mathrm{{sat},4}}\\delta ^{4}+\\mathcal{O}(\\delta ^{6})$ where $\\delta =(\\rho_{n}-\\rho_{p})/\\rho $ is the isospin asymmetry, and we find that the value of $K_{\\mathrm{{sat},4}}$ is generally comparable with that of the $K_{\\mathrm{{sat},2}}$. In addition, we study the effects of the $E...
Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
2013-01-01
In this contribution we present some results of potential energy surfaces of actinide and transfermium nuclei from multi-dimensional constrained relativistic mean field (MDC-RMF) models. Recently we developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) in which all shape degrees of freedom $\\beta_{\\lambda\\mu}$ with even $\\mu$ are allowed and the functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. In MDC-RMF models, the pairing correlations are treated with the BCS method. With MDC-RMF models, the potential energy surfaces of even-even actinide nuclei were investigated and the effect of triaxiality on the fission barriers in these nuclei was discussed. The non-axial reflection-asymmetric $\\beta_{32}$ shape in some transfermium nuclei with $N=150$, namely $^{246}$Cm, $^{248}$Cf, $^{250}$Fm, and $^{252}$No were also studied.
Multidimensionally constrained relativistic mean-field study of triple-humped barriers in actinides
Zhao, Jie; Lu, Bing-Nan; Vretenar, Dario; Zhao, En-Guang; Zhou, Shan-Gui
2015-01-01
Background: Potential energy surfaces (PES's) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier, the occurrence of a third barrier was predicted by macroscopic-microscopic model calculations in the 1970s, but contradictory results were later reported by a number of studies that used different methods. Purpose: Triple-humped barriers in actinide nuclei are investigated in the framework of covariant density functional theory (CDFT). Methods: Calculations are performed using the multidimensionally constrained relativistic mean field (MDC-RMF) model, with the nonlinear point-coupling functional PC-PK1 and the density-dependent meson exchange functional DD-ME2 in the particle-hole channel. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Results: Two-dimensional PES's of 226,228,230,232Th and 232,235,236,238U are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. The functional DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and 238U . The third minima in 230 ,232Th are very shallow, whereas those in 226 ,228Th and 238U are quite prominent. With the functional PC-PK1 a third barrier is found only in 226 ,228 ,230Th . Single-nucleon levels around the Fermi surface are analyzed in 226Th, and it is found that the formation of the third minimum is mainly due to the Z =90 proton energy gap at β20≈1.5 and β30≈0.7 . Conclusions: The possible occurrence of a third barrier on the PES's of actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases
Relativistic Few-Body Hadronic Physics Calculations
Polyzou, Wayne [Univ. of Iowa, Iowa City, IA (United States)
2016-06-20
The goal of this research proposal was to use ``few-body'' methods to understand the structure and reactions of systems of interacting hadrons (neutrons, protons, mesons, quarks) over a broad range of energy scales. Realistic mathematical models of few-hadron systems have the advantage that they are sufficiently simple that they can be solved with mathematically controlled errors. These systems are also simple enough that it is possible to perform complete accurate experimental measurements on these systems. Comparison between theory and experiment puts strong constraints on the structure of the models. Even though these systems are ``simple'', both the experiments and computations push the limits of technology. The important property of ``few-body'' systems is that the ``cluster property'' implies that the interactions that appear in few-body systems are identical to the interactions that appear in complicated many-body systems. Of particular interest are models that correctly describe physics at distance scales that are sensitive to the internal structure of the individual nucleons. The Heisenberg uncertainty principle implies that in order to be sensitive to physics on distance scales that are a fraction of the proton or neutron radius, a relativistic treatment of quantum mechanics is necessary. The research supported by this grant involved 30 years of effort devoted to studying all aspects of interacting two and three-body systems. Realistic interactions were used to compute bound states of two- and three-nucleon, and two- and three-quark systems. Scattering observables for these systems were computed for a broad range of energies - from zero energy scattering to few GeV scattering, where experimental evidence of sub-nucleon degrees of freedom is beginning to appear. Benchmark calculations were produced, which when compared with calculations of other groups provided an essential check on these complicated calculations. In
Study of the Alpha-Decay Chain for7753 194Rn with Relativistic Mean-Field Theory
SHENG Zong-Qiang; GUO Jian-You
2008-01-01
The structures of the nuclei on the alpha-decay chain of 194Rn are investigated in the deformed relativistic mean-field theory with the effective interaction TMA. We put an emphasis on the ground state properties of 194Rn. The calculated alpha-decay energies and lifetimes are both very close to the experimental data for 186pb and 190po. For 194 Rn, the deviations are a little large on both the alpha-decay energy and the lifetime. We also calculate the alpha-decay energies for the isotopes 192～208Rn. The tendency for the change of the alpha-decay energies with neutron number is correctly reproduced in the relativistic mean-field theory (RMF). In general, the RMF theory can give a good description of the alpha decay chain of 194Rn.
Shusu Shi
2016-01-01
Full Text Available Strange hadrons, especially multistrange hadrons, are good probes for the early partonic stage of heavy ion collisions due to their small hadronic cross sections. In this paper, I give a brief review on the elliptic flow measurements of strange and multistrange hadrons in relativistic heavy ion collisions at Relativistic Heavy Ion Collider (RHIC and Large Hadron Collider (LHC.
Geng, L S; Meng, J
2005-01-01
We perform a systematic study of the ground-state properties of all the nuclei from the proton drip line to the neutron drip line throughout the periodic table employing the relativistic mean field model. The TMA parameter set is used for the mean-field Lagrangian density, and a state-dependent BCS method is adopted to describe the pairing correlation. The ground-state properties of a total of 6969 nuclei with $Z,N\\ge 8$ and $Z\\le 100$ from the proton drip line to the neutron drip line, including the binding energies, the separation energies, the deformations, and the rms charge radii, are calculated and compared with existing experimental data and those of the FRDM and HFB-2 mass formulae. This study provides the first complete picture of the current status of the descriptions of nuclear ground-state properties in the relativistic mean field model. The deviations from existing experimental data indicate either that new degrees of freedom are needed, such as triaxial deformations, or that serious effort is ne...
Treating Coulomb exchange contributions in relativistic mean field calculations: why and how
Van Giai, Nguyen; Gu, Huai-Qiang; Long, Wenhui; Meng, Jie
2014-01-01
The energy density functional (EDF) method is very widely used in nuclear physics, and among the various existing functionals those based on the relativistic Hartree (RH) approximation are very popular because the exchange contributions (Fock terms) are numerically rather onerous to calculate. Although it is possible to somehow 'mock up' the effects of meson-induced exchange terms by adjusting the meson-nucleon couplings, the lack of Coulomb exchange contributions hampers the accuracy of predictions. In this note, we show that the Coulomb exchange effects can be easily included with a good accuracy in a perturbative approach. Therefore, it would be desirable for future relativistic EDF models to incorporate Coulomb exchange effects, at least to some order of perturbation.
Building relativistic mean field models for finite nuclei and neutron stars
Chen, Wei-Chia; Piekarewicz, J.
2014-10-01
Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed χ2 objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, "FSUGold2," is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron-star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter, suggesting a fairly large neutron-skin thickness in Pb208 and a moderate value of the nuclear incompressibility. Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme—properly supplemented by a covariance analysis—provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.
Hadron thermodynamics in relativistic nuclear collisions
Ammiraju, P.
1985-01-01
Various phenomenological models based on statistical thermodynamical considerations were used to fit the experimental data at high P sub T to a two temperature distribution. Whether this implies that the two temperatures belong to two different reaction mechanisms, or consequences of Lorentz-contraction factor, or related in a fundamental way to the intrinsic thermodynamics of Space-Time can only be revealed by further theoretical and experimental investigations of high P sub T phenomena in extremely energetic hadron-hadron collisions.
Building relativistic mean field models for finite nuclei and neutron stars
Chen, Wei-Chia
2014-01-01
Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed chi-square objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, FSUGold2, is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron star mass observed up to date. In particul...
Sudden Hadronization in Relativistic Nuclear Collisions
Rafelski, Johann; Rafelski, Johann; Letessier, Jean
2000-01-01
We formulate and study the mechanical instability criterion of dense matter fireballs without considering a specific equation of state (EoS). We demonstrate the consistency with the chemical freeze-out of a fireball of matter formed in 158AGeV Pb-Pb collisions. Assuming EoS appropriate for quark-gluon matter, we demonstrate the required deep QGP supercooling prior to sudden hadronization. In a model independent approach, but using results of hadron abundance analysis and lattice QCD, we show that the latent heat of the deconfined phase is bounded from below 0.14GeV/fm^3\\le B.
CHEN Jin-Gen; ZHOU Xing-Fei; WANG Kun; MA Guo-Liang; TIAN Wen-Dong; ZUO Jia-Xu; MA Chun-Wang; CHEN Jin-Hui; YAN Ting-Zhi; SHEN Wen-Qing; CAI Xiang-Zhou; WANG Ting-Tai; MA Yu-Gang; REN Zhong-Zhou; FANG De-Qing; ZHONG Chen; WEI Yi-Bin; GUO Wei
2004-01-01
@@ A candidate for proton halo nucleus 23Al is investigated based on the constrained calculations in the framework of the deformed relativistic mean field (RMF) model with the NL075 parameter set. It is shown by the constrained calculations that the ground state of 23Al has a large deformation that corresponds to the prolate shape. With that large deformation, the non-constrained RMF calculation predicts that there appears an inversion between the 2s1/2 [211] and 1d5/2 [202] shells. The valence proton of 23Al is weakly bound and occupies 2s1/2 [211] and 1d5/2 [202] with the weights of 56% and 29%, respectively. The calculated RMS radius for matter is in agreement with the experimental one. It is also predicted that the difference between the proton RMS radius and the neutron one is very large. This suggests that there exists a proton halo in 23Al.
Sulaksono, A; Agrawal, B K
2014-01-01
The model dependence and the symmetry energy dependence of the core-crust transition properties for the neutron stars are studied using three different families of systematically varied extended relativistic mean field model. Several forces within each of the families are so considered that they yield wide variations in the values of the nuclear symmetry energy $a_{\\rm sym}$ and its slope parameter $L$ at the saturation density. The core-crust transition density is calculated using a method based on random-phase-approximation. The core-crust transition density is strongly correlated, in a model independent manner, with the symmetry energy slope parameter evaluated at the saturation density. The pressure at the transition point dose not show any meaningful correlations with the symmetry energy parameters at the saturation density. At best, pressure at the transition point is correlated with the symmetry energy parameters and their linear combination evaluated at the some sub-saturation density. Yet, such corre...
Zhao, Jie; Niksic, Tamara; Vretenar, Dario; Zhou, Shan-Gui
2016-01-01
Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm are explored. Fission paths, action integrals and corresponding half-lives computed in the three-dimensional collective space of shape and pa...
Bai, Hong-Bo; Zhang, Zhen-Hua; Li, Xiao-Wei
2016-11-01
Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self-consistent relativistic mean field (RMF) model with the pairing correlations treated by a shell-mode-like approach (SLAP), in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF+SLAP calculations. Supported by NSFC (11465001,11275098, 11275248, 11505058,11165001) and Natural Science Foundation of Inner Mongolia of China (2016BS0102)
Afanasjev, A. V.; König, J.; Ring, P.
1996-02-01
The cranked relativistic mean field approach is applied for a systematic investigation of superdeformed rotational bands observed in the A ˜ 140-150 mass region. The present investigation covers yrast and in some cases also excited superdeformed bands of all nuclei of this mass region in which such bands have been observed so far. Using the parameter set NL1, which has been adjusted ten years ago to a few spherical nuclei, reasonable agreement with experimental data is obtained throughout the mass region under investigation. It is shown that the calculated properties of superdeformed rotational bands such as the dependence of the dynamic moment of inertia J(2) with respect to the rotational frequency and the absolute value of the charge quadrupole moment Q0 depends sensitively on the number of occupied high- N intruder orbitals. This is agreement both with previous investigations within the cranked Nilsson-Strutinsky and the cranked Woods-Saxon-Strutinsky approaches and with available experimental data.
Typel, S.; Wolter, H.H. [Sektion Physik, Univ. Muenchen, Garching (Germany)
1998-06-01
Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for {sigma}-, {omega}- and {rho}-mesons is obtained by fitting to properties of nuclear matter and some finite nuclei. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and an improved center-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines, e.g. for separation energies, spin-orbit splittings and density distributions. (orig.)
Parton-Hadron-String Dynamics at Relativistic Collider Energies
Bratkovskaya, E L; Konchakovski, V P; Linnyk, O
2011-01-01
The novel Parton-Hadron-String Dynamics (PHSD) transport approach is applied to nucleus-nucleus collisions at RHIC energies with respect to differential hadronic spectra in comparison to available data. The PHSD approach is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results from the Wuppertal-Budapest group in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy-momentum conservation. Our dynamical studies for heavy-ion collisions at relativistic collider energies are compared to earlier results from the Hadron-String Dynamics (HSD) approach - incorporating no explicit dynamical partonic phase - as well as to experimental data from the STAR, PHENIX, BRAHMS and PHOBOS collaborations for Au+Au collisions at the top RHIC energy...
Parton-Hadron-String Dynamics at relativistic collider energies
Bratkovskaya, E. L.; Cassing, W.; Konchakovski, V. P.; Linnyk, O.
2011-04-01
The novel Parton-Hadron-String Dynamics (PHSD) transport approach is applied to nucleus-nucleus collisions at RHIC energies with respect to differential hadronic spectra in comparison to available data. The PHSD approach is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results from the Wuppertal-Budapest group in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy-momentum conservation. Our dynamical studies for heavy-ion collisions at relativistic collider energies are compared to earlier results from the Hadron-String Dynamics (HSD) approach - incorporating no explicit dynamical partonic phase - as well as to experimental data from the STAR, PHENIX, BRAHMS and PHOBOS Collaborations for Au + Au collisions at the top RHIC energy of √{s}=200 GeV. We find a reasonable reproduction of hadron rapidity distributions and transverse mass spectra and also a fair description of the elliptic flow of charged hadrons as a function of the centrality of the reaction and the transverse momentum p. Furthermore, an approximate quark-number scaling of the elliptic flow v of hadrons is observed in the PHSD results, too.
Parton-Hadron-String Dynamics at relativistic collider energies
Bratkovskaya, E.L., E-mail: Elena.Bratkovskaya@th.physik.uni-frankfurt.d [Institut fuer Theoretische Physik, JWG Universitaet Frankfurt, D-60438 Frankfurt am Main (Germany); Frankfurt Institut for Advanced Studies, Frankfurt University, D-60438 Frankfurt-am-Main (Germany); Cassing, W.; Konchakovski, V.P. [Institut fuer Theoretische Physik, Universitaet Giessen, Heinrich-Buff-Ring 16, D-35392 Giessen (Germany); Linnyk, O. [Frankfurt Institut for Advanced Studies, Frankfurt University, D-60438 Frankfurt-am-Main (Germany)
2011-04-15
The novel Parton-Hadron-String Dynamics (PHSD) transport approach is applied to nucleus-nucleus collisions at RHIC energies with respect to differential hadronic spectra in comparison to available data. The PHSD approach is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results from the Wuppertal-Budapest group in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy-momentum conservation. Our dynamical studies for heavy-ion collisions at relativistic collider energies are compared to earlier results from the Hadron-String Dynamics (HSD) approach - incorporating no explicit dynamical partonic phase - as well as to experimental data from the STAR, PHENIX, BRAHMS and PHOBOS Collaborations for Au + Au collisions at the top RHIC energy of {radical}(s)=200 GeV. We find a reasonable reproduction of hadron rapidity distributions and transverse mass spectra and also a fair description of the elliptic flow of charged hadrons as a function of the centrality of the reaction and the transverse momentum p{sub T}. Furthermore, an approximate quark-number scaling of the elliptic flow v{sub 2} of hadrons is observed in the PHSD results, too.
The effect of tree-level and mean-field improvement on the light-hadron spectrum in quenched QCD
Shanahan, H P; Bowler, K C; Kenway, R D; Richards, D G; Ryan, S M; Rowland, P A; Lacock, P; Michael, C; Burford, D R; Stella, N; Wittig, H
1997-01-01
We compute the light hadron mass spectrum at beta=5.7 using the O(a) improved Sheikholeslami-Wohlert (SW) fermion action with two choices of the clover coefficient: the classical value, c=1, and a mean-field or tadpole-improved estimate c=1.57. We compare our results with those of the GF11 Collaboration who use the Wilson fermion action (c=0). We find that changing c from zero to 1 and 1.57 leads to significant differences in the masses of the chirally extrapolated and strange pseudoscalar and vector mesons, the nucleon, the Delta, and also in the Edinburgh plot. A number of other quantities, for example m_V^2-m_PS^2, J, am_K/am_\\rho and am_{K^*}/am_\\rho do not appear to change significantly. We also investigate the effect of changing the lattice volume from approximately (2 fm)^3 to (2.6 fm)^3. We find that the meson masses are consistent to within one standard deviation and baryon masses are consistent to within two standard deviations.
Afanasjev, A.V. [Technische Univ. Muenchen, Garching (Germany). Physik-Department]|[Latvian Acad. of Sci., Salaspils (Latvia). Dept. of Math. Phys.]|[Lund Inst. of Tech. (Sweden). Dept. of Mathematical Physics; Koenig, J. [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Ring, P. [Technische Univ. Muenchen, Garching (Germany). Physik-Department
1996-10-14
The cranked relativistic mean field approach is applied for a systematic investigation of superdeformed rotational bands observed in the A {proportional_to}140-150 mass region. The present investigation covers yrast and in some cases also excited superdeformed bands of all nuclei of this mass region in which such bands have been observed so far. Using the parameter set NL1, which has been adjusted ten years ago to a few spherical nuclei, reasonable agreement with experimental data is obtained throughout the mass region under investigation. It is shown that the calculated properties of superdeformed rotational bands such as the dependence of the dynamic moment of inertia J{sup (2)} with respect to the rotational frequency and the absolute value of the charge quadrupole moment Q{sub 0} depends sensitively on the number of occupied high-N intruder orbitals. This is in agreement both with previous investigations within the cranked Nilsson-Strutinsky and the cranked Woods-Saxon-Strutinsky approaches and with available experimental data. (orig.).
ZhangHongfei; ZuoWei; SoojaeRenIm; ZhouXiaohong; LiJunqing
2003-01-01
In recent years the discovery of Super Heavy Element (SHE) with atomic number Z=108～116 has opened up a new era of research in nuclear physics, however, the extreme difficulties to synthesize SHE greatly restrict the experimental studies on it, so that the theoretical studies are very important. The Relativistic Mean Field theory (RMF) is proved to be a simple and successful theory due to its great success in describing the bulk properties at the β-stable valley, as well as nuclei far from the β-stable line, and gives good predictions for nuclei far beyond the end of the known periodic table. In the framework of RMF we have calculated the properties on SHN such as the binding energy, the deformation, single and double neutron separation energy, and the a-decay half-life and so on for nuclei Z=108～114 and N=156～190. The axial deformations considered by using the expansion of harmonic oscillator basis. The Lagrangian wc have used is as the following form:
A systematic study of even-even nuclei in the nuclear chart by the relativistic mean field theory
Sumiyoshi, K.; Hirata, D.; Tanihata, I.; Sugahara, Y.; Toki, H. [Institute of Physical and Chemical Research, Wako, Saitama (Japan)
1997-03-01
We study systematically the properties of nuclei in the whole mass range up to the drip lines by the relativistic mean field (RMF) theory with deformations as a microscopic framework to provide the data of nuclear structure in the nuclear chart. The RMF theory is a phenomenological many-body framework, in which the self-consistent equations for nucleons and mesons are solved with arbitrary deformation, and has a potential ability to provide all the essential information of nuclear structure such as masses, radii and deformations together with single particle states and wave functions from the effective lagrangian containing nuclear interaction. As a first step toward the whole project, we study the ground state properties of even-even nuclei ranging from Z=8 to Z=120 up to the proton and neutron drip lines in the RMF theory. We adopt the parameter set TMA, which has been determined by the experimental masses and charge radii in a wide mass range, for the effective lagrangian of the RMF theory. We take into account the axially symmetric deformation using the constrained method on the quadrupole moment. We provide the properties of all even-even nuclei with all the possible ground state deformations extracted from the deformation energy curves by the constrained calculations. By studying the calculated ground state properties systematically, we aim to explore the general trend of masses, radii and deformations in the whole region of the nuclear chart. We discuss the agreement with experimental data and the predictions such as magicness and triaxial deformations beyond the experimental frontier. (author)
Cao, Shanshan; Bass, Steffen A
2015-01-01
We construct a theoretical framework to describe the evolution of heavy flavors produced in relativistic heavy-ion collisions. The in-medium energy loss of heavy quarks is described using our modified Langevin equation that incorporates both quasi-elastic scatterings and the medium-induced gluon radiation. The space-time profiles of the fireball is described by a (2+1)-dimensional hydrodynamics simulation. A hybrid model of fragmentation and coalescence is utilized for heavy quark hadronization, after which the produced heavy mesons together with the soft hadrons produced from the bulk QGP are fed into the hadron cascade UrQMD model to simulate the subsequent hadronic interactions. We find that the medium-induced gluon radiation contributes significantly to heavy quark energy loss at high $p_\\mathrm{T}$; heavy-light quark coalescence enhances heavy meson production at intermediate $p_\\mathrm{T}$; and scatterings inside the hadron gas further suppress the $D$ meson $R_\\mathrm{AA}$ at large $p_\\mathrm{T}$ and e...
Bhuyan, M.; Gupta, S. K. Patra Raj K.
2010-01-01
We have calculated the binding energy, root-mean-square radius and quadrupole deformation parameter for the recently synthesized superheavy element Z=117, using the axially deformed relativistic mean field (RMF) model. The calculation is extended to various isotopes of Z=117 element, strarting from A=286 till A=310. We predict almost spherical structures in the ground state for almost all the isotopes. A shape transition appears at about A=292 from prolate to a oblate shape structures of Z=11...
Relativistic hadrons and the origin of relativistic outflows in active galactic nuclei
Contopoulos, John; Kazanas, D.
1995-01-01
We examine the hydrodynamic origin of relativistic outflows in active galactic nuclei (AGN). Specifically, we propose that the presence of a population of relativistic hadrons in the AGN 'central engine' and the associated neutron production suffices to produce outflows which under rather general conditions could be relativistic. The main such condition is that the size of the neutron production region be larger than the neutron flight path tau(sub n) approximately 3 x 10(exp 13) cm. This condition guarantees that the mean energy per particle in the proton fluid, resulting from the decay of the neutrons outside their production region, be greater than the proton rest mass. The expansion of this fluid can then lead naturally to a relativistic outflow by conversion of its internal energy to directed motion. We follow the development of such flows by solving the mass, energy as well as the kinetic equation for the proton gas in steady state, taking into account the source terms due to compute accurately the adiabatic index of the expanding gas, and in conjunction with Bernoulli's equation the detailed evolution of the bulk Lorentz factor. We further examine the role of large-scale magnetic fields in confining these outflows to produce the jets observed at larger scales.
Bhuyan, M
2010-01-01
We have calculated the binding energy, root-mean-square radius and quadrupole deformation parameter for the recently synthesized superheavy element Z=117, using the axially deformed relativistic mean field (RMF) model. The calculation is extended to various isotopes of Z=117 element, strarting from A=286 till A=310. We predict almost spherical structures in the ground state for almost all the isotopes. A shape transition appears at about A=292 from prolate to a oblate shape structures of Z=117 nucleus in our mean field approach. The most stable isotope (largest binding energy per nucleon) is found to be the $^{288}$117 nucleus. Also, the Q-value of $\\alpha$-decay $Q_\\alpha$ and the half-lives $T_{\\alpha}$ are calculated for the $\\alpha$-decay chains of $^{293}$117 and $^{294}$117, supporting the magic numbers at N=172 and/ or 184.
PACIAE 2.0: An Updated Parton and Hadron Cascade Model (Program) for Relativistic Nuclear Collisions
SA; Ben-hao; ZHOU; Dai-mei; YAN; Yu-liang; LI; Xiao-mei; FENG; Sheng-qing; DONG; Bao-guo; CAI; Xu
2012-01-01
<正>We have updated the parton and hadron cascade model PACIAE for the relativistic nuclear collisions, from based on JETSET 6.4 and PYTHIA 5.7, and referred to as PACIAE 2.0. The main physics concerning the stages of the parton initiation, parton rescattering, hadronization, and hadron rescattering were discussed. The structures of the programs were briefly explained. In addition, some calculated examples were compared with the experimental data. It turns out that this model (program) works well.
Subrata Pal
2015-05-01
We review the transport models that are widely used to study the properties of the quark-gluon plasma formed in relativistic heavy-ion collisions at RHIC and LHC. We show that transport model analysis of two important and complementary observables, the anisotropic flow of bulk hadrons and suppression of hadron yields at high transverse momentum, provide exciting new information on the properties of the plasma formed.
M MOUSAVI; M R SHOJAEI
2017-02-01
In this work, we have obtained energy levels and charge radius for the $\\beta$-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magicnumber and a single nucleon energy level. Here we have taken $^{41}$Ca with a single neutron in the $^{40}$Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the coreand the single nucleon. By using parametric Nikiforov–Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for 17O, $^{41}$Ca, $^{49}$Ca and $^{57}$Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.
Hadronization conditions in relativistic nuclear collisions and the QCD pseudo-critical line
Becattini, F; Stock, R; Bleicher, M
2016-01-01
We compare the reconstructed hadronization conditions in relativistic nuclear collisions in the nucleon-nucleon centre-of-mass energy range 4.7-2760 GeV in terms of temperature and baryon-chemical potential with lattice QCD calculations, by using hadronic multiplicities. We obtain hadronization temperatures and baryon chemical potentials with a fit to measured multiplicities by correcting for the effect of post-hadronization rescattering. The post-hadronization modification factors are calculated by means of a coupled hydrodynamical-transport model simulation under the same conditions of isothermal and isochemical decoupling as assumed in the statistical hadronization model fits to the data. The fit quality is considerably better than without rescattering corrections, as already found in previous work. The curvature of the obtained "true" hadronization pseudo-critical line kappa is found to be 0.0048+-0.0026, in agreement with lattice QCD estimates; the pseudo-critical temperature at vanishing mu_B is found t...
Z-Scaling, Fractality and Principle of Relativity in Relativistic Collisions of Hadrons and Nuclei
Zborovský, I; Panebratsev, Yu A; Skoro, G P
2001-01-01
The formation length of particles produced in the relativistic collisions of hadrons and nuclei has relevance to the fundamental principles of physics at small interaction distances. The relation is phenomenologically expressed by a z-scaling observed in the differential cross sections for the inclusive reactions at high energies. The scaling variable reflects the length of the elementary particle trajectories in terms of a fractal measure. Characterizing the fractal approach, we demonstrate the relativity principle in space-time with broken isotropy. We derive relativistic transformations accounting for the asymmetry of space-time induced in the interactions by various parton fractal structures of hadrons and nuclei.
Re-hardening of hadron transverse mass spectra in relativistic heavy-ion collisions
P K Sahu; N Otuka; M Isse; Y Nara; A Ohnishi
2006-05-01
We analyze the spectra of pions and protons in heavy-ion collisions at relativistic energies from 2 A GeV to 65+65 A GeV by using a jet-implemented hadron-string cascade model. In this energy region, hadron transverse mass spectra first show softening until SPS energies, and re-hardening may emerge at RHIC energies. Since hadronic matter is expected to show only softening at higher energy densities, this re-hardening of spectra can be interpreted as a good signature of the quark-gluon plasma formation.
Wang, Zaijun; Ren, Zhongzhou; Dong, Tiekuang; Xu, Chang
2014-08-01
The ground-state spins and parities of the odd-A phosphorus isotopes 25-47P are studied with the relativistic mean-field (RMF) model and relativistic elastic magnetic electron-scattering theory (REMES). Results of the RMF model with the NL-SH, TM2, and NL3 parameters show that the 2s1/2 and 1d3/2 proton level inversion may occur for the neutron-rich isotopes 37-47P, and, consequently, the possible spin-parity values of 37-47P may be 3/2+, which, except for P47, differs from those given by the NUBASE2012 nuclear data table by Audi et al. Calculations of the elastic magnetic electron scattering of 37-47P with the single valence proton in the 2s1/2 and 1d3/2 state show that the form factors have significant differences. The results imply that elastic magnetic electron scattering can be a possible way to study the 2s1/2 and 1d3/2 level inversion and the spin-parity values of 37-47P. The results can also provide new tests as to what extent the RMF model, along with its various parameter sets, is valid for describing the nuclear structures. In addition, the contributions of the upper and lower components of the Dirac four-spinors to the form factors and the isotopic shifts of the magnetic form factors are discussed.
Relativistic Harmonic Oscillators and Hadronic Structures in the Quantum-Mechanics Curriculum
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A relativistic harmonic-oscillator formalism which is mathematically simple as the nonrelativistic harmonic oscillator is given. In view of its effectiveness in describing Lorentz-deformed hadrons, the inclusion of this formalism in a first-year graduate course will make the results of high-energy experiments more understandable. (BB)
Charged Hadron Multiplicity Distribution at Relativistic Heavy-Ion Colliders
Ashwini Kumar
2013-01-01
Full Text Available The present paper reviews facts and problems concerning charge hadron production in high energy collisions. Main emphasis is laid on the qualitative and quantitative description of general characteristics and properties observed for charged hadrons produced in such high energy collisions. Various features of available experimental data, for example, the variations of charged hadron multiplicity and pseudorapidity density with the mass number of colliding nuclei, center-of-mass energies, and the collision centrality obtained from heavy-ion collider experiments, are interpreted in the context of various theoretical concepts and their implications. Finally, several important scaling features observed in the measurements mainly at RHIC and LHC experiments are highlighted in the view of these models to draw some insight regarding the particle production mechanism in heavy-ion collisions.
Biswal, S K
2014-01-01
We study the isoscalar giant monopole resonance for drip-lines and super heavy nuclei in the frame work of a relativistic mean field theory with scaling approach. The well known extended Thomas-Fermi approximation in the non-linear $\\sigma$-$\\omega$ model is used to estimate the giant monopole excitation energy for some selected light spherical nuclei starting from the region of proton to neutron drip-lines. The application is extended to super heavy region for Z=114 and 120, which are predicted by several models as the next proton magic number beyond Z=82. We compared the excitation energy obtained by four successful force parameters NL1, NL3, NL3$^*$ and FSUGold. The monopole energy decreases toward the proton and neutron drip-lines in an isotopic chain for lighter mass nuclei contrary to a monotonous decrease for super heavy isotopes. The maximum and minimum monopole excitation energies are obtained for nuclei with minimum and maximum isospin, respectively in an isotopic chain.
Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
2013-01-01
We have developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) for finite nuclei in which the shape degrees of freedom \\beta_{\\lambda\\mu} with even \\mu, e.g., \\beta_{20}, \\beta_{22}, \\beta_{30}, \\beta_{32}, \\beta_{40}, etc., can be described simultaneously. The functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. For the pp channel, either the BCS approach or the Bogoliubov transformation is implemented. The MDC-CDFTs with the BCS approach for the pairing (in the following labelled as MDC-RMF models with RMF standing for "relativistic mean field") have been applied to investigate multi-dimensional potential energy surfaces and the non-axial octupole $Y_{32}$-correlations in N=150 isotones. In this contribution we present briefly the formalism of MDC-RMF models and some results from these models. The potential energy surfaces with and without triaxial deformatio...
Sharma, M M; Münzenberg, G
2004-01-01
We have investigated properties of $\\alpha$-decay chains of recently produced superheavy elements Z=115 and Z=113 using the new Lagrangian model NL-SV1 with inclusion of the vector self-coupling of $\\omega$ meson in the framework of the relativistic mean-field theory. It is shown that the experimentally observed alpha-decay energies and half-lives are reproduced well by this Lagrangian model. Further calculations for the heavier elements with Z=117-125 show that these nuclei are superdeformed with a prolate shape in the ground state. A superdeformed shell-closure at Z=118 lends an additional binding and an extra stability to nuclei in this region. Consequently, it is predicted that the corresponding $Q_\\alpha$ values provide $\\alpha$-decay half-lives for heavier superheavy nuclei within the experimentally feasible conditions. The results are compared with those of macroscopic-microscopic approaches. A perspective of the difference in shell effects amongst various approaches is presented and its consequences o...
Dinesh Kumar Srivastava
2001-08-01
The production of single photons in Pb+Pb collisions at the CERN SPS as measured by the WA98 experiment is analysed. A quark gluon plasma is assumed to be formed initially, which expands, cools, hadronizes, and undergoes freeze-out. A rich hadronic equation of state is used and the transverse expansion of the interacting system is taken into account. The recent estimates of photon production in quark-matter (at two loop level) along with the dominant reactions in the hadronic matter leading to photons are used. About half of the radiated photons are seen to have a thermal origin. The same treatment and the initial conditions provide a very good description to hadronic spectra measured by several groups and the intermediate mass dileptons measured by the NA50 experiment, lending a strong support to the conclusion that quark gluon plasma has been formed in these collisions. Predictions for RHIC and LHC energies are also given.
Hadronization conditions in relativistic nuclear collisions and the QCD pseudo-critical line
Becattini, Francesco; Steinheimer, Jan; Stock, Reinhard; Bleicher, Marcus
2017-01-01
We compare the reconstructed hadronization conditions in relativistic nuclear collisions in the nucleon-nucleon centre-of-mass energy range 4.7-2760 GeV in terms of temperature and baryon-chemical potential with lattice QCD calculations, by using hadronic multiplicities. We obtain hadronization temperatures and baryon chemical potentials with a fit to measured multiplicities by correcting for the effect of post-hadronization rescattering. The post-hadronization modification factors are calculated by means of a coupled hydrodynamical-transport model simulation under the same conditions of approximate isothermal and isochemical decoupling as assumed in the statistical hadronization model fits to the data. The fit quality is considerably better than without rescattering corrections, as already found in previous work. The curvature of the obtained "true" hadronization pseudo-critical line κ is found to be 0.0048 ± 0.0026, in agreement with lattice QCD estimates; the pseudo-critical temperature at vanishing μB is found to be 164.3 ± 1.8 MeV.
Test of Relativistic Gravity for Propulsion at the Large Hadron Collider
Felber, Franklin
2010-01-01
A design is presented of a laboratory experiment that could test the suitability of relativistic gravity for propulsion of spacecraft to relativistic speeds. An exact time-dependent solution of Einstein's gravitational field equation confirms that even the weak field of a mass moving at relativistic speeds could serve as a driver to accelerate a much lighter payload from rest to a good fraction of the speed of light. The time-dependent field of ultrarelativistic particles in a collider ring is calculated. An experiment is proposed as the first test of the predictions of general relativity in the ultrarelativistic limit by measuring the repulsive gravitational field of bunches of protons in the Large Hadron Collider (LHC). The estimated `antigravity beam' signal strength at a resonant detector of each proton bunch is 3 nm/s2 for 2 ns during each revolution of the LHC. This experiment can be performed off-line, without interfering with the normal operations of the LHC.
Test of relativistic gravity for propulsion at the Large Hadron Collider
Felber, Franklin
2009-01-01
A design is presented of a laboratory experiment that could test the suitability of relativistic gravity for propulsion of spacecraft to relativistic speeds. The first exact time-dependent solutions of Einstein's gravitational field equation confirm that even the weak field of a mass moving at relativistic speeds could serve as a driver to accelerate a much lighter payload from rest to a good fraction of the speed of light. The time-dependent field of ultrarelativistic particles in a collider ring is calculated. An experiment is proposed as the first test of the predictions of general relativity in the ultrarelativistic limit by measuring the repulsive gravitational field of bunches of protons in the Large Hadron Collider (LHC). The estimated 'antigravity beam' signal strength at a resonant detector of each proton bunch is 3 nm/s^2 for 2 ns during each revolution of the LHC. This experiment can be performed off-line, without interfering with the normal operations of the LHC.
Mean-field models and exotic nuclei
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); Rutz, K. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany)]|[Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Reinhard, P.G. [Inst. fuer Theoretische Physik, Univ. Erlangen (Germany)
1998-06-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Hadron Mass Spectra and Decay Rates in a Potential Model with Relativistic Wave Equations.
Namgung, Wuk
Hadron properties of mass spectra and decay rates are calculated in a quark potential model. Wave equations based on the Klein-Gordon and Todorov equations both of which incorporate the feature of relativistic two-body kinematics are used. The wave equations are modified to contain potentials which transform either like a Lorentz scalar or like a time-component of a four-vector. Potentials based on the Fogleman-Lichtenberg-Wills potential which has the properties suggested by QCD of both confinement and asymptotic freedom are used. The potentials, motivated by QCD but otherwise phenomenological, are further generalized to forms which can apply to any color representation. To break the degeneracy between vector and pseudoscalar mesons or between spin-3/2 and spin-1/2 baryons, the essential feature of spin dependence is included in the potentials. The masses of vector and pseudoscalar mesons are calculated with only a small number of adjustable parameters, and good qualitative agreement with experiment is obtained for both heavy and light mesons. Baryons are treated in this framework by making use of a quark-diquark two-body model of baryons. First, diquark properties are calculated without any additional parameters. The g-factors of diquarks and spin-flavor configuration of baryons, which are necessary for the calculation of baryons, are given. Then baryon masses are calculated also without additional parameters. The results of the masses of ground-state baryons are in good qualitative agreement with experiment. Also effective constituent quark masses are obtained using current quark masses as input. The calculated effective constituent quark masses are in the right range of the values that most theoretical estimates have given. The general qualitative features of hadron spectra are similar with the two relativistic wave equations, although there are differences in detail. The Van Royen-Weisskopf formula for electromagnetic decay widths of vector mesons into lepton
Liquid-gas phase transition in strange hadronic matter with relativistic models
Torres, James R; Menezes, Débora P
2015-01-01
Background: The advent of new dedicated experimental programs on hyperon physics is rapidly boosting the field, and the possibility of synthetizing multiple strange hypernuclei requires the addition of the strangeness degree of freedom to the models dedicated to nuclear structure and nuclear matter studies at low energy. Purpose: We want to settle the influence of strangeness on the nuclear liquid-gas phase transition. Because of the large uncertainties concerning the hyperon sector, we do not aim at a quantitative estimation of the phase diagram but rather at a qualitative description of the phenomenology, as model independent as possible. Method: We analyze the phase diagram of low density matter composed of neutrons, protons and $\\Lambda$ hyperons using a Relativistic Mean Field (RMF) model. We largely explore the parameter space to pin down generic features of the phase transition, and compare the results to ab-initio quantum Monte Carlo calculations. Results: We show that the liquid-gas phase transition ...
Gao, Y.-Q.; Liu, F.-H.
2016-03-01
The transverse momentum spectra of charged particles produced in Au + Au collisions at the relativistic heavy ion collider and in Pb + Pb collisions at the large hadron collider with different centrality intervals are described by the multisource thermal model which is based on different statistic distributions for a singular source. Each source in the present work is described by the Tsallis distribution and the Boltzmann distribution, respectively. Then, the interacting system is described by the (two-component) Tsallis distribution and the (two-component) Boltzmann distribution, respectively. The results calculated by the two distributions are in agreement with the experimental data of the Solenoidal Tracker At Relativistic heavy ion collider, Pioneering High Energy Nuclear Interaction eXperiment, and A Large Ion Collider Experiment Collaborations. The effective temperature parameters extracted from the two distributions on the descriptions of heavy-ion data at the relativistic heavy ion collider and large hadron collider are obtained to show a linear correlation.
Gomes, Diogo A.
2014-01-06
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
Liquid-gas phase transition in strange hadronic matter with relativistic models
Torres, James R.; Gulminelli, F.; Menezes, Débora P.
2016-02-01
Background: The advent of new dedicated experimental programs on hyperon physics is rapidly boosting the field, and the possibility of synthesizing multiple strange hypernuclei requires the addition of the strangeness degree of freedom to the models dedicated to nuclear structure and nuclear matter studies at low energy. Purpose: We want to settle the influence of strangeness on the nuclear liquid-gas phase transition. Because of the large uncertainties concerning the hyperon sector, we do not aim at a quantitative estimation of the phase diagram but rather at a qualitative description of the phenomenology, as model independent as possible. Method: We analyze the phase diagram of low-density matter composed of neutrons, protons, and Λ hyperons using a relativistic mean field (RMF) model. We largely explore the parameter space to pin down generic features of the phase transition, and compare the results to ab initio quantum Monte Carlo calculations. Results: We show that the liquid-gas phase transition is only slightly quenched by the addition of hyperons. Strangeness is seen to be an order parameter of the phase transition, meaning that dilute strange matter is expected to be unstable with respect to the formation of hyperclusters. Conclusions: More quantitative results within the RMF model need improved functionals at low density, possibly fitted to ab initio calculations of nuclear and Λ matter.
Petersen, Kaare Brandt
2006-01-01
This thesis describes investigations and improvements of a technique for Independent Component Analysis (ICA), called "Mean Field ICA". The main focus of the thesis is the optimization part of the algorithm, the so-called "EM algorithm". Using different approaches it is demonstrated that the EM...... Gradient Recipe is applicable to a wide selection of models. Furthermore, the Mean Field ICA model is extended to incorporate ltering over time in a so-called "convolutive ICA" model. Finally, by using mixture of Gaussians as source priors, the generative and ltering approach to ICA is compared...
Guerra, E.M. de [Inst. de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas (Spain)
2001-07-01
In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime,.., to detailed structure in excitation spectra (high spin, RPA modes,..), as well as charge, magnetization and velocity distributions. (orig.)
Andronic, A; Braun-Munzinger, P; Cleymans, J; Fukushima, K; McLerran, L D; Oeschler, H; Pisarski, R D; Redlich, K; Sasaki, C; Satz, H; Stachel, J
2009-01-01
We argue that features of hadron production in relativistic nuclear collisions, mainly at CERN-SPS energies, may be explained by the existence of three forms of matter: Hadronic Matter, Quarkyonic Matter, and a Quark-Gluon Plasma. We suggest that these meet at a triple point in the QCD phase diagram. Some of the features explained, both qualitatively and semi-quantitatively, include the curve for the decoupling of chemical equilibrium, along with the non-monotonic behavior of strange particle multiplicity ratios at center of mass energies near 10 GeV. If the transition(s) between the three phases are merely crossover(s), the triple point is only approximate.
Lambda Hypernuclei in a Chiral Hadronic Model
LIANG Yin-Hua; GUO Hua
2005-01-01
@@ Nuclear matter calculations in a chiral hadronic model have been performed. It has been found that the scalar and the vector potentials and binding energies per nucleon in the chiral hadronic model are very close to those of the microscopic relativistic Brueckner-Hartree-Fock calculations. The good results for finite nuclei can be obtained in the mean field approximation only if scalar mass ms and coupling constant gs have been improved with the fixed values of cs2 ≡ g2s(M/ms)2 as those given by the original parameter sets of the chiral hadronic model. Then the chiral hadronic model is extended to lambda hypernuclei. Our results predicted by the chiral hadronic model are compared with those by the nonlinear Walecka model. It has been shown that the hadronic model can also be used to describe lambda hypernuclei successfully.
Finite Volume Effect of Baryons in Strange Hadronic Matter
SUN Bao-Xi; LI Lei; NING Ping-Zhi; ZHAO En-Guang
2001-01-01
The finite volume effect of baryons in strange hadronic matter (SHM) is studied within the framework of relativistic mean-field theory. As this effect is concerned, the saturation density of SHM turns lower, and the binding energy per baryon decreases. Its influence to the compression modulus of SHM is also discussed.
Zhong, Yang; Yang, Chun-Bin; Cai, Xu; Feng, Sheng-Qin
2016-08-01
It has been proposed that electric fields may lead to chiral separation in quark-gluon plasma (QGP). This is called the chiral electric separation effect. The strong electromagnetic field and the QCD vacuum can both be completely produced in off-central nuclear-nuclear collision. We use the Woods-Saxon nucleon distribution to calculate the electric field distributions of off-central collisions. The chiral electric field spatial distribution at Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC) energy regions are systematically studied in this paper. The dependence of the electric field produced by the thermal quark in the central position with different impact parameters on the proper time with different collision energies in the RHIC and LHC energy regions are studied in this paper. Supported by National Natural Science Foundation of China (11375069, 11435054, 11075061, 11221504) and Key Laboratory Foundation of Quark and Lepton Physics (Hua-Zhong Normal University)(QLPL2014P01)
Chen, Lin; Wei, Shu-Yi; Xiao, Bo-Wen; Zhang, Han-Zhong
2016-01-01
Dijet, dihadron, hadron-jet angular correlations have been reckoned as important probes of the transverse momentum broadening effects in relativistic nuclear collisions. When a pair of high-energy jets created in hard collisions traverse the quark-gluon plasma produced in heavy-ion collisions, they become de-correlated due to the vacuum soft gluon radiation associated with the Sudakov logarithms and the medium-induced transverse momentum broadening. For the first time, we employ the systematical resummation formalism and establish a baseline calculation to describe the dihadron and hadron-jet angular correlation data in $pp$ and peripheral $AA$ collisions where the medium effect is negligible. We demonstrate that the medium effects, especially the so-called jet quenching parameter $\\hat q$, can be extracted from the angular de-correlations observed in $AA$ collisions. A global $\\chi^2$ analysis of dihadron and hadron-jet angular correlation data renders the best fit $\\langle \\hat q L\\rangle_{\\textrm{tot}} \\si...
Measurement of q ˆ in Relativistic Heavy Ion Collisions using di-hadron correlations
Tannenbaum, M. J.
2017-08-01
The propagation of partons from hard scattering through the Quark Gluon Plasma produced in A+A collisions at RHIC and the LHC is represented in theoretical analyses by the transport coefficient q ˆ and predicted to cause both energy loss of the outgoing partons, observed as suppression of particles or jets with large transverse momentum pT, and broadening of the azimuthal correlations of the outgoing di-jets or di-hadrons from the outgoing parton-pair, which has not been observed. The widths of azimuthal correlations of di-hadrons with the same trigger particle pTt and associated pTa transverse momenta in p+p and Au+Au are so-far statistically indistinguishable as shown in recent as well as older di-hadron measurements and also with jet-hadron and hadron-jet measurements. The azimuthal width of the di-hadron correlations in p+p collisions, beyond the fragmentation transverse momentum, jT, is dominated by kT, the so-called intrinsic transverse momentum of a parton in a nucleon, which can be measured. The broadening should produce a larger kT in A+A than in p+p collisions. The present work introduces the observation that the kT measured in p+p collisions for di-hadrons with pTt and pTa must be reduced to compensate for the energy loss of both the trigger and away parent partons when comparing to the kT measured with the same di-hadron pTt and pTa in Au+Au collisions. This idea is applied to a recent STAR di-hadron measurement, with result = 2.1 ± 0.6 GeV2. This is more precise but in agreement with a theoretical calculation of =14-14+42 GeV2 using the same data. Assuming a length ≈ 7 fm for central Au+Au collisions the present result gives q ˆ ≈ 0.30 ± 0.09 GeV2/fm, in fair agreement with the JET collaboration result from single hadron suppression of q ˆ ≈ 1.2 ± 0.3 GeV2/fm at an initial time τ0 = 0.6 fm/c in Au+Au collisions at √{sNN} = 200 GeV.
Abdelsalam, A; Hafiz, M E
2012-01-01
The behavior of the relativistic hadron (shower particle) multiplicity for (32)S-nucleus interactions is investigated. The experiment is carried out at 3.7A GeV (Dubna energy) and 200A GeV (SPS energy) to search for the incident energy effect on the interactions inside the different emulsion target nuclei. Data are presented in terms of the number of emitted relativistic hadrons in both forward and backward angular zones. The dependence on the target size is presented. For this purpose the statistical events are separated into groups according to the interactions with H, CNO, Em, and AgBr target nuclei. The separation of events, into these groups, is executed based on predictions of Glauber's multiple scattering theory. Features suggestive of a decay mechanism seem to be a characteristic of the backward emission of relativistic hadrons. The results strongly support the assumption that the relativistic hadrons may already be emitted during the de-excitation of the excited target nucleus, in a behavior like tha...
Schade, Henry
2010-09-15
Strange particles play an important role as probes of relativistic heavy-ion collisions where hot and dense matter is studied. The focus of this thesis is on the production of strange particles within a transport model of Boltzmann-Uehling-Uhlenbeck (BUU) type. Current data of the HADES Collaboration concerning K{sup {+-}} and {phi} spectra provide the appropriate experimental framework. Moreover, the double-strange hyperon {xi}{sup -} is analyzed below the free NN production threshold. Hadron multiplicities, transversemomentum and rapidity spectra are compared with recent experimental data. Further important issues are in-medium mass shifts, the nuclear equation of state as well as the mean field of nucleons. Besides the study of AA collisions a comparison with recent ANKE data regarding the {phi} yield in pA collisions is done. Transparency ratios are determined and primarily investigated for absorption of {phi} mesons by means of the BUU transport code. Thereby, secondary {phi} production channels, isospin asymmetry and detector acceptance are important issues. A systematic analysis is presented for different system sizes. The momentum integrated Boltzmann equations describe dense nuclear matter on a hadronic level appearing in the Big Bang as well as in little bangs, in the context of kinetic off-equilibrium dynamics. This theory is applied to antiprotons and numerically calculated under consideration of various expansion models. Here, the evolution of proton- and antiproton densities till freeze-out is analyzed for ultra-relativistic heavy-ion collisions within a hadrochemic resonance gas model acting as a possible ansatz for solving the ''antiproton puzzle''. Furthermore, baryonic matter and antimatter is investigated in the early universe and the adiabatic path of cosmic matter is sketched in the QCD phase diagram. (orig.)
Indications of conical emission of charged hadrons at the BNL relativistic heavy ion collider.
Abelev, B I; Aggarwal, M M; Ahammed, Z; Anderson, B D; Arkhipkin, D; Averichev, G S; Bai, Y; Balewski, J; Barannikova, O; Barnby, L S; Baudot, J; Baumgart, S; Beavis, D R; Bellwied, R; Benedosso, F; Betts, R R; Bhardwaj, S; Bhasin, A; Bhati, A K; Bichsel, H; Bielcik, J; Bielcikova, J; Biritz, B; Bland, L C; Bombara, M; Bonner, B E; Botje, M; Bouchet, J; Braidot, E; Brandin, A V; Bruna, E; Bueltmann, S; Burton, T P; Bystersky, M; Cai, X Z; Caines, H; Calderón de la Barca Sánchez, M; Callner, J; Catu, O; Cebra, D; Cendejas, R; Cervantes, M C; Chajecki, Z; Chaloupka, P; Chattopadhyay, S; Chen, H F; Chen, J H; Chen, J Y; Cheng, J; Cherney, M; Chikanian, A; Choi, K E; Christie, W; Chung, S U; Clarke, R F; Codrington, M J M; Coffin, J P; Cormier, T M; Cosentino, M R; Cramer, J G; Crawford, H J; Das, D; Dash, S; Daugherity, M; De Silva, C; de Moura, M M; Dedovich, T G; Dephillips, M; Derevschikov, A A; de Souza, R Derradi; Didenko, L; Djawotho, P; Dogra, S M; Dong, X; Drachenberg, J L; Draper, J E; Du, F; Dunlop, J C; Dutta Mazumdar, M R; Edwards, W R; Efimov, L G; Elhalhuli, E; Elnimr, M; Emelianov, V; Engelage, J; Eppley, G; Erazmus, B; Estienne, M; Eun, L; Fachini, P; Fatemi, R; Fedorisin, J; Feng, A; Filip, P; Finch, E; Fine, V; Fisyak, Y; Gagliardi, C A; Gaillard, L; Gangadharan, D R; Ganti, M S; Garcia-Solis, E; Ghazikhanian, V; Ghosh, P; Gorbunov, Y N; Gordon, A; Grebenyuk, O; Grosnick, D; Grube, B; Guertin, S M; Guimaraes, K S F F; Gupta, A; Gupta, N; Guryn, W; Haag, B; Hallman, T J; Hamed, A; Harris, J W; He, W; Heinz, M; Heppelmann, S; Hippolyte, B; Hirsch, A; Hjort, E; Hoffman, A M; Hoffmann, G W; Hofman, D J; Hollis, R S; Huang, H Z; Humanic, T J; Igo, G; Iordanova, A; Jacobs, P; Jacobs, W W; Jakl, P; Jin, F; Jones, P G; Joseph, J; Judd, E G; Kabana, S; Kajimoto, K; Kang, K; Kapitan, J; Kaplan, M; Keane, D; Kechechyan, A; Kettler, D; Khodyrev, V Yu; Kiryluk, J; Kisiel, A; Klein, S R; Knospe, A G; Kocoloski, A; Koetke, D D; Kopytine, M; Kotchenda, L; Kouchpil, V; Kravtsov, P; Kravtsov, V I; Krueger, K; Krus, M; Kuhn, C; Kumar, L; Kurnadi, P; Lamont, M A C; Landgraf, J M; Lapointe, S; Lauret, J; Lebedev, A; Lednicky, R; Lee, C-H; Levine, M J; Li, C; Li, Y; Lin, G; Lin, X; Lindenbaum, S J; Lisa, M A; Liu, F; Liu, H; Liu, J; Liu, L; Ljubicic, T; Llope, W J; Longacre, R S; Love, W A; Lu, Y; Ludlam, T; Lynn, D; Ma, G L; Ma, Y G; Mahapatra, D P; Majka, R; Mall, O I; Mangotra, L K; Manweiler, R; Margetis, S; Markert, C; Matis, H S; Matulenko, Yu A; McShane, T S; Meschanin, A; Millane, J; Miller, M L; Minaev, N G; Mioduszewski, S; Mischke, A; Mitchell, J; Mohanty, B; Molnar, L; Morozov, D A; Munhoz, M G; Nandi, B K; Nattrass, C; Nayak, T K; Nelson, J M; Nepali, C; Netrakanti, P K; Ng, M J; Nogach, L V; Nurushev, S B; Odyniec, G; Ogawa, A; Okada, H; Okorokov, V; Olson, D; Pachr, M; Page, B S; Pal, S K; Pandit, Y; Panebratsev, Y; Pawlak, T; Peitzmann, T; Perevoztchikov, V; Perkins, C; Peryt, W; Phatak, S C; Planinic, M; Pluta, J; Poljak, N; Poskanzer, A M; Potukuchi, B V K S; Prindle, D; Pruneau, C; Pruthi, N K; Putschke, J; Raniwala, R; Raniwala, S; Ray, R L; Reed, R; Ridiger, A; Ritter, H G; Roberts, J B; Rogachevskiy, O V; Romero, J L; Rose, A; Roy, C; Ruan, L; Russcher, M J; Rykov, V; Sahoo, R; Sakrejda, I; Sakuma, T; Salur, S; Sandweiss, J; Sarsour, M; Schambach, J; Scharenberg, R P; Schmitz, N; Seger, J; Selyuzhenkov, I; Seyboth, P; Shabetai, A; Shahaliev, E; Shao, M; Sharma, M; Shi, S S; Shi, X-H; Sichtermann, E P; Simon, F; Singaraju, R N; Skoby, M J; Smirnov, N; Snellings, R; Sorensen, P; Sowinski, J; Spinka, H M; Srivastava, B; Stadnik, A; Stanislaus, T D S; Staszak, D; Strikhanov, M; Stringfellow, B; Suaide, A A P; Suarez, M C; Subba, N L; Sumbera, M; Sun, X M; Sun, Y; Sun, Z; Surrow, B; Symons, T J M; Szanto de Toledo, A; Takahashi, J; Tang, A H; Tang, Z; Tarnowsky, T; Thein, D; Thomas, J H; Tian, J; Timmins, A R; Timoshenko, S; Tlusty, D; Tokarev, M; Trainor, T A; Tram, V N; Trattner, A L; Trentalange, S; Tribble, R E; Tsai, O D; Ulery, J; Ullrich, T; Underwood, D G; Van Buren, G; van Leeuwen, M; Vander Molen, A M; Vanfossen, J A; Varma, R; Vasconcelos, G M S; Vasilevski, I M; Vasiliev, A N; Videbaek, F; Vigdor, S E; Viyogi, Y P; Vokal, S; Voloshin, S A; Wada, M; Waggoner, W T; Wang, F; Wang, G; Wang, J S; Wang, Q; Wang, X; Wang, X L; Wang, Y; Webb, J C; Westfall, G D; Whitten, C; Wieman, H; Wissink, S W; Witt, R; Wu, Y; Xu, N; Xu, Q H; Xu, Y; Xu, Z; Yepes, P; Yoo, I-K; Yue, Q; Zawisza, M; Zbroszczyk, H; Zhan, W; Zhang, H; Zhang, S; Zhang, W M; Zhang, Y; Zhang, Z P; Zhao, Y; Zhong, C; Zhou, J; Zoulkarneev, R; Zoulkarneeva, Y; Zuo, J X
2009-02-06
Three-particle azimuthal correlation measurements with a high transverse momentum trigger particle are reported for pp, d+Au, and Au+Au collisions at sqrt[s_{NN}]=200 GeV by the STAR experiment. Dijet structures are observed in pp, d+Au and peripheral Au+Au collisions. An additional structure is observed in central Au+Au data, signaling conical emission of correlated charged hadrons. The conical emission angle is found to be theta=1.37+/-0.02(stat)-0.07+0.06(syst), independent of p_{ perpendicular}.
Remarks concerning bulk viscosity of hadron matter in relaxation time ansatz
Khvorostukhin, A.S., E-mail: hvorost@theor.jinr.ru [Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Institute of Applied Physics, Moldova Academy of Science, MD-2028 Kishineu (Moldova, Republic of); Toneev, V.D. [Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Voskresensky, D.N. [National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow 115409 (Russian Federation)
2013-10-03
The bulk viscosity is calculated for hadron matter produced in heavy-ion collisions, being described in the relaxation time approximation within the relativistic mean-field-based model with scaled hadron masses and couplings. We show how different approximations used in the literature affect the result. Numerical evaluations of the bulk viscosity with three considered models deviate not much from each other confirming earlier results.
The triple GEM detector as beam monitor for relativistic hadron beams
Aza, E; Murtas, F; Puddu, S; Silari, M
2014-01-01
triple GEM detector was tested at the CERF facility at CERN as an on-line beam imaging monitor and as a counting reference device. It was exposed to a 120 GeV/c positively charged hadron beam (approximately 2/3 pions and 1/3 protons), which hits a copper target gen- erating a wide spectrum of different kinds of particles used for various experiments. The flux of beam particles ranged over three orders of magnitude, from 8 10 4 s 1 to 8 10 7 s 1 . The profile of the beam acquired with the GEM was compared to the one measured with a MWPC and no satu- ration was observed. In addition, the count rate measured with the GEM was compared to the one measured with an Ionization Chamber, which is routinely used for monitoring the beam intensity. Another way of monitoring the intensity of the beam was also explored, which is based on the total current driven from the GEM foils. The digital readout allows making a 2D online image of the beam for the alignment with the copper target in the CERF facility. A low residual ac...
Acceleration in perpendicular relativistic shocks for plasmas consisting of leptons and hadrons
Stockem, A; Fonseca, R A; Silva, L O
2012-01-01
We investigate the acceleration of light particles in perpendicular shocks for plasmas consisting of a mixture of leptonic and hadronic particles. Starting from the full set of conservation equations for the mixed plasma constituents, we generalize the magneto-hydrodynamical jump conditions for a multi-component plasma, including information about the specific adiabatic constants for the different species. The impact of deviations from the standard model of an ideal gas is compared in theory and particle-in-cell simulations, showing that the standard-MHD model is a good approximation. The simulations of shocks in electron-positron-ion plasmas are for the first time multi-dimensional, transverse effects are small in this configuration and 1D simulations are a good representation if the initial magnetization is chosen high. 1D runs with a mass ratio of 1836 are performed, which identify the Larmor frequency \\omega_{ci} as the dominant frequency that determines the shock physics in mixed component plasmas. The m...
Identifying Charged Hadrons on the Relativistic Rise Using the ALICE TPC at LHC
Gros, Philippe
2011-01-01
The chain from hadron collisions to the physics results requires several important links. First the outcome of the collision is measured by the detectors. Then, the signal from the detector is processed and transformed into information relevant for the study of the physics processes. The data is made available to physicists to be analysed and used to improve theories. This thesis presents work done on no most of these steps for the ALICE experiment at LHC. First a study of the main processes in the TPC detector for ALICE was done using simulation and test beam data. The results are shown in paper I. The study was deepened with the analysis of test beam data from a TPC prototype for the ILC, as shown in paper III. Concurrently, a study on the Grid – computing framework for distributed computing and storage resources – was performed. This involved the development of an interface module between the ALICE software AliEn and the ARC software developped in the Nordic countries. This work is presented in paper I...
Hadron production in relativistic heavy ion interactions and the search for the quark-gluon plasma
Tannenbaum, M.J.
1989-12-01
The course starts with an introduction, from the experimentalist's point of view, of the challenge of measuring Relativistic Heavy Ion interactions. A review of some theoretical predictions for the expected signatures of the quark gluon plasma will be made, with a purpose to understand how they relate to quantities which may be experimentally measured. A short exposition of experimental techniques and details is given including charged particles in matter, momentum resolution, kinematics and Lorentz Transformations, calorimetry. Principles of particle identification including magnetic spectrometers, time of flight measurement. Illustrations using the E802 spectrometer and other measured results. Resolution smearing of spectra, and binning effects. Parent to daughter effects in decay, with {pi}{sup 0} {yields} {gamma} {gamma} as an example. The experimental situation from the known data in p -- p collisions and proton-nucleus reactions is reviewed and used as a basis for further discussions. The Cronin Effect'' and the Seagull Effect'' being two arcana worth noting. Then, selected experiments from the BNL and CERN heavy ion programs are discussed in detail. 118 refs., 45 figs.
Acceleration in Perpendicular Relativistic Shocks for Plasmas Consisting of Leptons and Hadrons
Stockem, A.; Fiúza, F.; Fonseca, R. A.; Silva, L. O.
2012-08-01
We investigate the acceleration of light particles in perpendicular shocks for plasmas consisting of a mixture of leptonic and hadronic particles. Starting from the full set of conservation equations for the mixed plasma constituents, we generalize the magnetohydrodynamical jump conditions for a multi-component plasma, including information about the specific adiabatic constants for the different species. The impact of deviations from the standard model of an ideal gas is compared in theory and particle-in-cell simulations, showing that the standard MHD model is a good approximation. The simulations of shocks in electron-positron-ion plasmas are for the first time multi-dimensional, transverse effects are small in this configuration, and one-dimensional (1D) simulations are a good representation if the initial magnetization is chosen high. 1D runs with a mass ratio of 1836 are performed, which identify the Larmor frequency ω ci as the dominant frequency that determines the shock physics in mixed component plasmas. The maximum energy in the non-thermal tail of the particle spectra evolves in time according to a power law vpropt α with α in the range 1/3 < α < 1, depending on the initial parameters. A connection is made with transport theoretical models by Drury and Gargaté & Spitkovsky, which predict an acceleration time vpropγ and the theory for small wavelength scattering by Kirk & Reville, which predicts a behavior rather as vpropγ2. Furthermore, we compare different magnetic field orientations with B 0 inside and out of the plane, observing qualitatively different particle spectra than in pure electron-ion shocks.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists of approximating large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networks with few entities. In this paper, we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric valuation distributions, and spiteful bidders.
Vollhardt, D.; Byczuk, K.; Kollar, M.
2011-01-01
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the ...
Bauso, Dario
2014-01-06
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Santilli, R M
1997-01-01
We present a new realization of relativistic hadronic me- chanics and its underlying iso-Poincar'e symmetry specifically constructed for nuclear physics which: 1) permits the representation of nucleons as ex- tended, nonspherical and deformable charge distributions with alterable mag- netic moments yet conventional angular momentum and spin; 2) results to be a nonunitary ``completion'' of relativistic quantum mechanics much along the EPR argument; yet 3) is axiom-preserving, thus preserves conventional quantum laws and the axioms of the special relativity. We show that the proposed new formalism permits the apparently first exact representation of the total magnetic moments of new-body nuclei under conventional physical laws. We then point out that, if experimentally confirmed the alterability of the intrinsic characteristics of nucleons would imply new forms of recycling nuclear waste by the nuclear power plants in their own site, thus avoiding its transportation and storage in a (yet unidentified) dumping a...
Song, Jun; Liang, Zuo-tang
2014-01-01
We propose a new kind of two-particle correlation of identified hadrons in longitudinal rapidity space, called $G_{\\alpha\\beta}(y_{\\alpha},y_{\\beta})$, which can reflect clearly the charge correlations of hot quark system produced in AA collisions at LHC energies. It is derived from the basic scenario of quark combination mechanism of hadron production. Like the elliptic flow of identified hadrons at intermediate transverse momentum, this correlation is independent of the absolute hadronic yields but dependent only on the flavor compositions of hadrons, and thus exhibits interesting properties for different kinds of hadron species. We suggest the measurement of this observable in AA collisions at LHC to gain more insights into the charge correlation properties of produced hot quark matter.
MALFLIET, R
1993-01-01
We discuss the present status of relativistic transport theory. Special emphasis is put on problems of topical interest: hadronic features, thermodynamical consistent approximations and spectral properties.
Multi-Λ Hypernuclei in an Effective Hadronic Model
LIANG Yin-Hua; GUO Hua; LIU Yu-Xin
2007-01-01
@@ We extend the chiral hadronic model (FST) with an inclusion of Λ hyperon to investigate the propertiks of multi-Λ hypernuclei. With such an effective hadronic model in the relativistic mean-field approximation, we accomplish the calculations with both the conventional strong Λ-Λ interaction and the weak Λ-Λ interaction determined from recent experiment. Our calculations indicate that not only the strong but also the weak Λ-Λ interaction provide tighter binding for multi-Λ hypernuclei than the ones with only nucleons. However the strong interaction generates a binding slightly tighter than the weak interaction.
Karkheck, John; Stell, George
1981-08-01
A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several
Quantum corrections to the Relativistic mean-field theory
Maydanyuk, Sergei P; Bakry, Ahmed
2016-01-01
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{\\rm shell}$. But, a difference between $V_{RMF}$ and $V_{\\rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indica...
Pang, Long-Gang; Endrődi, Gergely; Petersen, Hannah
2016-04-01
In off-central heavy-ion collisions, quark-gluon plasma (QGP) is exposed to the strongest magnetic fields ever created in the universe. Because of the paramagnetic nature of the QGP at high temperatures, the spatially inhomogeneous magnetic field configuration exerts an anisotropic force density that competes with the pressure gradients resulting from purely geometric effects. In this paper, we simulate (3+1)-dimensional ideal hydrodynamics with external magnetic fields to estimate the effect of this force density on the anisotropic expansion of the QGP in collisions at the Relativistic Heavy Ion Collider and at the Large Hadron Collider (LHC). While negligible for quickly decaying magnetic fields, we find that long-lived fields generate a substantial force density that suppresses the momentum anisotropy of the plasma by up to 20 % at the LHC energy and also leaves its imprint on the elliptic flow v2 of charged pions.
Back-to-back correlations of high-p(T) hadrons in relativistic heavy-ion collisions.
Hirano, Tetsufumi; Nara, Yasushi
2003-08-22
We investigate the suppression factor and the azimuthal correlation function for high p(T) hadrons in central Au+Au collisions at sqrt[s(NN)]=200 GeV by using a dynamical model in which hydrodynamics is combined with explicitly traveling jets. We study the effects of parton energy loss in a hot medium, intrinsic k(T) of partons in a nucleus, and p (perpendicular) broadening of jets on the back-to-back correlations of high p(T) hadrons. Parton energy loss is found to be a dominant effect on the reduction of the awayside peaks in the correlation function.
Mean field interaction in biochemical reaction networks
Tembine, Hamidou
2011-09-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits and illustrate them with numerical examples. © 2011 IEEE.
HBT Pion Interferometry with Phenomenological Mean Field Interaction
Hattori, K.
2010-11-01
To extract information on hadron production dynamics in the ultrarelativistic heavy ion collision, the space-time structure of the hadron source has been measured using Hanbury Brown and Twiss interferometry. We study the distortion of the source images due to the effect of a final state interaction. We describe the interaction, taking place during penetrating through a cloud formed by evaporating particles, in terms of a one-body mean field potential localized in the vicinity of the source region. By adopting the semiclassical method, the modification of the propagation of an emitted particle is examined. In analogy to the optical model applied to nuclear reactions, our phenomenological model has an imaginary part of the potential, which describes the absorption in the cloud. In this work, we focus on the pion interferometry and mean field interaction obtained using a phenomenological pipi forward scattering amplitude in the elastic channels. The p-wave scattering wit h rho meson resonance leads to an attractive mean field interaction, and the presence of the absorptive part is mainly attributed to the formation of this resonance. We also incorporate a simple time dependence of the potential reflecting the dynamics of the evaporating source. Using the obtained potential, we examine how and to what extent the so-called HBT Gaussian radius is varied by the modification of the propagation.
Albright, M
2016-01-01
We develop a flexible quasiparticle theory of transport coefficients of hot hadronic matter at finite baryon density. We begin with a hadronic quasiparticle model which includes a scalar and a vector mean field. Quasiparticle energies and the mean fields depend on temperature and baryon chemical potential. Starting with the quasiparticle dispersion relation, we derive the Boltzmann equation and use the Chapman-Enskog expansion to derive formulas for the shear and bulk viscosities and thermal conductivity. We obtain both relaxation time approximation formulas and more general integral equations. Throughout the work, we explicitly enforce the Landau-Lifshitz conditions of fit and ensure the theory is thermodynamically self-consistent. The derived formulas should be useful for predicting the transport coefficients of the hadronic phase of matter produced in heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and at other accelerators.
Berdnikov, Yu A; Ivanov, A N; Ivanova, V A; Kosmach, V F; Samsonov, V M; Troitskaya, N I; Berdnikov, Ya. A.
2000-01-01
We describe the quark gluon plasma (QGP) as a thermalized quark-gluon system, the thermalized QGP phase of QCD. The hadronization of the thermalized QGP phase is given in a way resembling a simple coalescence model. The input parameters of the approach are the spatial volumes of the hadronization. We introduce three dimensionless parameters C_M, C_B and C_\\bar{B} related to the spatial volumes of the production of low-lying mesons (M), baryons (B) and antibaryons (\\bar{B}). We show that at the temperature T= 175 MeV our predictions for the ratios of multiplicities agree good with the presently available set of hadron ratios measured for various experiments given by NA44, NA49, NA50 and WA97 Collaborations on Pb+Pb collisions at 158 GeV/nucleon, NA35 Collaboration on S+S collisions and NA38 Collaboration on O+U and S+U collisions at 200 GeV/nucleon.
Risk-sensitive mean-field games
Tembine, Hamidou
2014-04-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Continuous time finite state mean field games
Gomes, Diogo A.
2013-04-23
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Exotic Hadron Bound State Production at Hadronic Colliders
Jin, Yi; Liu, Yan-Rui; Meng, Lu; Si, Zon-Guo; Zhang, Xiao-Feng
2016-01-01
The non-relativistic wave function framework is applied to study the production and decay of the exotic hadrons which can be effectively described as bound states of other hadrons. The ingredient hadron production can be calculated by event generators. We investigate the production of exotic hadrons in the multiproduction processes at high energy hadronic colliders with the help of the event generators. We illustrate the crucial information such as their momentum distributions and production rate for the measurements at the large hadron collider. This study provides crucial information for the measurements of the relevant exotic hadrons.
Extended Deterministic Mean-Field Games
Gomes, Diogo A.
2016-04-21
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Mean field theory for fermion-based U(2) anyons
McGraw, P
1996-01-01
The energy density is computed for a U(2) Chern-Simons theory coupled to a non-relativistic fermion field (a theory of ``non-Abelian anyons'') under the assumptions of uniform charge and matter density. When the matter field is a spinless fermion, we find that this energy is independent of the two Chern-Simons coupling constants and is minimized when the non-Abelian charge density is zero. This suggests that there is no spontaneous breaking of the SU(2) subgroup of the symmetry, at least in this mean-field approximation. For spin-1/2 fermions, we find self-consistent mean-field states with a small non-Abelian charge density, which vanishes as the theory of free fermions is approached.
Mean field approaches for $\\Xi^-$ hypernuclei and current experimental data
Sun, T T; Sagawa, H; Schulze, H -J; Meng, J
2016-01-01
Motivated by the recently observed hypernucleus (Kiso event) $^{15}_{\\Xi}$C ($^{14}$N$+\\Xi^-$), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme-Hartree-Fock models. The $\\Xi N$ interactions are constructed to reproduce the two possibly observed $\\Xi^-$ removal energies, $4.38\\pm 0.25$ MeV or $1.11\\pm 0.25$ MeV. The present result is preferable to be $^{14}{\\rm N}({\\rm g.s.})+\\Xi^-(1p)$, corresponding to the latter value.
Bauso, Dario
2014-05-07
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple\\'s network on their feeling states and their well-being. © 2014 Bauso et al.
Strangeness in QGP: Hadronization Pressure
Rafelski, Jan; Petran, Michal
2014-01-01
We review strangeness as signature of quark gluon plasma (QGP) and the hadronization process of a QGP fireball formed in relativistic heavy-ion collisions in the entire range of today accessible reaction energies. We discuss energy dependence of the statistical hadronization parameters within the context of fast QGP hadronization. We find that QGP breakup occurs for all energies at the universal hadronization pressure $P = 80\\pm 3\\,\\mathrm{MeV/fm}^3 $.
Degenerate second order mean field games systems
Tonon, Daniela; Cardaliaguet, Pierre; Graber, Philip,; Poretta, Alessio
2014-01-01
Parallel session; International audience; We consider degenerate second order mean field games systems with a local coupling. The starting point is the idea that mean field games systems can be understood as an optimality condition for optimal control of PDEs. Developing this strategy for the degenerate second order case, we discuss the existence and uniqueness of a weak solution as well as its stability (vanishing viscosity limit). Speaker: Daniela TONON
Back-reaction beyond the mean field approximation
Kluger, Y.
1993-12-01
A method for solving an initial value problem of a closed system consisting of an electromagnetic mean field and its quantum fluctuations coupled to fermions is presented. By tailoring the large N{sub f} expansion method to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured, and a systematic energy conserving and gauge invariant expansion about the electromagnetic mean field in powers of 1/N{sub f} is developed. The resulting equations may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes of a relativistic e{sup +}e{sup {minus}} plasma. Using the Bjorken ansatz of boost invariance initial conditions in which the initial electric mean field depends on the proper time only, we show numerical results for the case in which the N{sub f} expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation.
Nonrelativistic mean-field description of the deformation of Λ hypernuclei
无
2009-01-01
The deformations of light Λ hypernuclei are studied in an extended nonrelativistic deformed Skyrme-Hartree-Fock approach with realistic modern nucleonic Skyrme forces,pairing correlations,and a microscopical lambda-nucleon interaction derived from Brueckner-Hartree-Fock calculations.Compared to the large effect of an additional Λ particle on nuclear deformation in the light soft nuclei within relativistic mean field method,this effect is much smaller in the nonrelativistic mean-field approximation.
Cooper, S.
1985-10-01
Heavy quark systems and glueball candidates, the particles which are relevant to testing QCD, are discussed. The review begins with the heaviest spectroscopically observed quarks, the b anti-b bound states, including the chi state masses, spins, and hadronic widths and the non-relativistic potential models. Also, P states of c anti-c are mentioned. Other heavy states are also discussed in which heavy quarks combine with lighter ones. The gluonium candidates iota(1460), theta(1700), and g/sub T/(2200) are then covered. The very lightest mesons, pi-neutral and eta, are discussed. 133 refs., 24 figs., 16 tabs. (LEW)
Pion mean fields and heavy baryons
Yang, Ghil-Seok; Polyakov, Maxim V; Praszałowicz, Michał
2016-01-01
We show that the masses of the lowest-lying heavy baryons can be very well described in a pion mean-field approach. We consider a heavy baryon as a system consisting of the $N_c-1$ light quarks that induce the pion mean field, and a heavy quark as a static color source under the influence of this mean field. In this approach we derive a number of \\textit{model-independent} relations and calculate the heavy baryon masses using those of the lowest-lying light baryons as input. The results are in remarkable agreement with the experimental data. In addition, the mass of the $\\Omega_b^*$ baryon is predicted.
Mean Field Games with a Dominating Player
Bensoussan, A., E-mail: axb046100@utdallas.edu [The University of Texas at Dallas, International Center for Decision and Risk Analysis, Jindal School of Management (United States); Chau, M. H. M., E-mail: michaelchaumanho@gmail.com; Yam, S. C. P., E-mail: scpyam@sta.cuhk.edu.hk [The Chinese University of Hong Kong, Department of Statistics (Hong Kong, People’s Republic of China) (China)
2016-08-15
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.
Mean field games for cognitive radio networks
Tembine, Hamidou
2012-06-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing and is subject to long-term energy constraint. We formulate the interaction between primary user and large number of secondary users as an hierarchical mean field game. In contrast to the classical large-scale approaches based on stochastic geometry, percolation theory and large random matrices, the proposed mean field framework allows one to describe the evolution of the density distribution and the associated performance metrics using coupled partial differential equations. We provide explicit formulas and algorithmic power management for both primary and secondary users. A complete characterization of the optimal distribution of energy and probability of success is given.
Vector interaction strength in Polyakov-Nambu-Jona-Lasinio models from hadron-quark phase diagrams
Lourenço, O; Frederico, T; Delfino, A; Malheiro, M
2012-01-01
We estimate the vector interaction strength of the Polyakov-Nambu-Jona-Lasinio (PNJL) parametrizations, assuming that its transition curves should be as close as possible of the recently studied RMF-PNJL hadron-quark phase diagrams. Such diagrams are obtained matching relativistic mean-field hadronic models, and the PNJL quark ones. By using this method we found for the magnitude of the vector interaction, often treated as a free parameter, a range of 7.66 GeV$^{-2}\\lesssim G_V \\lesssim 16.13$ GeV$^{-2}$, or equivalently, $1.52 \\lesssim G_V/G_s \\lesssim 3.2$, with $G_s$ being the scalar coupling constant of the model. These values are compatible but restricts the range of 4 GeV$^{-2}\\lesssim G_V \\lesssim 19$ GeV$^{-2}$, recently obtained from lattice QCD data through a different mean-field model approach.
Obstacle mean-field game problem
Gomes, Diogo A.
2015-01-01
In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Bubble dynamics and the quark-hadron phase transition in nuclear collisions
Fogaça, D A; Fariello, R; Navarra, F S
2016-01-01
We study the nucleation of a quark gluon plasma (QGP) phase in a hadron gas at low temperatures and high baryon densities. This kind of process will presumably happen very often in nuclear collisions at FAIR and NICA. When the right energy density (or baryon density) is reached the conversion of one phase into another is not instantaneous. It is a complex process, which involves the nucleation of bubbles of the new phase. One important element of this transition process is the rate of growth of a QGP bubble. In order to estimate it we solve the Relativistic Rayleigh$-$Plesset equation which governs the dynamics of a relativistic spherical bubble in a cold and strongly interacting medium. The baryon rich hadron gas is represented by the nonlinear Walecka model and the QGP is described by the MIT bag model and also by a mean field model of QCD.
Propagation peculiarities of mean field massive gravity
S. Deser
2015-10-01
Full Text Available Massive gravity (mGR describes a dynamical “metric” on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its “mean field theory”. Analyzing mean field massive gravity (m‾GR propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita–Schwinger (RS theory. The fiducial and mGR mean field background metrics in the m‾GR model correspond to the RS Minkowski metric and external EM field. The common implications in both systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories; a situation in stark contrast with general relativity (GR which is at least a consistent classical theory. Moreover, even though both m‾GR and RS theories can still in principle be considered as predictive effective models in the weak regime, their lower helicities then exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. Thus our approach has uncovered a novel, dispersive, “crystal-like” phenomenon of differing helicities having differing propagation speeds. This applies both to m‾GR and mGR, and is a peculiar feature that is also problematic for consistent coupling to matter.
Weakly coupled mean-field game systems
Gomes, Diogo A.
2016-07-14
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem. Finally, by a limiting procedure, we obtain solutions to the MFG problem. © 2016 Elsevier Ltd
A mean field approach to watershed hydrology
Bartlett, Mark; Porporato, Amilcare
2016-04-01
Mean field theory (also known as self-consistent field theory) is commonly used in statistical physics when modeling the space-time behavior of complex systems. The mean field theory approximates a complex multi-component system by considering a lumped (or average) effect for all individual components acting on a single component. Thus, the many body problem is reduced to a one body problem. For watershed hydrology, a mean field theory reduces the numerous point component effects to more tractable watershed averages, resulting in a consistent method for linking the average watershed fluxes to the local fluxes at each point. We apply this approach to the spatial distribution of soil moisture, and as a result, the numerous local interactions related to lateral fluxes of soil water are parameterized in terms of the average soil moisture. The mean field approach provides a basis for unifying and extending common event-based models (e.g. Soil Conservation Service curve number (SCS-CN) method) with more modern semi-distributed models (e.g. Variable Infiltration Capacity (VIC) model, the Probability Distributed (PDM) model, and TOPMODEL). We obtain simple equations for the fractions of the different source areas of runoff, the spatial variability of runoff, and the average runoff value (i.e., the so-called runoff curve). The resulting space time distribution of soil moisture offers a concise description of the variability of watershed fluxes.
A regularized stationary mean-field game
Yang, Xianjin
2016-04-19
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
Thermal Effects in Dense Matter Beyond Mean Field Theory
Constantinou, Constantinos; Prakash, Madappa
2016-01-01
The formalism of next-to-leading order Fermi Liquid Theory is employed to calculate the thermal properties of symmetric nuclear and pure neutron matter in a relativistic many-body theory beyond the mean field level which includes two-loop effects. For all thermal variables, the semi-analytical next-to-leading order corrections reproduce results of the exact numerical calculations for entropies per baryon up to 2. This corresponds to excellent agreement down to sub-nuclear densities for temperatures up to $20$ MeV. In addition to providing physical insights, a rapid evaluation of the equation of state in the homogeneous phase of hot and dense matter is achieved through the use of the zero-temperature Landau effective mass function and its derivatives.
Mean-field learning for satisfactory solutions
Tembine, Hamidou
2013-12-01
One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.
Mean field methods for cortical network dynamics
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases with the stren...... cortex. Finally, an extension of the model to describe an orientation hypercolumn provides understanding of how cortical interactions sharpen orientation tuning, in a way that is consistent with observed firing statistics...
Bosonic Dynamical Mean-Field Theory
Snoek, Michiel; Hofstetter, Walter
2013-02-01
We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.
Mean field games systems of first order
Cardaliaguet, Pierre; Graber, Philip Jameson
2014-01-01
International audience; We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.
'Phase diagram' of a mean field game
Swiecicki, Igor; Ullmo, Denis
2015-01-01
Mean field games were introduced by J-M.Lasry and P-L. Lions in the mathematical community, and independently by M. Huang and co-workers in the engineering community, to deal with optimization problems when the number of agents becomes very large. In this article we study in detail a particular example called the 'seminar problem' introduced by O.Gu\\'eant, J-M Lasry, and P-L. Lions in 2010. This model contains the main ingredients of any mean field game but has the particular feature that all agent are coupled only through a simple random event (the seminar starting time) that they all contribute to form. In the mean field limit, this event becomes deterministic and its value can be fixed through a self consistent procedure. This allows for a rather thorough understanding of the solutions of the problem, through both exact results and a detailed analysis of various limiting regimes. For a sensible class of initial configurations, distinct behaviors can be associated to different domains in the parameter space...
Hadron star models. [neutron stars
Cohen, J. M.; Boerner, G.
1974-01-01
The properties of fully relativistic rotating hadron star models are discussed using models based on recently developed equations of state. All of these stable neutron star models are bound with binding energies as high as about 25%. During hadron star formation, much of this energy will be released. The consequences, resulting from the release of this energy, are examined.
Relativistic hadronic models in LDA
Silva, J.B.; Delfino, A.; Malheiro, M. [Universidade Federal Fluminense, Niteroi, RJ (Brazil). Inst. de Fisica
2001-07-01
In the framework of the Walecka model we perform a model approximation ({rho}{sub s} = {rho}), in which some nuclear matter observable are calculated analytically. The results are very close to those obtained by the original Walecka model. (author)
Time-odd mean fields in covariant density functional theory: Rotating systems
Afanasjev, A V; 10.1103/PhysRev.82.034329
2010-01-01
Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration and rotational frequency dependences of their impact on the moments of inertia have been analysed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid body value. On the contrary, superdeformed and hyperdeformed nuclei have ...
Mean field methods for cortical network dynamics
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases...... with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the connection between the firing statistics and the high- conductance state observed experimentally in visual...
Mean-field behavior of cluster dynamics
Persky, N.; Ben-Av, R.; Kanter, I.; Domany, E.
1996-09-01
The dynamic behavior of cluster algorithms is analyzed in the classical mean-field limit. Rigorous analytical results below Tc establish that the dynamic exponent has the value zSW=1 for the Swendsen-Wang algorithm and zW=0 for the Wolff algorithm. An efficient Monte Carlo implementation is introduced, adapted for using these algorithms for fully connected graphs. Extensive simulations both above and below Tc demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data.
Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.
2016-08-01
We compute analytically the masses, binding energies and hamiltonians of gravitationally bound Bohr-type states via the rotating relativistic lepton model which utilizes the de Broglie wavelength equation in conjunction with special relativity and Newton's relativistic gravitational law. The latter uses the inertial-gravitational masses, rather than the rest masses, of the rotating particles. The model also accounts for the electrostatic charge- induced dipole interactions between a central charged lepton, which is usually a positron, with the rotating relativistic lepton ring. We use three rotating relativistic neutrinos to model baryons, two rotating relativistic neutrinos to model mesons, and a rotating relativistic electron neutrino - positron (or electron) pair to model the W± bosons. It is found that gravitationally bound ground states comprising three relativistic neutrinos have masses in the baryon mass range (∼⃒ 0.9 to 1 GeV/c2), while ground states comprising two neutrinos have masses in the meson mass range (∼⃒ 0.4 to 0.8 GeV/c2). It is also found that the rest mass values of quarks are in good agreement with the heaviest neutrino mass value of 0.05 eV/c2 and that the mass of W± bosons (∼⃒ 81 GeV/c2) corresponds to the mass of a rotating gravitationally confined e± — ve pair. A generalized expression is also derived for the gravitational potential energy of such relativistic Bohr-type structures.
Pedestrian Flow in the Mean Field Limit
Haji Ali, Abdul Lateef
2012-11-01
We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.
Mean field magnetization of gapped anisotropic multiplet
Paixão, L. S.; Reis, M. S.
2014-06-01
Some materials have a large gap between the ground and first excited states. At temperatures smaller than the gap value, the thermodynamic properties of such materials are mainly ruled by the ground state. It is also common to find materials with magnetocrystalline anisotropy, which arises due to interatomic interactions. The present paper uses a classical approach to deal large angular momenta in such materials. Based on analytical expressions for the thermodynamics of paramagnetic gapped anisotropic multiplets, we use mean field theory to study the influence of the anisotropy upon the properties of interacting systems. We also use Landau theory to determine the influence of the anisotropy in first and second order phase transitions. It is found that the anisotropy increases the critical temperature, and enlarges the hysteresis of first order transitions. We present analytical expressions for the quantities analyzed.
Invisible dynamo in mean-field models
Reshetnyak, M. Yu.
2016-07-01
The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.
Mean-field models for disordered crystals
Cancès, Eric; Lewin, Mathieu
2012-01-01
In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of such disordered crystals, for the reduced Hartree-Fock model (rHF). We consider both (short-range) Yukawa and (long-range) Coulomb interactions. In the former case, we prove in addition that the rHF ground state density matrix satisfies a self-consistent equation, and that our model for disordered crystals is the thermodynamic limit of the supercell model.
Mean-field Ensemble Kalman Filter
Law, Kody
2015-01-07
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Influence of pions on the hadron-quark phase transition
Lourenço, O; Frederico, T; Delfino, A; Malheiro, M
2013-01-01
In this work we present the features of the hadron-quark phase transition diagrams in which the pions are included in the system. To construct such diagrams we use two different models in the description of the hadronic and quark sectors. At the quark level, we consider two distinct parametrizations of the Polyakov-Nambu-Jona-Lasinio (PNJL) models. In the hadronic side, we use a well known relativistic mean-field (RMF) nonlinear Walecka model. We show that the effect of the pions on the hadron-quark phase diagrams is to move the critical end point (CEP) of the transitions lines. Such an effect also depends on the value of the critical temperature (T_0) in the pure gauge sector used to parametrize the PNJL models. Here we treat the phase transitions using two values for T_0, namely, T_0 = 270 MeV and T_0 = 190 MeV. The last value is used to reproduce lattice QCD data for the transition temperature at zero chemical potential.
Influence of pions on the hadron-quark phase transition
Lourenco, O.; Dutra, M.; Frederico, T.; Malheiro, M. [Departamento de Fisica, Instituto Tecnologico de Aeronautica-CTA, 12228-900, Sao Jose dos Campos (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminense, Av. Litoranea s/n, 24210-150, Boa Viagem, Niteroi RJ (Brazil)
2013-05-06
In this work we present the features of the hadron-quark phase transition diagrams in which the pions are included in the system. To construct such diagrams we use two different models in the description of the hadronic and quark sectors. At the quark level, we consider two distinct parametrizations of the Polyakov-Nambu-Jona-Lasinio (PNJL) models. In the hadronic side, we use a well known relativistic mean-field (RMF) nonlinear Walecka model. We show that the effect of the pions on the hadron-quark phase diagrams is to move the critical end point (CEP) of the transitions lines. Such an effect also depends on the value of the critical temperature (T{sub 0}) in the pure gauge sector used to parametrize the PNJL models. Here we treat the phase transitions using two values for T{sub 0}, namely, T{sub 0}= 270 MeV and T{sub 0}= 190 MeV. The last value is used to reproduce lattice QCD data for the transition temperature at zero chemical potential.
Melting Hadrons, Boiling Quarks
Rafelski, Johann
2015-01-01
In the context of the Hagedorn temperature half-centenary I describe our understanding of the hot phases of hadronic matter both below and above the Hagedorn temperature. The first part of the review addresses many frequently posed questions about properties of hadronic matter in different phases, phase transition and the exploration of quark-gluon plasma (QGP). The historical context of the discovery of QGP is shown and the role of strangeness and strange antibaryon signature of QGP illustrated. In the second part I discuss the corresponding theoretical ideas and show how experimental results can be used to describe the properties of QGP at hadronization. Finally in two appendices I present previously unpublished reports describing the early prediction of the different forms of hadron matter and of the formation of QGP in relativistic heavy ion collisions, including the initial prediction of strangeness and in particular strange antibaryon signature of QGP.
Melting hadrons, boiling quarks
Rafelski, Johann [CERN-PH/TH, Geneva 23 (Switzerland); The University of Arizona, Department of Physics, Tucson, Arizona (United States)
2015-09-15
In the context of the Hagedorn temperature half-centenary I describe our understanding of the hot phases of hadronic matter both below and above the Hagedorn temperature. The first part of the review addresses many frequently posed questions about properties of hadronic matter in different phases, phase transition and the exploration of quark-gluon plasma (QGP). The historical context of the discovery of QGP is shown and the role of strangeness and strange antibaryon signature of QGP illustrated. In the second part I discuss the corresponding theoretical ideas and show how experimental results can be used to describe the properties of QGP at hadronization. The material of this review is complemented by two early and unpublished reports containing the prediction of the different forms of hadron matter, and of the formation of QGP in relativistic heavy ion collisions, including the discussion of strangeness, and in particular strange antibaryon signature of QGP. (orig.)
Time dependent mean-field games
Gomes, Diogo A.
2014-01-06
We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Nonequilibrium dynamical mean-field theory
Eckstein, Martin
2009-12-21
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Time-odd mean fields in the rotating frame microscopic nature of nuclear magnetism
Afanasiev, A V
2000-01-01
The microscopic role of nuclear magnetism in rotating frame is investigated for the first time in the framework of the cranked relativistic mean field theory. It is shown that nuclear magnetism modifies the expectation values of single-particle spin, orbital and total angular momenta along the rotational axis effectively creating additional angular momentum. This effect leads to the increase of kinematic and dynamic moments of inertia at given rotational frequency and has an impact on effective alignments.
Shell Effect of Superheavy Nuclei in Self-consistent Mean-Field Models
RENZhong-Zhou; TAIFei; XUChang; CHENDing-Han; ZHANGHu-Yong; CAIXiang-Zhou; SHENWen-Qing
2004-01-01
We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoreticalresults are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached.Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupysignificantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of vaJence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ，ω and ρ mesons because there is no parityviolating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.
Relativistic Hydrodynamics for Heavy-Ion Collisions
Ollitrault, Jean-Yves
2008-01-01
Relativistic hydrodynamics is essential to our current understanding of nucleus-nucleus collisions at ultrarelativistic energies (current experiments at the Relativistic Heavy Ion Collider, forthcoming experiments at the CERN Large Hadron Collider). This is an introduction to relativistic hydrodynamics for graduate students. It includes a detailed…
Hussain, Nur; Bhattacharjee, Buddhadeb
2017-08-01
Widths of the rapidity distributions of various identified hadrons generated with the UrQMD-3.4 event generator at all the Super Proton Synchrotron (SPS) energies have been presented and compared with the existing experimental results. An increase in the width of the rapidity distribution of Λ could be seen with both Monte Carlo (MC) and experimental data for the studied energies. Using MC data, the study has been extended to Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies. A similar jump, as observed in the plot of rapidity width versus rest mass at Alternating Gradient Synchrotron (AGS) and all SPS energies, persists even at RHIC and LHC energies, confirming its universal nature from AGS to the highest LHC energies. Such observation indicates that pair production may not be the only mechanism of particle production at the highest LHC energies. However, with MC data, the separate mass scaling for mesons and baryons is found to exist even at the top LHC energy.
Identifying multiquark hadrons from heavy ion collisions.
Cho, Sungtae; Furumoto, Takenori; Hyodo, Tetsuo; Jido, Daisuke; Ko, Che Ming; Lee, Su Houng; Nielsen, Marina; Ohnishi, Akira; Sekihara, Takayasu; Yasui, Shigehiro; Yazaki, Koichi
2011-05-27
Identifying hadronic molecular states and/or hadrons with multiquark components either with or without exotic quantum numbers is a long-standing challenge in hadronic physics. We suggest that studying the production of these hadrons in relativistic heavy ion collisions offers a promising resolution to this problem as yields of exotic hadrons are expected to be strongly affected by their structures. Using the coalescence model for hadron production, we find that, compared to the case of a nonexotic hadron with normal quark numbers, the yield of an exotic hadron is typically an order of magnitude smaller when it is a compact multiquark state and a factor of 2 or more larger when it is a loosely bound hadronic molecule. We further find that some of the newly proposed heavy exotic states could be produced and realistically measured in these experiments.
Hyperon puzzle and the RMF model with scaled hadron masses and coupling constants
Kolomeitsev, E. E.; Maslov, K. A.; Voskresensky, D. N.
2016-01-01
The equation of state of cold baryonic matter is studied within a relativistic mean-field model with hadron masses and coupling constants depending on a scalar field. We demonstrate that if the effective nucleon mass stops to decrease with a density increase at densities n > n*> n0, where n0 is the nuclear saturation density, the equation of state stiffens for these densities and the limiting neutron star mass increases. The stabilization of the nucleon mass can be realised if in the equation of motion for the scalar mean-field there appear a term sharply varying in a narrow vicinity of the field value corresponding to the density n*. We show several possible realizations of this mechanism getting sufficiently stiff equations of state. The appearance of hyperons in dense neutron star interiors is accounted for. The obtained equations of state remain sufficiently stiff if the reduction of the ϕ meson mass is incorporated. Thereby, the hyperon puzzle can be resolved.
Month, M.; Weng, W.T.
1983-06-21
The objective is to investigate whether existing technology might be extrapolated to provide the conceptual framework for a major hadron-hadron collider facility for high energy physics experimentation for the remainder of this century. One contribution to this large effort is to formalize the methods and mathematical tools necessary. In this report, the main purpose is to introduce the student to basic design procedures. From these follow the fundamental characteristics of the facility: its performance capability, its size, and the nature and operating requirements on the accelerator components, and with this knowledge, we can determine the technology and resources needed to build the new facility.
Probing the hadron-quark mixed phase at high isospin and baryon density. Sensitive observables
Di Toro, Massimo; Greco, Vincenzo [INFN-Laboratori Nazionali del Sud, Catania (Italy); University of Catania, Physics and Astronomy Dept., Catania (Italy); Colonna, Maria [INFN-Laboratori Nazionali del Sud, Catania (Italy); Shao, Guo-Yun [Xi' an Jiaotong University, Department of Applied Physics, Xi' an (China)
2016-08-15
We discuss the isospin effect on the possible phase transition from hadronic to quark matter at high baryon density and finite temperatures. The two-Equation of State (Two-EoS) model is adopted to describe the hadron-quark phase transition in dense matter formed in heavy-ion collisions. For the hadron sector we use Relativistic Mean-Field (RMF) effective models, already tested on heavy-ion collision (HIC). For the quark phase we consider various effective models, the MIT-Bag static picture, the Nambu-Jona-Lasinio (NJL) approach with chiral dynamics and finally the NJL coupled to the Polyakov-loop field (PNJL), which includes both chiral and (de)confinement dynamics. The idea is to extract mixed phase properties which appear robust with respect to the model differences. In particular we focus on the phase transitions of isospin asymmetric matter, with two main results: (i) an earlier transition to a mixed hadron-quark phase, at lower baryon density/chemical potential with respect to symmetric matter; (ii) an ''Isospin Distillation'' to the quark component of the mixed phase, with predicted effects on the final hadron production. Possible observation signals are suggested to probe in heavy-ion collision experiments at intermediate energies, in the range of the NICA program. (orig.)
Bugaev, K A; Sagun, V V; Ivanytskyi, A I; Cleymans, J; Mironchuk, E S; Nikonov, E G; Taranenko, A V; Zinovjev, G M
2016-01-01
We present an elaborate version of the hadron resonance gas model with the combined treatment of separate chemical freeze-outs for strange and non-strange hadrons and with an additional $\\gamma_{s}$ factor which accounts for the remaining strange particle non-equilibration. Within suggested approach the parameters of two chemical freeze-outs are connected by the conservation laws of entropy, baryonic charge, third isospin projection and strangeness. The developed model enables us to perform a high-quality fit of the hadron multiplicity ratios measured at AGS, SPS and RHIC with $\\chi^2/dof \\simeq 0.93$. A special attention is paid to a successful description of the Strangeness Horn. The well-known problem of selective suppression of $\\bar \\Lambda $ and $\\bar \\Xi$ hyperons is also discussed. The main result is that for all collision energies the $\\gamma_{s}$ factor is about 1 within the error bars, except for the center of mass collision energy 7.6 GeV at which we find about 20\\% enhancement of strangeness. Als...
Point form relativistic quantum mechanics and relativistic SU(6)
Klink, W. H.
1993-01-01
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
2015-01-01
This book shows how the study of multi-hadron production phenomena in the years after the founding of CERN culminated in Hagedorn's pioneering idea of limiting temperature, leading on to the discovery of the quark-gluon plasma - announced, in February 2000 at CERN. Following the foreword by Herwig Schopper -- the Director General (1981-1988) of CERN at the key historical juncture -- the first part is a tribute to Rolf Hagedorn (1919-2003) and includes contributions by contemporary friends and colleagues, and those who were most touched by Hagedorn: Tamás Biró, Igor Dremin, Torleif Ericson, Marek Gázdzicki, Mark Gorenstein, Hans Gutbrod, Maurice Jacob, István Montvay, Berndt Müller, Grazyna Odyniec, Emanuele Quercigh, Krzysztof Redlich, Helmut Satz, Luigi Sertorio, Ludwik Turko, and Gabriele Veneziano. The second and third parts retrace 20 years of developments that after discovery of the Hagedorn temperature in 1964 led to its recognition as the melting point of hadrons into boiling quarks, and t...
Validation of Hadronic Models in GEANT4
Koi, Tatsumi; Wright, Dennis H.; /SLAC; Folger, Gunter; Ivanchenko, Vladimir; Kossov, Mikhail; Starkov, Nikolai; /CERN; Heikkinen, Aatos; /Helsinki Inst. of Phys.; Truscott,; Lei, Fan; /QinetiQ; Wellisch, Hans-Peter
2007-09-26
Geant4 is a software toolkit for the simulation of the passage of particles through matter. It has abundant hadronic models from thermal neutron interactions to ultra relativistic hadrons. An overview of validations in Geant4 hadronic physics is presented based on thin target measurements. In most cases, good agreement is available between Monte Carlo prediction and experimental data; however, several problems have been detected which require some improvement in the models.
Validation of hadronic models in GEANT4
Koi, Tatsumi; Folger, Günter; Ivanchenko, Vladimir; Kossov, Mikhail; Starkov, Nikolai; Heikkinen, Aatos; Truscott, Pete; Lei, Fan; Wellisch, Hans-Peter
2007-01-01
Geant4 is a software toolkit for the simulation of the passage of particles through matter. It has abundant hadronic models from thermal neutron interactions to ultra relativistic hadrons. An overview of validations in Geant4 hadronic physics is presented based on thin-target measurements. In most cases, good agreement is available between Monte Carlo prediction and experimental data; however, several problems have been detected which require some improvement in the models.
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bos...
Modified Mean Field approximation for the Ising Model
Di Bartolo, Cayetano
2009-01-01
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the Mean-Field or the Bethe-Peierls-Weiss methods, we take an infinite chain of fluctuating spins coupled to the mean field of the rest of the lattice. This results in a significative improvement of the Mean-Field approximation with a small extra effort.
Li, Ming; Kapusta, Joseph I.
2017-01-01
In very high-energy collisions nuclei are practically transparent to each other but produce very hot nearly baryon-free matter in the so-called central rapidity region. The energy in the central rapidity region comes from the kinetic energy of the colliding nuclei. We calculate the energy and rapidity loss of the nuclei using the color glass condensate model. This model also predicts the excitation energy of the nuclear fragments. Using a space-time picture of the collision we calculate the baryon and energy densities of the receding baryonic fireballs. For central collisions of gold nuclei at the highest energy attainable at the Relativistic Heavy-Ion Collider, for example, we find baryon densities more than ten times that of atomic nuclei over a large volume.
Li, Ming
2016-01-01
In very high energy collisions nuclei are practically tranparent to each other but produce very hot, nearly baryon-free, matter in the so-called central rapidity region. The energy in the central rapidity region comes from the kinetic energy of the colliding nuclei. We calculate the energy and rapidity loss of the nuclei using the color glass condensate model. This model also predicts the excitation energy of the nuclear fragments. Using a space-time picture of the collision we calculate the baryon and energy densities of the receding baryonic fireballs. For central collisions of gold nuclei at the highest energy attainable at the Relativistic Heavy Ion Collider, for example, we find baryon densities more than ten times that of atomic nuclei over a large volume.
Verbalization of Mean Field Utterances in German Instructions
Tayupova O. I.
2013-01-01
Full Text Available The article investigates ways of actualization of mean field utterances used in modern German instructions considering the type of the text. The author determines and analyzes similarities and differences in linguistic means used in mean field utterances in the context of such text subtypes as instructions to household appliances, cosmetic products directions and prescribing information for pharmaceutical drugs use.
Influence of the nuclear equation of state on the hadron-quark phase transition in neutron stars
YANG Fang; SHEN Hong
2008-01-01
We study the hadron-quark phase transition in the interior of neutron stars, and examine the influence of the nuclear equation of state on the phase transition and neutron star properties. The relativistic mean field theory with several parameter sets is used to construct the nuclear equation of state, while the Nambu-Jona-Lasinio model is used for the description of the deconfined quark phase. Our results show that a harder nuclear equation of state leads to an earlier onset of a mixed phase of hadronic and quark matter. We find that a massive neutron star possesses a mixed phase core, but it is not dense enough to possess a pure quark core.
Neutrino emissivity in the quark-hadron mixed phase of neutron stars
Spinella, William M; Contrera, Gustavo A; Orsaria, Milva G
2015-01-01
Numerous theoretical studies using various equation of state models have shown that quark matter may exist at the extreme densities in the cores of high-mass neutron stars. It has also been shown that a phase transition from hadronic matter to quark matter would result in an extended mixed phase region that would segregate phases by net charge to minimize the total energy of the phase, leading to the formation of a crystalline lattice. The existence of quark matter in the core of a neutron star may have significant consequences for its thermal evolution, which for thousands of years is facilitated primarily by neutrino emission. In this work we investigate the effect a crystalline quark-hadron mixed phase can have on the neutrino emissivity from the core. To this end we calculate the equation of state using the relativistic mean-field approximation to model hadronic matter and a nonlocal extension of the three-flavor Nambu-Jona-Lasinio model for quark matter. Next we determine the extent of the quark-hadron m...
Effects of the quark-hadron phase transition on highly magnetized neutron stars
Franzon, B.; Gomes, R. O.; Schramm, S.
2016-11-01
The presence of quark-hadron phase transitions in neutron stars can be related to several interesting phenomena. In particular, previous calculations have shown that fast rotating neutron stars, when subjected to a quark-hadron phase transition in their interiors, could give rise to the backbending phenomenon characterized by a spin-up era. In this work, we use an equation of state composed of two phases, containing nucleons (and leptons) and quarks. The hadronic phase is described in a relativistic mean field formalism that takes many-body forces into account, and the quark phase is described by the MIT bag model with a vector interaction. Stationary and axisymmetric stellar models are obtained in a self-consistent way by solving numerically the Einstein-Maxwell equations by means of a pseudo-spectral method. As a result, we obtain the interesting backbending phenomenon for fast spinning neutron stars. More importantly, we show that a magnetic field, which is assumed to be axisymmetric and poloidal, can also be enhanced due to the phase transition from normal hadronic matter to quark matter on highly magnetized neutron stars. Therefore, in parallel to the spin-up era, classes of neutron stars endowed with strong magnetic fields may go through a `magnetic-up era' in their lives.
Shock wave produced by hadron-quark phase transition in neutron star
Gustavo de Almeida, Luis, E-mail: lgalmeida@cbpf.br [Universidade Federal do Acre – Campus Floresta, Estrada do Canela Fina, km 12, CEP 69980-000, Cruzeiro do Sul, AC (Brazil); Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro, RJ (Brazil); Duarte, Sérgio José Barbosa, E-mail: sbd@cbpf.br [Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro, RJ (Brazil); Rodrigues, Hilário, E-mail: harg.astrophys@gmail.com [Centro Federal de Educação Tecnológica Celso Suckow da Fonseca Av. Maracanã, 229, CEP 20271-110, Rio de Janeiro, RJ (Brazil)
2015-12-17
In this work we present a schematic description of the detonation wave in hadronic matter inside a neutron star core. We have used a simplified two shells model where the inner shell medium is initially composed of a small lump of strange quark matter surrounded by a large outer shell composed of hadronic matter. We have utilized an equation of state (EOS) based on Relativistic Mean Field Theory with the parameter set NL3 to describe the nuclear and subnuclear phases. We use the MIT bag model to describe the strange quark matter. The hadron-quark phase transition actually induces highly non equilibrium modes, which may become a detonation process (faster) or a burning process (slower). The main purpose of the work is to study the formation of a remnant quark star and the possibility of mass ejection caused by the hadron-quark phase transition. We have found that the total amount of ejected mass is dependant of the bag constant utilized in the strange matter description.
On Social Optima of Non-Cooperative Mean Field Games
Li, Sen; Zhang, Wei; Zhao, Lin; Lian, Jianming; Kalsi, Karanjit
2016-12-12
This paper studies the social optima in noncooperative mean-field games for a large population of agents with heterogeneous stochastic dynamic systems. Each agent seeks to maximize an individual utility functional, and utility functionals of different agents are coupled through a mean field term that depends on the mean of the population states/controls. The paper has the following contributions. First, we derive a set of control strategies for the agents that possess *-Nash equilibrium property, and converge to the mean-field Nash equilibrium as the population size goes to infinity. Second, we study the social optimal in the mean field game. We derive the conditions, termed the socially optimal conditions, under which the *-Nash equilibrium of the mean field game maximizes the social welfare. Third, a primal-dual algorithm is proposed to compute the *-Nash equilibrium of the mean field game. Since the *-Nash equilibrium of the mean field game is socially optimal, we can compute the equilibrium by solving the social welfare maximization problem, which can be addressed by a decentralized primal-dual algorithm. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.
Quantum correlations in nuclear mean field theory through source terms
Lee, S J
1996-01-01
Starting from full quantum field theory, various mean field approaches are derived systematically. With a full consideration of external source dependence, the stationary phase approximation of an action gives a nuclear mean field theory which includes quantum correlation effects (such as particle-hole or ladder diagram) in a simpler way than the Brueckner-Hartree-Fock approach. Implementing further approximation, the result can be reduced to Hartree-Fock or Hartree approximation. The role of the source dependence in a mean field theory is examined.
Mean Field Games for Stochastic Growth with Relative Utility
Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)
2016-12-15
This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.
Mean-field instabilities and cluster formation in nuclear reactions
Colonna, M; Baran, V
2016-01-01
We review recent results on intermediate mass cluster production in heavy ion collisions at Fermi energy and in spallation reactions. Our studies are based on modern transport theories, employing effective interactions for the nuclear mean-field and incorporating two-body correlations and fluctuations. Namely we will consider the Stochastic Mean Field (SMF) approach and the recently developed Boltzmann-Langevin One Body (BLOB) model. We focus on cluster production emerging from the possible occurrence of low-density mean-field instabilities in heavy ion reactions. Within such a framework, the respective role of one and two-body effects, in the two models considered, will be carefully analysed. We will discuss, in particular, fragment production in central and semi-peripheral heavy ion collisions, which is the object of many recent experimental investigations. Moreover, in the context of spallation reactions, we will show how thermal expansion may trigger the development of mean-field instabilities, leading to...
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.
2013-11-20
The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.
Shear modulus of the hadron-quark mixed phase
Johnson-McDaniel, Nathan K
2012-01-01
Robust arguments predict that a hadron-quark mixed phase may exist in the cores of some "neutron" stars. Such a phase forms a crystalline lattice with a shear modulus higher than that of the crust due to the high density and charge separation, even allowing for the effects of charge screening. This may lead to strong continuous gravitational-wave emission from rapidly rotating neutron stars and gravitational-wave bursts associated with magnetar flares and pulsar glitches. We present the first detailed calculation of the shear modulus of the mixed phase. We describe the quark phase using the bag model plus first-order quantum chromodynamics corrections and the hadronic phase using relativistic mean-field models with parameters allowed by the most massive pulsar. Most of the calculation involves treating the "pasta phases" of the lattice via dimensional continuation, and we give a general method for computing dimensionally continued lattice sums including the Debye model of charge screening. We compute all the ...
Nuclear matter properties in the relativistic mean field model with $\\sigma-\\omega$ coupling
Chung, K C; Santiago, A J; Zhang, J W
2001-01-01
The possibility of extending the linear sigma-omega model by introducing a sigma-omega coupling phenomenologically is explored. It is shown that, in contrast to the usual Walecka model, not only the effective nucleon mass M* but also the effective sigma meson mass m*_sigma and the effective omega meson mass m*_omega are nucleon density dependent. When the model parameters are fitted to the nuclear saturation point (the nuclear radius constant r_0=1.14fm and volume energy a_1=16.0MeV) as well as to the effective nucleon mass M*=0.85M, the model yields m*_sigma=1.09m_sigma and m*_omega=0.90m_omega at the saturation point, and the nuclear incompressibility K_0=501MeV. The lowest value of K_0 given by this model by adjusting the model parameters is around 227MeV.
Deformed neutron stars due to strong magnetic field in terms of relativistic mean field theories
Yanase, Kota; Yoshinaga, Naotaka
2014-09-01
Some observations suggest that magnetic field intensity of neutron stars that have particularly strong magnetic field, magnetars, reaches values up to 1014-15G. It is expected that there exists more strong magnetic field of several orders of magnitude in the interior of such stars. Neutron star matter is so affected by magnetic fields caused by intrinsic magnetic moments and electric charges of baryons that masses of neutron stars calculated by using Tolman-Oppenheimer-Volkoff equation is therefore modified. We calculate equation of state (EOS) in density-dependent magnetic field by using sigma-omega-rho model that can reproduce properties of stable nuclear matter in laboratory Furthermore we calculate modified masses of deformed neutron stars.
Fast equilibration of hadrons in an expanding fireball.
Noronha-Hostler, J; Greiner, C; Shovkovy, I A
2008-06-27
Because of long chemical equilibration times for standard hadronic reactions in a hadron gas in relativistic heavy ion collisions, it was suggested that hadrons are born into equilibrium after the quark gluon plasma is formed. We develop a dynamical scheme, using master equations, in which Hagedorn states contribute to fast chemical equilibration times of baryons and kaons, just below the critical temperature, estimates of which are derived analytically. The hadrons quickly equilibrate for an initial over- or underpopulation of Hagedorn states. Our particle ratios compared to BNL Relativistic Heavy Ion Collider show a close match.
Towards a realistic description of hadron resonances
Schmidt, R. A.; Canton, L.; Schweiger, W.; Plessas, W.
2016-08-01
We report on our attempts of treating excited hadron states as true quantum resonances. Hitherto the spectroscopy of mesons, usually considered as quark-antiquark systems, and of baryons, usually considered as three-quark systems, has been treated through excitation spectra of bound states (namely, confined few-quark systems), corresponding to poles of the quantum-mechanical resolvent at real negative values in the complex energy plane. As a result the wave functions, i.e. the residua of the resolvent, have not exhibited the behaviour as required for hadron resonances with their multiple decay modes. This has led to disturbing shortcomings in the description of hadronic resonance phenomena. We have aimed at a more realistic description of hadron resonances within relativistic constituent-quark models taking into account explicitly meson-decay channels. The corresponding coupled-channels theory is based on a relativistically invariant mass operator capable of producing hadron ground states with real energies and hadron resonances with complex energies, the latter corresponding to poles in the lower half-plane of the unphysical sheet of the complex energy plane. So far we have demonstrated the feasibility of the coupled-channels approach to hadron resonances along model calculations producing indeed the desired properties. The corresponding spectral properties will be discussed in this contribution. More refined studies are under way towards constructing a coupled-channels relativistic constituent-quark model for meson and baryon resonances.
Uncertainty quantification for mean field games in social interactions
Dia, Ben Mansour
2016-01-09
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
Regularity theory for mean-field game systems
Gomes, Diogo A; Voskanyan, Vardan
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Accretion Disks and Dynamos: Toward a Unified Mean Field Theory
Blackman, Eric G
2012-01-01
Conversion of gravitational energy into radiation near stars and compact objects in accretion disks the origin of large scale magnetic fields in astrophysical rotators have long been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory have exemplified such distinct pursuits. Both are presently incomplete, but 21st century MFD theory has nonlinear predictive power compared to 20th century MFD. in contrast, alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory ar...
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
Strand, Hugo U. R.; Eckstein, Martin; Werner, Philipp
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium "phase diagrams" that map out the different dynamical regimes.
Mean field limit for bosons and propagation of Wigner measures
Ammari, Z
2008-01-01
We consider the N-body Schr\\"{o}dinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work \\cite{AmNi}, the mean field limit is translated into a semiclassical problem with a small parameter $\\epsilon\\to 0$, after introducing an $\\epsilon$-dependent bosonic quantization. The limit is expressed as a push-forward by a nonlinear flow (e.g. Hartree) of the associated Wigner measures. These object and their basic properties were introduced in \\cite{AmNi} in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for rather general class of quantum states in their mean field limit.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.
2016-09-14
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
A mean field theory of coded CDMA systems
Yano, Toru [Graduate School of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522 (Japan); Tanaka, Toshiyuki [Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)], E-mail: yano@thx.appi.keio.ac.jp
2008-08-15
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.
Large amplitude motion with a stochastic mean-field approach
Yilmaz Bulent
2012-12-01
Full Text Available In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.
An Adaptive Filtering Algorithm using Mean Field Annealing Techniques
Persson, Per; Nordebo, Sven; Claesson, Ingvar
2002-01-01
We present a new approach to discrete adaptive filtering based on the mean field annealing algorithm. The main idea is to find the discrete filter vector that minimizes the matrix form of the Wiener-Hopf equations in a least-squares sense by a generalized mean field annealing algorithm. It is indicated by simulations that this approach, with complexity O(M^2) where M is the filter length, finds a solution comparable to the one obtained by the recursive least squares (RLS) algorithm but withou...
Socio-economic applications of finite state mean field games
Gomes, Diogo A.
2014-10-06
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
Suppression of oscillations in mean-field diffusion
Neeraj Kumar Kamal; Pooja Rani Sharma; Manish Dev Shrimali
2015-02-01
We study the role of mean-field diffusive coupling on suppression of oscillations for systems of limit cycle oscillators. We show that this coupling scheme not only induces amplitude death (AD) but also oscillation death (OD) in coupled identical systems. The suppression of oscillations in the parameter space crucially depends on the value of mean-field diffusion parameter. It is also found that the transition from oscillatory solutions to OD in conjugate coupling case is different from the case when the coupling is through similar variable. We rationalize our study using linear stability analysis.
Sugano, Junpei; Yahiro, Masahiro
2016-01-01
We aim at drawing the hadron-quark phase transition line in the QCD phase diagram by using the two phase model (TPM) in which the entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model with vector-type four-quark interaction is used for the quark phase and the relativistic mean field (RMF) model is for the hadron phase. Reasonable TPM is constructed by using lattice QCD data and neutron star observations as reliable constraints. For the EPNJL model, we determine the strength of vector-type four-quark interaction at zero quark chemical potential from lattice QCD data on quark number density normalized by its Stefan-Boltzmann limit. For the hadron phase, we consider three RMF models, NL3, TM1 and model proposed by Maruyama, Tatsumi, Endo and Chiba (MTEC). We find that MTEC is most consistent with the neutron star observations and TM1 is the second best. Assuming that the hadron-quark phase transition occurs in the core of neutron star, we explore the density-dependence of vector-type four-quark i...
Mean-field versus microconvection effects in nanofluid thermal conduction.
Eapen, Jacob; Williams, Wesley C; Buongiorno, Jacopo; Hu, Lin-Wen; Yip, Sidney; Rusconi, Roberto; Piazza, Roberto
2007-08-31
Transient hot-wire data on thermal conductivity of suspensions of silica and perfluorinated particles show agreement with the mean-field theory of Maxwell but not with the recently postulated microconvection mechanism. The influence of interfacial thermal resistance, convective effects at microscales, and the possibility of thermal conductivity enhancements beyond the Maxwell limit are discussed.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-07
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
Robust mean field games for coupled Markov jump linear systems
Moon, Jun; Başar, Tamer
2016-07-01
We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents' individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.
Mean Field Approach to the Giant Wormhole Problem
Gamba, A.; Kolokolov, I.; Martellini, M.
We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.
Critical fluctuations for quantum mean-field models
Fannes, M.; Kossakowski, A.; Verbeure, A. (Univ. Louvain (Belgium))
1991-11-01
A Ginzburg-Landau-type approximation is proposed for the local Gibbs states for quantum mean-field models that leads to the exact thermodynamics. Using this approach, the spin fluctuations are computed for some spin-1/2 models. At the critical temperature, the distribution function showing abnormal fluctuations is found explicitly.
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-09
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Mean-field dynamo action in renovating shearing flows.
Kolekar, Sanved; Subramanian, Kandaswamy; Sridhar, S
2012-08-01
We study mean-field dynamo action in renovating flows with finite and nonzero correlation time (τ) in the presence of shear. Previous results obtained when shear was absent are generalized to the case with shear. The question of whether the mean magnetic field can grow in the presence of shear and nonhelical turbulence, as seen in numerical simulations, is examined. We show in a general manner that, if the motions are strictly nonhelical, then such mean-field dynamo action is not possible. This result is not limited to low (fluid or magnetic) Reynolds numbers nor does it use any closure approximation; it only assumes that the flow renovates itself after each time interval τ. Specifying to a particular form of the renovating flow with helicity, we recover the standard dispersion relation of the α(2)Ω dynamo, in the small τ or large wavelength limit. Thus mean fields grow even in the presence of rapidly growing fluctuations, surprisingly, in a manner predicted by the standard quasilinear closure, even though such a closure is not strictly justified. Our work also suggests the possibility of obtaining mean-field dynamo growth in the presence of helicity fluctuations, although having a coherent helicity will be more efficient.
Condition monitoring with Mean field independent components analysis
Pontoppidan, Niels Henrik; Sigurdsson, Sigurdur; Larsen, Jan
2005-01-01
We discuss condition monitoring based on mean field independent components analysis of acoustic emission energy signals. Within this framework it is possible to formulate a generative model that explains the sources, their mixing and also the noise statistics of the observed signals. By using...
Mean-Field Versus Microconvection Effects in Nanofluid Thermal Conduction
Eapen, Jacob; Williams, Wesley C.; Buongiorno, Jacopo; Hu, Lin-Wen; Yip, Sidney; Rusconi, Roberto; Piazza, Roberto
2007-08-01
Transient hot-wire data on thermal conductivity of suspensions of silica and perfluorinated particles show agreement with the mean-field theory of Maxwell but not with the recently postulated microconvection mechanism. The influence of interfacial thermal resistance, convective effects at microscales, and the possibility of thermal conductivity enhancements beyond the Maxwell limit are discussed.
Model-checking mean-field models: algorithms & applications
Kolesnichenko, Anna Victorovna
2014-01-01
Large systems of interacting objects are highly prevalent in today's world. In this thesis we primarily address such large systems in computer science. We model such large systems using mean-field approximation, which allows to compute the limiting behaviour of an infinite population of identical o
Merging Belief Propagation and the Mean Field Approximation
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2010-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence...
Correlated emission of hadrons from recombination of correlated partons.
Fries, R J; Bass, S A; Müller, B
2005-04-01
We discuss different sources of hadron correlations in relativistic heavy ion collisions. We show that correlations among partons in a quasithermal medium can lead to the correlated emission of hadrons by quark recombination and argue that this mechanism offers a plausible explanation for the dihadron correlations in the few GeV/c momentum range observed in Au+Au collisions at the BNL Relativistic Heavy Ion Collider.
Effects of the quark-hadron phase transition on highly magnetized neutron stars
Franzon, B; Schramm, S
2016-01-01
The presence of quark-hadron phase transitions in neutron stars can be related to several interesting phenomena. In particular, previous calculations have shown that fast rotating neutron stars, when subjected to a quark-hadron phase transition in their interiors, could give rise to the backbending phenomenon characterized by a spin-up era. In this work, we use an equation of state composed of two phases, containing nucleons (and leptons) and quarks. The hadronic phase is described in a relativistic mean field formalism that takes many-body forces into account, and the quark phase is described by the MIT bag model with a vector interaction. Stationary and axi-symmetric stellar models are obtained in a self-consistent way by solving numerically the Einstein-Maxwell equations by means of a pseudo-spectral method. As a result, we obtain the interesting backbending phenomenon for fast spinning neutron stars. More importantly, we show that a magnetic field, which is assumed to be axi-symmetric and poloidal, can al...
Yamazaki, Takeshi
2015-01-01
Understanding hadronic interactions is crucial for investigating the properties of unstable hadrons, since measuring physical quantities for unstable hadrons including the resonance mass and decay width requires simultaneous calculations of final scattering states. Recent studies of hadronic scatterings and decays are reviewed from this point of view. The nuceon-nucleon and multi-nucleon interactions are very important to understand the formation of nucleus from the first principle of QCD. These interactions have been studied mainly by two methods, due originally to L\\"uscher and to HALQCD. The results obtained from the two methods are compared in three channels, $I=2$ two-pion, H-dibaryon, and two-nucleon channels. So far the results from the two methods for the two-nucleon channels are different even at the level of the presence or absence of bound states. We then discuss possible uncertainties in each method. Recent results on the binding energy for helium nuclei are also reviewed.
Strange Hadronic Matter in a Chiral Model
ZHANG Li-Liang; SONG Hong-Qiu; WANG Ping; SU Ru-Keng
2000-01-01
The strange hadronic matter with nucleon, Λ-hyperon and E-hyperon is studied by using a chiral symmetry model in a mean-field approximation. The saturation properties and stabilities of the strange hadronic matter are discussed. The result indicates a quite large strangeness fraction (fs) region where the strange hadronic matter is stable against particle emission. In the large fs region, the component dominates, resulting in a deep minimum in the curve of the binding energy per baryon EB versus the strangeness fraction fs with (EB, fs) -～ (-26.0MeV, 1.23).
K. Orginos
2011-12-01
In this talk I am reviewing recent calculations of properties of multi-hadron systems in lattice QCD. In particular, I am reviewing results of elastic scattering phase shifts in meson-meson, meson-baryon and baryon-baryon systems, as well as discussing results indicating possible existence of bound states in two baryon systems. Finally, calculations of properties of systems with more than two hadrons are presented.
Neutrino emissivity in the quark-hadron mixed phase of neutron stars
Spinella, William M. [Computational Science Research Center San Diego State University, San Diego, CA (United States); San Diego State University, Department of Physics, San Diego, CA (United States); Weber, Fridolin [San Diego State University, Department of Physics, San Diego, CA (United States); University of California San Diego, Center for Astrophysics and Space Sciences, La Jolla, CA (United States); Contrera, Gustavo A. [CONICET, Buenos Aires (Argentina); CONICET - Dept. de Fisica, UNLP, IFLP, La Plata (Argentina); Universidad Nacional de La Plata, Grupo de Gravitacion, Astrofisica y Cosmologia, Facultad de Ciencias Astronomicas y Geofisicas, La Plata (Argentina); Orsaria, Milva G. [CONICET, Buenos Aires (Argentina); Universidad Nacional de La Plata, Grupo de Gravitacion, Astrofisica y Cosmologia, Facultad de Ciencias Astronomicas y Geofisicas, La Plata (Argentina)
2016-03-15
Numerous theoretical studies using various equation of state models have shown that quark matter may exist at the extreme densities in the cores of high-mass neutron stars. It has also been shown that a phase transition from hadronic matter to quark matter would result in an extended mixed phase region that would segregate phases by net charge to minimize the total energy of the phase, leading to the formation of a crystalline lattice. The existence of quark matter in the core of a neutron star may have significant consequences for its thermal evolution, which for thousands of years is facilitated primarily by neutrino emission. In this work we investigate the effect a crystalline quark-hadron mixed phase can have on the neutrino emissivity from the core. To this end we calculate the equation of state using the relativistic mean-field approximation to model hadronic matter and a nonlocal extension of the three-flavor Nambu-Jona-Lasinio model for quark matter. Next we determine the extent of the quark-hadron mixed phase and its crystalline structure using the Glendenning construction, allowing for the formation of spherical blob, rod, and slab rare phase geometries. Finally we calculate the neutrino emissivity due to electron-lattice interactions utilizing the formalism developed for the analogous process in neutron star crusts. We find that the contribution to the neutrino emissivity due to the presence of a crystalline quark-hadron mixed phase is substantial compared to other mechanisms at fairly low temperatures (
From hadron gas to quark matter, 1
Hagedorn, Rolf
1981-01-01
An analytical, non-perturbative description of a strongly interacting hadron gas is presented. Its main features are: the formulation is relativistically covariant, hadrons have finite extensions which are treated a la Van der Waals and their strong interactions are simulated by a hadronic mass spectrum generated by a bootstrap equation under the constraints of baryon number conservation. The system exhibits a singularity, which has the typical features of a phase transition gas to liquid, but which the authors interpret here as the transition into a quark-gluon plasma phase, which, however, cannot be described by this model. (16 refs).
Entanglement spectrum in cluster dynamical mean-field theory
Udagawa, Masafumi; Motome, Yukitoshi
2015-01-01
We study the entanglement spectrum of the Hubbard model at half filling on a kagome lattice. The entanglement spectrum is defined by the set of eigenvalues of a reduced thermal density matrix, which is naturally obtained in the framework of the dynamical mean-field theory. Adopting the cluster dynamical mean-field theory combined with continuous-time auxiliary-field Monte Carlo method, we calculate the entanglement spectrum for a three-site triangular cluster in the kagome Hubbard model. We find that the results at the three-particle sector well capture the qualitative nature of the system. In particular, the eigenvalue of the reduced density matrix, corresponding to the chiral degrees of freedom, exhibits a characteristic temperature scale Tchiral, below which a metallic state with large quasiparticle mass is stabilized. The entanglement spectra at different particle number sectors also exhibit characteristic changes around Tchiral, implying the development of inter-triangular ferromagnetic correlations in the correlated metallic regime.
Mean-field theory of echo state networks
Massar, Marc; Massar, Serge
2013-04-01
Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study “echo state networks,” networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion.
Analytic Beyond-Mean-Field BEC Wave Functions
Dunn, Martin; Laing, W. Blake; Watson, Deborah K.; Loeser, John G.
2006-05-01
We present analytic N-body beyond-mean-field wave functions for Bose-Einstein condensates. This extends our previous beyond-mean-field energy calculations to the substantially more difficult problem of determining correlated N-body wave functions for a confined system. The tools used to achieve this have been carefully chosen to maximize the use of symmetry and minimize the dependence on numerical computation. We handle the huge number of interactions when N is large (˜N^2/2 two-body interactions) by bringing together three theoretical methods. These are dimensional perturbation theory, the FG method of Wilson et al, and the group theory of the symmetric group. The wave function is then used to derive the density profile of a condensate in a cylindrical trap.This method makes no assumptions regarding the form or strength of the interactions and is applicable to both small-N and large-N systems.
Characterizing the mean-field dynamo in turbulent accretion disks
Gressel, Oliver
2015-01-01
The formation and evolution of a wide class of astrophysical objects is governed by turbulent, magnetized accretion disks. Understanding their secular dynamics is of primary importance. Apart from enabling mass accretion via the transport of angular momentum, the turbulence affects the long-term evolution of the embedded magnetic flux, which in turn regulates the efficiency of the transport. In this paper, we take a comprehensive next step towards an effective mean-field model for turbulent astrophysical disks by systematically studying the key properties of magnetorotational turbulence in vertically-stratified, isothermal shearing boxes. This allows us to infer emergent properties of the ensuing chaotic flow as a function of the shear parameter as well as the amount of net-vertical flux. Using the test-field method, we furthermore characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale fields. We simultaneously infer the vertical shape and the spectral scale depen...
Nuclear collective vibrations in extended mean-field theory
Lacroix, D. [Lab. de Physique Corpusculaire/ ENSICAEN, 14 - Caen (France); Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2003-07-01
The extended mean-field theory, which includes both the incoherent dissipation mechanism due to nucleon-nucleon collisions and the coherent dissipation mechanism due to coupling to low-lying surface vibrations, is briefly reviewed. Expressions of the strength functions for the collective excitations are presented in the small amplitude limit of this approach. This fully microscopic theory is applied by employing effective Skyrme forces to various giant resonance excitations at zero and finite temperature. The theory is able to describe the gross properties of giant resonance excitations, the fragmentation of the strength distributions as well as their fine structure. At finite temperature, the success and limitations of this extended mean-field description are discussed. (authors)
Schrödinger Approach to Mean Field Games
Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis
2016-03-01
Mean field games (MFG) provide a theoretical frame to model socioeconomic systems. In this Letter, we study a particular class of MFG that shows strong analogies with the nonlinear Schrödinger and Gross-Pitaevskii equations introduced in physics to describe a variety of physical phenomena. Using this bridge, many results and techniques developed along the years in the latter context can be transferred to the former, which provides both a new domain of application for the nonlinear Schrödinger equation and a new and fruitful approach in the study of mean field games. Utilizing this approach, we analyze in detail a population dynamics model in which the "players" are under a strong incentive to coordinate themselves.
Mean-field theory of a recurrent epidemiological model.
Nagy, Viktor
2009-06-01
Our purpose is to provide a mean-field theory for the discrete time-step susceptible-infected-recovered-susceptible (SIRS) model on uncorrelated networks with arbitrary degree distributions. The effect of network structure, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations. Consideration of two scenarios for disease contagion demonstrates that the manner in which contagion is transmitted from an infected individual to a contacted susceptible individual is of primary importance. In particular, the manner of contagion transmission determines how the degree distribution affects model behavior. We find excellent agreement between our theoretical results and numerical simulations on networks with large average connectivity.
Dynamical mean field theory of optical third harmonic generation
Jafari, S. A.; Tohyama, T.; Maekawa, S.
2006-01-01
We formulate the third harmonic generation (THG) within the dynamical mean field theory (DMFT) approximation of the Hubbard model. In the limit of large dimensions, where DMFT becomes exact, the vertex corrections to current vertices are identically zero, and hence the calculation of the THG spectrum reduces to a time-ordered convolution, followd by appropriate analytic continuuation. We present the typical THG spectrum of the Hubbard model obtained by this method. Within our DMFT calculation...
Communication patterns in mean field models for wireless sensor networks
2015-01-01
Wireless sensor networks are usually composed of a large number of nodes, and with the increasing processing power and power consumption efficiency they are expected to run more complex protocols in the future. These pose problems in the field of verification and performance evaluation of wireless networks. In this paper, we tailor the mean-field theory as a modeling technique to analyze their behavior. We apply this method to the slotted ALOHA protocol, and establish results on the long term...
A new approach to spinel ferrites through mean field approximation
Yazdani, A. [Tarbyat Modares University, Tehran P.C 14115-175 (Iran, Islamic Republic of)]. E-mail: yazdania@modares.ac.ir; Jalilian Nosrati, M.R. [Islamic Azad University Central Tehran Branch, Tehran P.C 14168-94351 (Iran, Islamic Republic of); Ghasemi, R. [Islamic Azad University Central Tehran Branch, Tehran P.C 14168-94351 (Iran, Islamic Republic of)
2006-09-15
The magnetic behavior and specification of spinel ferrites regarding exchange interactions is being studied. The strength of interactions has been examined through the cation substitution with application of mean field approximation of exchange interaction J{sub ij} . Two correlation and approximation parameters have been defined: correlation length R {sub c} in super-exchange and the magnetic effect of ion on the electron fluctuation J {sub 0}.
Thermodynamics of Hot Hadronic Gases at Finite Baryon Densities
Albright, Michael Glenn
In this thesis we investigate equilibrium and nonequilibrium thermodynamic properties of Quantum Chromodynamics (QCD) matter at finite baryon densities. We begin by constructing crossover models for the thermodynamic equation of state. These use switching functions to smoothly interpolate between a hadronic gas model at low energy densities to a perturbative QCD equation of state at high energy densities. We carefully design the switching function to avoid introducing first-, second-, or higher-order phase transitions which lattice QCD indicates are not present at small baryon chemical potentials. We employ three kinds of hadronic models in the crossover constructions, two of which include repulsive interactions via an excluded volume approximation while one model does not. We find that the three crossover models are in excellent agreement with accurate lattice QCD calculations of the equation of state over a wide range of temperatures and baryon chemical potentials. Hence, the crossover models should be very useful for parameterizing the equation of state at finite baryon densities, which is needed to build next-generation hydrodynamic simulations of heavy-ion collisions. We next calculate the speed of sound and baryon number fluctuations predicted by the crossover models. We find that crossover models with hadronic repulsion are most successful at reproducing the lattice results, while the model without repulsion is less successful, and hadron (only) models show poor agreement. We then compare the crossover models to net-proton fluctuation measurements from the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC). The comparisons suggest baryon number fluctuations freeze-out well below the chemical freeze-out temperature. We also search for signs of critical fluctuations in the STAR data, but we find no evidence for them at this time. Finally, we derive kinetic theory formulas for the shear and bulk viscosity and thermal conductivity of hot hadronic
Dynamical mean-field theory for flat-band ferromagnetism
Nguyen, Hong-Son; Tran, Minh-Tien
2016-09-01
The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.
Resummed mean-field inference for strongly coupled data
Jacquin, Hugo; Rançon, A.
2016-10-01
We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation expansion of the log-likelihood, the method outperforms standard mean-field inference methods, even when they are regularized. The inference is stable with respect to sampling noise, contrarily to previous works based either on the small correlation expansion, on the Bethe free energy, or on the mean-field and Gaussian models. Because it is mostly analytic, its complexity is still very low, requiring an iterative algorithm to solve for N auxiliary variables, that resorts only to matrix inversions and multiplications. We test our algorithm on the Sherrington-Kirkpatrick model submitted to a random external field and large random couplings, and demonstrate that even without regularization, the inference is stable across the whole phase diagram. In addition, the calculation leads to a consistent estimation of the entropy of the data and allows us to sample form the inferred distribution to obtain artificial data that are consistent with the empirical distribution.
High-pT hadron production and triggered particle correlations
Mischke, A.
2006-01-01
The STAR experiment at the Relativistic Heavy-Ion Collider has performed measurements of high transverse momentum particle production in ultra-relativistic heavy-ion collisions. High-pT hadrons are generated from hard parton scatterings early in the collision. The outgoing partons probe the surround
Mean-field and non-mean-field behaviors in scale-free networks with random Boolean dynamics
Castro e Silva, A [Departamento de Fisica, Universidade Federal de Ouro Preto, Campus Universitario, 35.400-000 Ouro Preto, Minas Gerais (Brazil); Kamphorst Leal da Silva, J, E-mail: alcidescs@gmail.co, E-mail: jaff@fisica.ufmg.b [Departamento de Fisica, Universidade Federal de Minas Gerais, Caixa Postal 702, 30.161-970, Belo Horizonte, Minas Gerais (Brazil)
2010-06-04
We study two types of simplified Boolean dynamics in scale-free networks, both with a synchronous update. Assigning only the Boolean functions AND and XOR to the nodes with probabilities 1 - p and p, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamics as its own input (self-regulation) or not. The same conclusion holds for the Kauffman NK model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation and (ii) disagree for small p when self-regulation is present in the model.
Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics
Silva, A Castro e
2009-01-01
We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.
Relativistic RPA in axial symmetry
Arteaga, D Pena; 10.1103/PhysRevC.77.034317
2009-01-01
Covariant density functional theory, in the framework of self-consistent Relativistic Mean Field (RMF) and Relativistic Random Phase approximation (RPA), is for the first time applied to axially deformed nuclei. The fully self-consistent RMF+RRPA equations are posed for the case of axial symmetry and non-linear energy functionals, and solved with the help of a new parallel code. Formal properties of RPA theory are studied and special care is taken in order to validate the proper decoupling of spurious modes and their influence on the physical response. Sample applications to the magnetic and electric dipole transitions in $^{20}$Ne are presented and analyzed.
Skymapping with OSSE via the Mean Field Annealing Pixon Technique
Dixon, D D; Zych, A D; Cheng, L X; Johnson, W N; Kurfess, J D; Pina, R K; Pütter, R C; Purcell, W R; Wheaton, W A; Wheaton, Wm. A.
1997-01-01
We present progress toward using scanned OSSE observations for mapping and sky survey work. To this end, we have developed a technique for detecting pointlike sources of unknown number and location, given that they appear in a background which is relatively featureless or which can be modeled. The technique, based on the newly developed concept and mean field annealing, is described, with sample reconstructions of data from the OSSE Virgo Survey. The results demonstrate the capability of reconstructing source information without any a priori information about the number and/or location of pointlike sources in the field-of-view.
Fictive impurity approach to dynamical mean field theory
Fuhrmann, A.
2006-10-15
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Small-world network spectra in mean-field theory.
Grabow, Carsten; Grosskinsky, Stefan; Timme, Marc
2012-05-25
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean-field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions agree well with the actual spectra (obtained by numerical diagonalization) for undirected and directed networks and from fully regular to strongly random topologies. These results may provide analytical insights to empirically found features of dynamics on small-world networks from various research fields, including biology, physics, engineering, and social science.
Mean Field Evolution of Fermions with Coulomb Interaction
Porta, Marcello; Rademacher, Simone; Saffirio, Chiara; Schlein, Benjamin
2017-03-01
We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles. For initial data describing approximate Slater determinants, we prove convergence of the many-body evolution towards Hartree-Fock dynamics. Our result holds under a condition on the solution of the Hartree-Fock equation, that we can only show in a very special situation (translation invariant data, whose Hartree-Fock evolution is trivial), but that we expect to hold more generally.
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Dynamical mean-field theory for quantum chemistry.
Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R
2011-03-04
The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.
A mean-field game economic growth model
Gomes, Diogo A.
2016-08-05
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks to maximize his/her utility by taking into account statistical data about the whole population. The individual actions drive the evolution of the players, and a market-clearing condition determines the relative price of capital and consumer goods. We study the existence and uniqueness of optimal strategies of the agents and develop numerical methods to compute these strategies and the equilibrium price.
Mean-field theory and self-consistent dynamo modeling
Yoshizawa, Akira; Yokoi, Nobumitsu [Tokyo Univ. (Japan). Inst. of Industrial Science; Itoh, Sanae-I [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics; Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2001-12-01
Mean-field theory of dynamo is discussed with emphasis on the statistical formulation of turbulence effects on the magnetohydrodynamic equations and the construction of a self-consistent dynamo model. The dynamo mechanism is sought in the combination of the turbulent residual-helicity and cross-helicity effects. On the basis of this mechanism, discussions are made on the generation of planetary magnetic fields such as geomagnetic field and sunspots and on the occurrence of flow by magnetic fields in planetary and fusion phenomena. (author)
Asymptotics of Mean-Field O( N) Models
Kirkpatrick, Kay; Nawaz, Tayyab
2016-12-01
We study mean-field classical N-vector models, for integers N≥2. We use the theory of large deviations and Stein's method to study the total spin and its typical behavior, specifically obtaining non-normal limit theorems at the critical temperatures and central limit theorems away from criticality. Important special cases of these models are the XY (N=2) model of superconductors, the Heisenberg (N=3) model [previously studied in Kirkpatrick and Meckes (J Stat Phys 152:54-92, 2013) but with a correction to the critical distribution here], and the Toy (N=4) model of the Higgs sector in particle physics.
Asymptotics of the mean-field Heisenberg model
Kirkpatrick, Kay
2012-01-01
We consider the mean-field classical Heisenberg model and obtain detailed information about the magnetization by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cram\\`er- and Sanov-type large deviations principles for the magnetization and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the magnetization throughout the phase transition using Stein's method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.
A mechanical approach to mean field spin models
Genovese, Giuseppe
2008-01-01
Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the thermodynamics of mean-field models defined on lattice, whose order parameters self average. We show the whole procedure by analyzing in full details the simplest test case, namely the Curie-Weiss model. Further we report some applications also to models whose order parameters do not self-average, by using the Sherrington-Kirkpatrick spin glass as a guide.
Mean field theory for U(n) dynamical groups
Rosensteel, G, E-mail: george.rosensteel@tulane.edu [Department of Physics, Tulane University, New Orleans, LA 70118 (United States)
2011-04-22
Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick su(2) model and the Elliott su(3) model. When the energy in the su(3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
Control and Nash Games with Mean Field Effect
Alain BENSOUSSAN; Jens FREHSE
2013-01-01
Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007,of Gueant-Lasry-Lions in 2011,of HuangCaines-Malham in 2007 and many others).There are a lot of applications.In general,the applications concern approximating an infinite number of players with common behavior by a representative agent.This agent has to solve a control problem perturbed by a field equation,representing in some way the behavior of the average infinite number of agents.This approach does not lead easily to the problems of Nash equilibrium for a finite number of players,perturbed by field equations,unless one considers averaging within different groups,which has not been done in the literature,and seems quite challenging.In this paper,the authors approach similar problems with a different motivation which makes sense for control and also for differential games.Thus the systems of nonlinear partial differential equations with mean field terms,which have not been addressed in the literature so far,are considered here.
Simulated Tempering and Swapping on Mean-Field Models
Bhatnagar, Nayantara; Randall, Dana
2016-08-01
Simulated and parallel tempering are families of Markov Chain Monte Carlo algorithms where a temperature parameter is varied during the simulation to overcome bottlenecks to convergence due to multimodality. In this work we introduce and analyze the convergence for a set of new tempering distributions which we call entropy dampening. For asymmetric exponential distributions and the mean field Ising model with an external field simulated tempering is known to converge slowly. We show that tempering with entropy dampening distributions mixes in polynomial time for these models. Examining slow mixing times of tempering more closely, we show that for the mean-field 3-state ferromagnetic Potts model, tempering converges slowly regardless of the temperature schedule chosen. On the other hand, tempering with entropy dampening distributions converges in polynomial time to stationarity. Finally we show that the slow mixing can be very expensive practically. In particular, the mixing time of simulated tempering is an exponential factor longer than the mixing time at the fixed temperature.
Non-local correlations within dynamical mean field theory
Li, Gang
2009-03-15
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Benchmarking mean-field approximations to level densities
Alhassid, Y; Gilbreth, C N; Nakada, H
2015-01-01
We assess the accuracy of finite-temperature mean-field theory using as a standard the Hamiltonian and model space of the shell model Monte Carlo calculations. Two examples are considered: the nucleus $^{162}$Dy, representing a heavy deformed nucleus, and $^{148}$Sm, representing a nearby heavy spherical nucleus with strong pairing correlations. The errors inherent in the finite-temperature Hartree-Fock and Hartree-Fock-Bogoliubov approximations are analyzed by comparing the entropies of the grand canonical and canonical ensembles, as well as the level density at the neutron resonance threshold, with shell model Monte Carlo (SMMC) calculations, which are accurate up to well-controlled statistical errors. The main weak points in the mean-field treatments are seen to be: (i) the extraction of number-projected densities from the grand canonical ensembles, and (ii) the symmetry breaking by deformation or by the pairing condensate. In the absence of a pairing condensate, we confirm that the usual saddle-point appr...
Nonlinear regimes in mean-field full-sphere dynamo
Pipin, V V
2016-01-01
The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\\odot}$ rotating with period of 10 days. The differential rotation law was estimated using the mean-field hydrodynamic and heat transport equations. For the intermediate parameter of the turbulent magnetic Reynolds number, $Pm_{T}=3$ we found the oscillating dynamo regimes with period about 40Yr. The higher $Pm_{T}$ results to longer dynamo periods. The meridional circulation has one cell per hemisphere. It is counter-clockwise in the Northen hemisphere. The amplitude of the flow at the surface around 1 m/s. Tne models with regards for meridional circulation show the anti-symmetric relative to equator magnetic field. If the large-scale flows is fixed we find that the dynamo transits from axisymmetric to non-axisymmetric regimes for the overcritical parameter of the $\\alpha$effect. The change of dynamo regime occurs because of the non-axisymmetric non-linear $\\alpha$-effect. The situation pe...
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-01-01
We introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat. Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that models also the geometric Brownian motion and can be studied analytically. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate. The relationship between the kinetic and the diffusion models allow to introduce an easy-to- implement expression for computing the Fourier transform o...
Topological properties of the mean-field ϕ4 model
Andronico, A.; Angelani, L.; Ruocco, G.; Zamponi, F.
2004-10-01
We study the thermodynamics and the properties of the stationary points (saddles and minima) of the potential energy for a ϕ4 mean-field model. We compare the critical energy vc [i.e., the potential energy v(T) evaluated at the phase transition temperature Tc ] with the energy vθ at which the saddle energy distribution show a discontinuity in its derivative. We find that, in this model, vc≫vθ , at variance to what has been found in different mean-field and short ranged systems, where the thermodynamic phase transitions take place at vc=vθ [Casetti, Pettini and Cohen, Phys. Rep. 337, 237 (2000)]. By direct calculation of the energy vs(T) of the “inherent saddles,” i.e., the saddles visited by the equilibrated system at temperature T , we find that vs(Tc)˜vθ . Thus, we argue that the thermodynamic phase transition is related to a change in the properties of the inherent saddles rather than to a change of the topology of the potential energy surface at T=Tc . Finally, we discuss the approximation involved in our analysis and the generality of our method.
The effectiveness of mean-field theory for avalanche distributions
Lee, Edward; Raju, Archishman; Sethna, James
We explore the mean-field theory of the pseudogap found in avalanche systems with long-range anisotropic interactions using analytical and numerical tools. The pseudogap in the density of low-stability states emerges from the competition between stabilizing interactions between spins in an avalanche and the destabilizing random movement towards the threshold caused by anisotropic couplings. Pazmandi et al. have shown that for the Sherrington-Kirkpatrick model, the pseudogap scales linearly and produces a distribution of avalanche sizes with exponent t=1 in contrast with that predicted from RFIM t=3/2. Lin et al. have argued that the scaling exponent ? of the pseudogap depends on the tail of the distribution of couplings and on non-universal values like the strain rate and the magnitude of the coupling strength. Yet others have argued that the relationship between the pseudogap scaling and the distribution of avalanche sizes is dependent on dynamical details. Despite the theoretical arguments, the class of RFIM mean-field models is surprisingly good at predicting the distribution of avalanche sizes in a variety of different magnetic systems. We investigate these differences with a combination of theory and simulation.
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-11-01
I introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat (1930, 1931). Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that can be studied analytically, by virtue of a transformation of variables recently utilized in Iagar and Sánchez (2013) to study the heat equation in a nonhomogeneous medium with critical density. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
RELATIVISTIC CALCULATIONS OF THE SUPERHEAVY NUCLEUS 114-298
BOERSMA, HF
1993-01-01
We investigate ground-state properties of the superheavy nucleus with N = 184 and Z = 114, (298)114, using conventional relativistic mean-field theory and density-dependent mean-field theory, which reproduces Dirac-Brueckner calculations in nuclear matter. Our calculations provide support for N = 18
Decaying hadrons within constituent-quark models
Kleinhappel, Regina
2012-01-01
Within conventional constituent-quark models hadrons come out as stable bound states of the valence (anti)quarks. Thereby the resonance character of hadronic excitations is completely ignored. A more realistic description of hadron spectra can be achieved by including explicit mesonic degrees of freedom, which couple directly to the constituent quarks. We will present a coupled-channel formalism that describes such hybrid systems in a relativistically invariant way and allows for the decay of excited hadrons. The formalism is based on the point-form of relativistic quantum mechanics. If the confining forces between the (anti)quarks are described by instantaneous interactions it can be formally shown that the mass-eigenvalue problem for a system that consists of dynamical (anti)quarks and mesons reduces to a hadronic eigenvalue problem in which the eigenstates of the pure confinement problem (bare hadrons) are coupled via meson loops. The only point where the quark substructure enters are form factors at the m...
Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)
2016-12-15
We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.
Equilibration of hadrons in HICs via Hagedorn States
Beitel, M; Greiner, C
2015-01-01
Hagedorn states (HS) are a tool to model the hadronization process which occurs in the phase transition region between the quark gluon plasma (QGP) and the hadron resonance gas (HRG). These states are believed to appear near the Hagedorn temperature $T_H$ which in our understanding equals the critical temperature $T_c$. A covariantly formulated bootstrap equation is solved to generate the zoo of these particles characterized baryon number $B$, strangeness $S$ and electric charge $Q$. These hadron-like resonances are characterized by being very massive and by not being limited to quantum numbers of known hadrons. All hadronic properties like masses, spectral functions etc.are taken from the hadronic transport model Ultra Relativistic Quantum Molecular Dynamics (UrQMD). Decay chains of single Hagedorn states provide a well description of experimentally observed multiplicity ratios of strange and multi-strange particles. In addition, the final energy spectra of resulting hadrons show a thermal-like distribution ...
Neural Population Dynamics Modeled by Mean-Field Graphs
Kozma, Robert; Puljic, Marko
2011-09-01
In this work we apply random graph theory approach to describe neural population dynamics. There are important advantages of using random graph theory approach in addition to ordinary and partial differential equations. The mathematical theory of large-scale random graphs provides an efficient tool to describe transitions between high- and low-dimensional spaces. Recent advances in studying neural correlates of higher cognition indicate the significance of sudden changes in space-time neurodynamics, which can be efficiently described as phase transitions in the neuropil medium. Phase transitions are rigorously defined mathematically on random graph sequences and they can be naturally generalized to a class of percolation processes called neuropercolation. In this work we employ mean-field graphs with given vertex degree distribution and edge strength distribution. We demonstrate the emergence of collective oscillations in the style of brains.
Spectral Synthesis via Mean Field approach Independent Component Analysis
Hu, Ning; Kong, Xu
2015-01-01
In this paper, we apply a new statistical analysis technique, Mean Field approach to Bayesian Independent Component Analysis (MF-ICA), on galaxy spectral analysis. This algorithm can compress the stellar spectral library into a few Independent Components (ICs), and galaxy spectrum can be reconstructed by these ICs. Comparing to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, MF-ICA approach offers a large improvement in the efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter-recover for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters from the Sloan Digital Sky Survey galaxies. We find that our MF-ICA method not only can fit the observed galaxy spectra efficiently, but also can recover the physical parameters of galaxies accurately. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find...
Non-mean-field screening by multivalent counterions
Loth, M S; Shklovskii, B I, E-mail: loth@physics.umn.ed [Department of Physics, University of Minnesota, Minneapolis, MN 55455 (United States)
2009-10-21
Screening of a strongly charged macroion by its multivalent counterions cannot be described in the framework of a mean-field Poisson-Boltzmann (PB) theory because multivalent counterions form a strongly correlated liquid (SCL) on the surface of the macroion. It was predicted that a distant counterion polarizes the SCL as if it were a metallic surface and creates an electrostatic image. The attractive potential energy of the image is the reason why the charge density of counterions decreases faster with distance from the charged surface than in PB theory. Using the Monte Carlo method to find the equilibrium distribution of counterions around the macroion, we confirm the existence of the image potential energy. It is also shown that, due to the negative screening length of the SCL, -2xi, the effective metallic surface is actually above the SCL by |xi|.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-04-05
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin
2014-04-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Mean-field vs. Stochastic Models for Transcriptional Regulation
Blossey, Ralf; Giuraniuc, Claudiu
2009-03-01
We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: the repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.
Mean-field versus stochastic models for transcriptional regulation
Blossey, R.; Giuraniuc, C. V.
2008-09-01
We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ODE’s representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results that both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: The repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.
Nuclear Level Density: Shell Model vs Mean Field
Sen'kov, Roman
2015-01-01
The knowledge of the nuclear level density is necessary for understanding various reactions including those in the stellar environment. Usually the combinatorics of Fermi-gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from the conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally...
Metabifurcation analysis of a mean field model of the cortex
Frascoli, Federico; Bojak, Ingo; Liley, David T J
2010-01-01
Mean field models (MFMs) of cortical tissue incorporate salient features of neural masses to model activity at the population level. One of the common aspects of MFM descriptions is the presence of a high dimensional parameter space capturing neurobiological attributes relevant to brain dynamics. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two families. After investigating and characterizing these, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli, distribution of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs ...
Double binding energy differences: Mean-field or pairing effect?
Qi, Chong
2012-10-01
In this Letter we present a systematic analysis on the average interaction between the last protons and neutrons in atomic nuclei, which can be extracted from the double differences of nuclear binding energies. The empirical average proton-neutron interaction Vpn thus derived from experimental data can be described in a very simple form as the interplay of the nuclear mean field and the pairing interaction. It is found that the smooth behavior as well as the local fluctuations of the Vpn in even-even nuclei with N ≠ Z are dominated by the contribution from the proton-neutron monopole interactions. A strong additional contribution from the isoscalar monopole interaction and isovector proton-neutron pairing interaction is seen in the Vpn for even-even N = Z nuclei and for the adjacent odd-A nuclei with one neutron or proton being subtracted.
Mean-field games with logistic population dynamics
Gomes, Diogo A.
2013-12-01
In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.
Glauber Dynamics for the mean-field Potts Model
Cuff, Paul; Louidor, Oren; Lubetzky, Eyal; Peres, Yuval; Sly, Allan
2012-01-01
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\\beta_s(q)$ strictly lower than the critical $\\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\\beta_s(q)$ is the spinodal point marking the onset of metastability. We prove that when $\\beta\\beta_s(q)$ the mixing time is exponentially large in $n$. Furthermore, as $\\beta \\uparrow \\beta_s$ with $n$, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of $O(n^{-2/3})$ around $\\beta_s$. These results form the first complete analysis of the critical slowdown of a dynamics with a first order phase transition.
Glauber Dynamics for the Mean-Field Potts Model
Cuff, P.; Ding, J.; Louidor, O.; Lubetzky, E.; Peres, Y.; Sly, A.
2012-11-01
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with q≥3 states and show that it undergoes a critical slowdown at an inverse-temperature β s ( q) strictly lower than the critical β c ( q) for uniqueness of the thermodynamic limit. The dynamical critical β s ( q) is the spinodal point marking the onset of metastability. We prove that when β β s ( q) the mixing time is exponentially large in n. Furthermore, as β↑ β s with n, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of O( n -2/3) around β s . These results form the first complete analysis of mixing around the critical dynamical temperature—including the critical power law—for a model with a first order phase transition.
Quasi-isotropic cascade in MHD turbulence with mean field
Grappin, Roland; Gürcan, Özgür
2012-01-01
We propose a phenomenological theory of incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale magnetic field, which establishes a link between the known anisotropic models of strong and weak MHD turbulence We argue that the Iroshnikov-Kraichnan isotropic cascade develops naturally within the plane perpendicular to the mean field, while oblique-parallel cascades with weaker amplitudes can develop, triggered by the perpendicular cascade, with a reduced flux resulting from a quasi-resonance condition. The resulting energy spectrum $E(k_\\parallel,k_\\bot)$ has the same slope in all directions. The ratio between the extents of the inertial range in the parallel and perpendicular directions is equal to $b_{rms}/B_0$. These properties match those found in recent 3D MHD simulations with isotropic forcing reported in [R. Grappin and W.-C. M\\"uller, Phys. Rev. E \\textbf{82}, 26406 (2010)].
Two stochastic mean-field polycrystal plasticity methods
Tonks, Michael [Los Alamos National Laboratory
2008-01-01
In this work, we develop two mean-field polycrystal plasticity models in which the L{sup c} are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the L{sup c} tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the STM and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates D{sup c} are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the FCM, and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.
Mean field theory for U(n) dynamical groups
Rosensteel, G.
2011-04-01
Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick {\\mathfrak s}{\\mathfrak u} (2) model and the Elliott {\\mathfrak s}{\\mathfrak u} (3) model. When the energy in the {\\mathfrak s}{\\mathfrak u} (3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
Nakazato, Ken'ichiro; Yamada, Shoichi
2008-01-01
We construct an equation of state including the hadron-quark phase transition. The mixed phase is obtained by the Gibbs conditions for finite temperature. We adopt the equation of state based on the relativistic mean field theory for the hadronic phase taking into account pions. As for the quark phase, the MIT bag model of the deconfined 3-flavor strange quark matter is used. As a result, our equation of state is thermodynamically stable and exhibits qualitatively the desired properties of hadron-quark mixed matter, such as the temperature dependence of the transition density. The pions raise the transition density because they make the equation of state softer. Using the equation of state constructed here, we study its astrophysical implications. The maximum mass of compact stars is investigated, and our equation of state is consistent with recent observations. We also compute the collapse of a massive star with 100 solar masses using our equation of state and find that the interval time from the bounce to t...
Gutsche, Thomas; Faessler, Amand; Lee, Ian Woo; Lyubovitskij, Valery E
2010-01-01
We discuss a possible interpretation of the open charm mesons $D_{s0}^*(2317)$, $D_{s1}(2460)$ and the hidden charm mesons X(3872), Y(3940) and Y(4140) as hadron molecules. Using a phenomenological Lagrangian approach we review the strong and radiative decays of the $D_{s0}^* (2317)$ and $D_{s1}(2460)$ states. The X(3872) is assumed to consist dominantly of molecular hadronic components with an additional small admixture of a charmonium configuration. Determing the radiative ($\\gamma J/\\psi$ and $\\gamma \\psi(2s)$) and strong ($J/\\psi 2\\pi $ and $ J/\\psi 3\\pi$) decay modes we show that present experimental observation is consistent with the molecular structure assumption of the X(3872). Finally we give evidence for molecular interpretations of the Y(3940) and Y(4140) related to the observed strong decay modes $J/\\psi + \\omega$ or $J/\\psi + \\phi$, respectively.
Phi meson propagation in a hot hadronic gas
Alvarez-Ruso, Luis; Koch, Volker
2002-02-20
The Hidden Local Symmetry Lagrangian is used to study the interactions of phi mesons with other pseudoscalar and vector mesons in a hadronic gas at finite temperature. We have found a significantly small phi mean free path (less than 2.4 fm at T > 170 MeV) due to large collision rates with rho mesons, kaons and predominantly K* in spite of their heavy mass. This implies that phi mesons produced after hadronization in relativistic heavy ion collisions will not leave the hadronic system without scattering. The effect of these interactions on the time evolution of the phi density in the expanding hadronic fireball is investigated.
Phi meson propagation in a hot hadronic gas
Alvarez-Ruso, L
2002-01-01
The Hidden Local Symmetry Lagrangian is used to study the interactions of phi mesons with other pseudoscalar and vector mesons in a hadronic gas at finite temperature. We have found a significantly small phi mean free path (less than 2.4 fm at T > 170 MeV) due to large collision rates with rho mesons, kaons and predominantly K* in spite of their heavy mass. This implies that phi mesons produced after hadronization in relativistic heavy ion collisions will not leave the hadronic system without scattering. The effect of these interactions on the time evolution of the phi density in the expanding hadronic fireball is investigated.
Phi meson propagation in a hot hadronic gas
Alvarez-Ruso, Luis; Koch, Volker
2002-02-20
The Hidden Local Symmetry Lagrangian is used to study the interactions of phi mesons with other pseudoscalar and vector mesons in a hadronic gas at finite temperature. We have found a significantly small phi mean free path (less than 2.4 fm at T > 170 MeV) due to large collision rates with rho mesons, kaons and predominantly K* in spite of their heavy mass. This implies that phi mesons produced after hadronization in relativistic heavy ion collisions will not leave the hadronic system without scattering. The effect of these interactions on the time evolution of the phi density in the expanding hadronic fireball is investigated.
Exotic hadrons from heavy ion collisions
Cho, Sungtae; Hyodo, Tetsuo; Jido, Daisuke; Ko, Che Ming; Lee, Su Houng; Maeda, Saori; Miyahara, Kenta; Morita, Kenji; Nielsen, Marina; Ohnishi, Akira; Sekihara, Takayasu; Song, Taesoo; Yasui, Shigehiro; Yazaki, Koichi
2017-07-01
High energy heavy ion collisions are excellent ways for producing heavy hadrons and composite particles, including the light (anti)nuclei. With upgraded detectors at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), it has become possible to measure hadrons beyond their ground states. Therefore, heavy ion collisions provide a new method for studying exotic hadrons that are either molecular states made of various hadrons or compact system consisting of multiquarks. Because their structures are related to the fundamental properties of Quantum Chromodynamics (QCD), studying exotic hadrons is currently one of the most active areas of research in hadron physics. Experiments carried out at various accelerator facilities have indicated that some exotic hadrons may have already been produced. The present review is a summary of the current understanding of a selected set of exotic particle candidates that can be potentially measured in heavy ion collisions. It also includes discussions on the production of resonances, exotics and hadronic molecular states in these collisions based on the coalescence model and the statistical model. A more detailed discussion is given on the results from these models, leading to the conclusion that the yield of a hadron that is a compact multiquark state is typically an order of magnitude smaller than if it is an excited hadronic state with normal quark numbers or a loosely bound hadronic molecule. Attention is also given to some of the proposed heavy exotic hadrons that could be produced with sufficient abundance in heavy ion collisions because of the significant numbers of charm and bottom quarks that are produced at RHIC and even larger numbers at LHC, making it possible to study them in these experiments. Further included in the discussion are the general formalism for the coalescence model that involves resonance particles and its implication on the present estimated yield for resonance production. Finally
Gravitationally confined relativistic neutrinos
Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.
2017-09-01
Combining special relativity, the equivalence principle, and Newton’s universal gravitational law with gravitational rather than rest masses, one finds that gravitational interactions between relativistic neutrinos with kinetic energies above 50 MeV are very strong and can lead to the formation of gravitationally confined composite structures with the mass and other properties of hadrons. One may model such structures by considering three neutrinos moving symmetrically on a circular orbit under the influence of their gravitational attraction, and by assuming quantization of their angular momentum, as in the Bohr model of the H atom. The model contains no adjustable parameters and its solution, using a neutrino rest mass of 0.05 eV/c2, leads to composite state radii close to 1 fm and composite state masses close to 1 GeV/c2. Similar models of relativistic rotating electron - neutrino pairs give a mass of 81 GeV/c2, close to that of W bosons. This novel mechanism of generating mass suggests that the Higgs mass generation mechanism can be modeled as a latent gravitational field which gets activated by relativistic neutrinos.
Hyperon puzzle and the RMF model with scaled hadron masses and coupling constants
Kolomeitsev, E E; Voskresensky, D N
2015-01-01
The equation of state of cold baryonic matter is studied within a relativistic mean-field model with hadron masses and coupling constants depending on a scalar field. We demonstrate that if the effective nucleon mass stops to decrease with a density increase at densities $n>n_*>n_0$, where $n_0$ is the nuclear saturation density, the equation of state stiffens for these densities and the limiting neutron star mass increases. The stabilization of the nucleon mass can be realised if in the equation of motion for the scalar mean-field there appear a term sharply varying in a narrow vicinity of the field value corresponding to the density $n_*$. We show several possible realizations of this mechanism getting sufficiently stiff equations of state. The appearance of hyperons in dense neutron star interiors is accounted for. The obtained equations of state remain sufficiently stiff if the reduction of the $\\phi$ meson mass is incorporated. Thereby, the hyperon puzzle can be resolved.
The quark mean field model with pion and gluon corrections
Xing, Xueyong; Shen, Hong
2016-01-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pion and gluon into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pion and gluon on the nucleon structure are treated in second-order perturbation theory. For the nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, $m_q$, we determine three parameter sets about the coupling constants between mesons and quarks, named as QMF-NK1, QMF-NK2, and QMF-NK3 by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give satisfactory description on properties of nuclear matter and finite nuclei, meanwhile they can also predict the larger neutron star mass around $2.3M_\\odot$ without the hypero...
Quark mean field model with pion and gluon corrections
Xing, Xueyong; Hu, Jinniu; Shen, Hong
2016-10-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pions and gluons on the nucleon structure are treated in second-order perturbation theory. In a nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, mq, we determine three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1, QMF-NK2, and QMF-NK3, by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give a satisfactory description of properties of nuclear matter and finite nuclei, moreover they also predict a larger neutron star mass around 2.3 M⊙ without hyperon degrees of freedom.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A.
2016-11-01
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
Nuclear mean field from chiral pion-nucleon dynamics
Kaiser, N; Weise, W
2002-01-01
Using the two-loop approximation of chiral perturbation theory, we calculate the momentum- and density-dependent single-particle potential of nucleons in isospin-symmetric nuclear matter. The contributions from one- and two-pion exchange diagrams give rise to a potential depth for a nucleon at rest of U(0,k sub f sub 0)=-53.2 MeV at saturation density. The momentum dependence of the real part of the single-particle potential U(p,k sub f sub 0) is nonmonotonic and can be translated into a mean effective nucleon mass of M*bar approx =0.8M. The imaginary part of the single-particle potential W(p,k sub f) is generated to that order entirely by iterated one-pion exchange. The resulting half width of a nucleon hole-state at the bottom of the Fermi sea comes out as W(0,k sub f sub 0)=29.7 MeV. The basic theorems of Hugenholtz-Van-Hove and Luttinger are satisfied in our perturbative two-loop calculation of the nuclear mean field.
Modeling distributed axonal delays in mean-field brain dynamics
Roberts, J. A.; Robinson, P. A.
2008-11-01
The range of conduction delays between connected neuronal populations is often modeled as a single discrete delay, assumed to be an effective value averaging over all fiber velocities. This paper shows the effects of distributed delays on signal propagation. A distribution acts as a linear filter, imposing an upper frequency cutoff that is inversely proportional to the delay width. Distributed thalamocortical and corticothalamic delays are incorporated into a physiologically based mean-field model of the cortex and thalamus to illustrate their effects on the electroencephalogram (EEG). The power spectrum is acutely sensitive to the width of the thalamocortical delay distribution, and more so than the corticothalamic distribution, because all input signals must travel along the thalamocortical pathway. This imposes a cutoff frequency above which the spectrum is overly damped. The positions of spectral peaks in the resting EEG depend primarily on the distribution mean, with only weak dependences on distribution width. Increasing distribution width increases the stability of fixed point solutions. A single discrete delay successfully approximates a distribution for frequencies below a cutoff that is inversely proportional to the delay width, provided that other model parameters are moderately adjusted. A pair of discrete delays together having the same mean, variance, and skewness as the distribution approximates the distribution over the same frequency range without needing parameter adjustment. Delay distributions with large fractional widths are well approximated by low-order differential equations.
A Mean-Field Theory for Coarsening Faceted Surfaces
Norris, Scott A
2009-01-01
A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems [1-3], but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling the work of Smoluchowski [4] and Schumann [5] on coalescence. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a framework for the investigation of faceted surfaces evolving under arbitrary dynamics. [1] I. Lifshitz, V. Slezov, Soviet Physics JETP 38 (1959) 331-339. [2] I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19 (1961) 35-50. [3] C. Wagner, Elektrochemie 65 (1961) 581-591. [4] M. von S...
Spectral Synthesis via Mean Field approach to Independent Component Analysis
Hu, Ning; Su, Shan-Shan; Kong, Xu
2016-03-01
We apply a new statistical analysis technique, the Mean Field approach to Independent Component Analysis (MF-ICA) in a Bayseian framework, to galaxy spectral analysis. This algorithm can compress a stellar spectral library into a few Independent Components (ICs), and the galaxy spectrum can be reconstructed by these ICs. Compared to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, the MF-ICA approach offers a large improvement in efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter recovery for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters derived with galaxies from the Sloan Digital Sky Survey. We find that our MF-ICA method can not only fit the observed galaxy spectra efficiently, but can also accurately recover the physical parameters of galaxies. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find it can provide excellent fitting results for low signal-to-noise spectra.
Metastability for the Exclusion Process with Mean-Field Interaction
Asselah, Amine; Giacomin, Giambattista
1998-12-01
We consider an exclusion particle system with long-range, mean-field-type interactions at temperature 1/β. The hydrodynamic limit of such a system is given by an integrodifferential equation with one conservation law on the circle C: it is the gradient flux of the Kac free energy functional F β. For β≤1, any constant function with value m ∈ [-1, +1] is the global minimizer of F β in the space \\{ u:int_C {u(x)} dx = m\\} . For β>1, F β restricted to \\{ u:int_C {u(x)} dx = m\\} may have several local minima: in particular, the constant solution may not be the absolute minimizer of F β. We therefore study the long-time behavior of the particle system when the initial condition is close to a homogeneous stable state, giving results on the time of exit from (suitable) subsets of its domain of attraction. We follow the Freidlin-Wentzell approach: first, we study in detail F β together with the time asymptotics of the solution of the hydrodynamic equation; then we study the probability of rare events for the particle system, i.e., large deviations from the hydrodynamic limit.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A., E-mail: diogo.gomes@kaust.edu.sa; Nurbekyan, Levon; Sedjro, Marc [King Abdullah University of Science and Technology (KAUST), CEMSE Division (Saudi Arabia)
2016-12-15
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
Mean-field study of $^{12}$C+$^{12}$C fusion
Chien, Le Hoang; Khoa, Dao T
2016-01-01
The nuclear mean-field potential arising from the $^{12}$C+$^{12}$C interaction at the low energies relevant for the astrophysical carbon burning process has been constructed within the double-folding model, using the realistic nuclear ground-state density of the $^{12}$C nucleus and the effective M3Y nucleon-nucleon (NN) interaction constructed from the G-matrix of the Paris (free) NN potential. To explore the nuclear medium effect, both the original density independent M3Y-Paris interaction and its density dependent CDM3Y6 version have been used in the folding model calculation of the $^{12}$C+$^{12}$C potential. The folded potentials at the different energies were used in the optical model description of the elastic $^{12}$C+$^{12}$C scattering at the energies around and below the Coulomb barrier, as well as in the barrier penetration model to estimate the fusion cross section and astrophysical $S$ factor of the $^{12}$C+$^{12}$C reactions at the low energies. The obtained results are in good agreement wit...
Individual based and mean-field modeling of direct aggregation
Burger, Martin
2013-10-01
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the firstorder model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. 2012 Elsevier B.V. All rights reserved.
Real-space renormalized dynamical mean field theory
Kubota, Dai; Sakai, Shiro; Imada, Masatoshi
2016-05-01
We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.
Nuclear matter EOS with light clusters within the mean-field approximation
Ferreira, Márcio
2013-01-01
The crust of a neutron star is essentially determined by the low-density region ($\\rho<\\rho_0\\approx0.15-0.16\\unit{fm}^{-3}$) of the equation of state. At the bottom of the inner crust, where the density is $\\rho\\lesssim0.1\\rho_0$, the formation of light clusters in nuclear matter will be energetically favorable at finite temperature. At very low densities and moderate temperatures, the few body correlations are expected to become important and light nuclei like deuterons, tritons, helions and $\\alpha$-particles will form. Due to Pauli blocking, these clusters will dissolve at higher densities $\\rho\\gtrsim 0.1\\rho_0$. The presence of these clusters influences the cooling process and quantities, such as the neutrino emissivity and gravitational waves emission. The dissolution density of these light clusters, treated as point-like particles, will be studied within the Relativistic Mean Field approximation. In particular, the dependence of the dissolution density on the clusters-meson couplings is studied.
Transport Coefficients of Interacting Hadrons
Wiranata, Anton
A detailed quantitative comparison between the results of shear viscosities from the Chapman-Enskog and Relaxation Time methods is performed for the following test cases with specified elastic differential cross sections between interacting hadrons: (1) The non-relativistic, relativistic and ultra-relativistic hard sphere gas with angle and energy independent differential cross section sigma = a2/4, where a is the hard sphere radius, (2) The Maxwell gas with sigma(g, theta) = mGamma(theta)/2g, where m is the mass of the heat bath particles, Gamma(theta) is an arbitrary function of theta, and g is the relative velocity, (3) Chiral pions for which the t-averaged cross section sigma = s/(64pi2 f4p ) x (1 + 1/3 x cos2 theta), where s and t are the usual Mandelstam variables and fpi is the pion-decay constant, and (4) Massive pions for which the differential elastic cross section is taken from experiments. Quantitative results of the comparative study conducted revealed that • the extent of agreement (or disagreement) depends very sensitively on the energy dependence of the differential cross sections employed, stressing the need to combine all available experimental knowledge concerning differential cross sections for low mass hadrons and to supplement it with theoretical guidance for the as yet unknown cross sections so that the temperature dependent shear viscosity to entropy ratio can be established for use in viscous hydordynamics. • The result found for the ultra-relativistic hard sphere gas for which the shear viscosity etas = 1.2676 k BT c--1/(pia 2) offers the opportunity to validate ultra-relativistic quantum molecular dynamical (URQMD) codes that employ Green-Kubo techniques. • shear viscosity receives only small contributions from number changing inelastic processes. The dependence of the bulk viscosity on the adiabatic speed of sound is studied in depth highlighting why only hadrons in the intermediate relativistic regime contribute the most to the
The relativistic virial theorem and scale invariance
Gaite, Jose
2013-01-01
The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. However, for very relativistic bound states, scale invariance is broken by quantum effects and the virial theorem must include the energy-momentum tensor trace anomaly. This quantum field theory virial theorem is directly related to the Callan-Symanzik equations. The virial theorem is applied to QED and then to QCD, focusing on the bag model of hadrons. In massless QCD, according to the virial theorem, 3/4 of a hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly.
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo
Schrinner, M; Schmitt, D; Rheinhardt, M; Christensen, U R
2006-01-01
A comparison is made between mean-field models and direct numerical simulations of rotating magnetoconvection and the geodynamo. The mean-field coefficients are calculated with the fluid velocity taken from the direct numerical simulations. The magnetic fields resulting from mean-field models are then compared with the mean magnetic field from the direct numerical simulations.
Olsen, Stephen Lars
2016-01-01
A number of candidate multiquark hadrons, i.e., particle resonances with substructures that are more complex than the quark-antiquark mesons and three-quark baryons that are prescribed in the textbooks, have recently been observed. In this talk I present: some recent preliminary BESIII results on the near-threshold behavior of sigma(e+e- --> Lambda Lambda-bar) that may or may not be related to multiquark mesons in the light- and strange-quark sectors; results from Belle and LHCb on the electrically charged, charmoniumlike Z(4430)^+ --> pi^+ psi ' resonance that necessarily has a four-quark substructure; and the recent LHCb discovery of the P_c(4380) and P_c(4450) hidden-charm resonances seen as a complex structure in the J/psi p invariant mass distribution for Lambda_b --> K^-J/psi p decays and necessarily have a five-quark substructure and are, therefore, prominent candidates for pentaquark baryons.
Medium-induced color flow softens hadronization
Beraudo, A; Wiedemann, U A
2012-01-01
Medium-induced parton energy loss, resulting from gluon exchanges between the QCD matter and partonic projectiles, is expected to underly the strong suppression of jets and high-$p_T$ hadron spectra observed in ultra-relativistic heavy ion collisions. Here, we present the first color-differential calculation of parton energy loss. We find that color exchange between medium and projectile enhances the invariant mass of energetic color singlet clusters in the parton shower by a parametrically large factor proportional to the square root of the projectile energy. This effect is seen in more than half of the most energetic color-singlet fragments of medium-modified parton branchings. Applying a standard cluster hadronization model, we find that it leads to a characteristic additional softening of hadronic spectra. A fair description of the nuclear modification factor measured at the LHC may then be obtained for relatively low momentum transfers from the medium.
Thermal and chemical equilibration of hadronic matter
Bratkovskaya, E L; Greiner, C; Effenberger, M; Mosel, U; Sibirtsev, A A
2001-01-01
We study thermal and chemical equilibration in 'infinite' hadron matter as well as in finite size relativistic nucleus-nucleus collisions using a BUU cascade transport model with resonance and string degrees-of-freedom. The 'infinite' hadron matter is simulated within a cubic box employing periodic boundary conditions. The various equilibration times depend on baryon density and energy density and are much shorter for particles consisting of light quarks then for particles including strangeness. For kaons and antikaons the chemical equilibration time is found to be larger than $\\simeq$ 40 fm/c for all baryon and energy densities considered. The inclusion of continuum excitations, i.e. hadron 'strings', leads to a limiting temperature of $T_s\\simeq$ 150 MeV.
A relativistic symmetry in nuclei
Ginocchio, J N [MS B283, Theoretical Division, Los Alamos National Laboratory Los Alamos, New Mexico 87545 (Mexico)
2007-11-15
We review some of the empirical and theoretical evidence supporting pseudospin symmetry in nuclei as a relativistic symmetry. We review the case that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry in nuclei. We discuss the implications of pseudospin symmetry for magnetic dipole transitions and Gamow-Teller transitions between states in pseudospin doublets. We explore a more fundamental rationale for pseudospin symmetry in terms of quantum chromodynamics (QCD), the basic theory of the strong interactions. We show that pseudospin symmetry in nuclei implies spin symmetry for an anti-nucleon in a nuclear environment. We also discuss the future and what role pseudospin symmetry may be expected to play in an effective field theory of nucleons.
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
Universal QGP Hadronization Conditions at RHIC and LHC
Rafelski Johann
2014-01-01
Full Text Available We address the principles governing QGP hadronization and particle production in relativistic heavy-ion collisions. We argue that chemical non-equilibrium is required and show that once this condition is assumed a very good description of hadron production in collider RHIC and LHC heavy ion experiments follows. We present results of our analysis as a function of centrality. Comparing most extreme experimental conditions we show that only the reaction volume and degree of strangeness phase space saturation change. We determine the universal QGP fireball hadronization conditions.
Universal QGP Hadronization Conditions at RHIC and LHC
Rafelski, Johann
2014-01-01
We address the principles governing QGP hadronization and particle production in relativistic heavy-ion collisions. We argue that chemical non-equilibrium is required and show that once this condition is assumed a very good description of hadron production in collider RHIC and at LHC heavy ion experiments follows. We present results of our analysis as a function of centrality. Comparing most extreme experimental conditions we show that only the reaction volume and degree of strangeness phase space saturation change. We determine the universal QGP fireball hadronization conditions.
Quarkonium+{gamma} production in coherent hadron-hadron interactions at LHC energies
Goncalves, V.P. [Universidade Federal de Pelotas, Instituto de Fisica e Matematica, Caixa Postal 354, Pelotas, RS (Brazil); Machado, M.M. [IF - Farroupilha, Instituto Federal de Educacao, Ciencia e Tecnologia, Sao Borja, RS (Brazil)
2012-11-15
In this paper we study the H+{gamma} (H=J/{Psi} and and upsilon;) production in coherent hadron-hadron interactions at LHC energies. Considering the ultrarelativistic protons as a source of photons, we estimate the {gamma}+p{yields}H+{gamma}+X cross section using the non-relativistic QCD (NRQCD) factorization formalism and considering different sets of values for the matrix elements. Our results for the total p+p{yields}p+H+{gamma}+X cross sections and rapidity distributions at {radical}(s) = 7 and 14 TeV demonstrate that the experimental analysis of the J/{Psi}+{gamma} production at LHC is feasible. (orig.)
Cosmic rays and hadronic interactions
Lipari Paolo
2015-01-01
Full Text Available The study of cosmic rays, and more in general of the “high energy universe” is at the moment a vibrant field that, thanks to the observations by several innovative detectors for relativistic charged particles, gamma–rays, and neutrinos continue to generate surprising and exciting results. The progress in the field is rapid but many fundamental problems remain open. There is an intimate relation between the study of the high energy universe and the study of the properties of hadronic interactions. High energy cosmic rays can only be studied detecting the showers they generate in the atmosphere, and for the interpretation of the data one needs an accurate modeling of the collisions between hadrons. Also the study of cosmic rays inside their sources and in the Galaxy requires a precise description of hadronic interactions. A program of experimental studies at the LHC and at lower energy, designed to address the most pressing problems, could significantly reduce the existing uncertainties and is very desirable. Such an experimental program would also have a strong intrinsic scientific interest, allowing the broadening and deepening of our understanding of Quantum Chromo Dynamics in the non–perturbative regime, the least understood sector of the Standard Model of particle physics. It should also be noted that the cosmic ray spectrum extends to particles with energy E ∼ 1020 eV, or a nucleon–nucleon c.m. energy √s ≃ 430 TeV, 30 times higher than the current LHC energy. Cosmic ray experiments therefore offer the possibility to perform studies on the properties of hadronic interactions that are impossible at accelerators.
Lu, K Q; Li, Z P; Yao, J M; Meng, J
2015-01-01
We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean-field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD-ME$\\delta$ (2.29 MeV) and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by $\\sim34\\%$ in comparison with cranking prescription.
Parton-hadron dynamics in heavy-ion collisions
Bratkovskaya, E L; Cassing, W; Konchakovski, V P; Linnyk, O; Marty, R; Berrehrah, H
2013-01-01
The dynamics of partons and hadrons in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for the partonic phase (DQPM) including a dynamical hadronization scheme. The PHSD approach is applied to nucleus-nucleus collisions from low SPS to LHC energies. The traces of partonic interactions are found in particular in the elliptic flow of hadrons and in their transverse mass spectra. We investigate also the equilibrium properties of strongly-interacting infinite parton-hadron matter characterized by transport coefficients such as shear and bulk viscosities and the electric conductivity in comparison to lattice QCD results.
Kouno, H.; Kakuta, N.; Noda, N.; Koide, K.; Mitsumori, T.; Hasegawa, A.; Nakano, M. (Department of Physics, Saga University, Saga 840 (Japan))
1995-04-01
We have studied the equations of state of nuclear matter using the nonlinear [sigma]-[omega] model. At the normal density, there is a strong correlation among the effective nucleon mass [ital M][sub 0][sup *], the incompressibility, [ital K] and the third derivative [ital K][prime] of binding energy. The results are compared with the empirical analysis of the giant isoscalar monopole resonances data. It is difficult to fit the data when [ital K][approx lt]200 MeV, using the model. It is also found that [ital K]=300[plus minus]50 MeV is favorable to account for the volume-symmetry properties of nuclear matter.
Alpha-decay chains of $^{288}_{173}115$ and $^{287}_{172}115$ in the Relativistic Mean Field theory
Geng, L S; Meng, J
2003-01-01
The results of experiments designed to synthesize element 115 in the $^{243}$Am+$^{48}$Ca reaction are reported at Dubna in Russia \\cite{ogan.03}. With a beam dose of $4.3\\times 10^{18}$ 248-MeV $^{48}$Ca projectiles, three similar decay chains consisting of five consecutive $\\alpha$-decays are observed. At a higher bombarding energy of 253 MeV, with an equal $^{48}$Ca beam dose, a different decay chain of four consecutive $\\alpha$-decays are detected. The decay properties of these synthesized nuclei are consistent with consecutive $\\alpha$-decay originating from the parent isotopes of the new element 115, $^{288}115$ and $^{287}115$, respectively. In the present work, the recently developed deformed RMF+BCS method with a density-independent delta-function interaction in the pairing channel is applied to the analysis of these newly synthesized superheavy nuclei $^{288}115$, $^{287}115$, and their $\\alpha$-decay daughter nuclei. The calculated $\\alpha$-decay energies and half-lives agree well with the experime...
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
Probing the early-time dynamics of relativistic heavy-ion collisions with electromagnetic radiation
Vujanovic, Gojko; Denicol, Gabriel S; Luzum, Matthew; Schenke, Bjoern; Jeon, Sangyong; Gale, Charles
2014-01-01
Using 3+1D viscous relativistic fluid dynamics, we show that electromagnetic probes are sensitive to the initial conditions and to the out-of-equilibrium features of relativistic heavy-ion collisions. Within the same approach, we find that hadronic observables show a much lesser sensitivity to these aspects. We conclude that electromagnetic observables allow access to dynamical regions that are beyond the reach of soft hadronic probes.
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
The Accuracy of Mean-Field Approximation for Susceptible-Infected-Susceptible Epidemic Spreading
Qu, Bo
2016-01-01
The epidemic spreading has been studied for years by applying the mean-field approach in both homogeneous case, where each node may get infected by an infected neighbor with the same rate, and heterogeneous case, where the infection rates between different pairs of nodes are different. Researchers have discussed whether the mean-field approaches could accurately describe the epidemic spreading for the homogeneous cases but not for the heterogeneous cases. In this paper, we explore under what conditions the mean-field approach could perform well when the infection rates are heterogeneous. In particular, we employ the Susceptible-Infected-Susceptible (SIS) model and compare the average fraction of infected nodes in the metastable state obtained by the continuous-time simulation and the mean-field approximation. We concentrate on an individual-based mean-field approximation called the N-intertwined Mean Field Approximation (NIMFA), which is an advanced approach considered the underlying network topology. Moreove...
QCD in hadron-hadron collisions
Albrow, M.
1997-03-01
Quantum Chromodynamics provides a good description of many aspects of high energy hadron-hadron collisions, and this will be described, along with some aspects that are not yet understood in QCD. Topics include high E{sub T} jet production, direct photon, W, Z and heavy flavor production, rapidity gaps and hard diffraction.
General characteristics of hadron-hadron collisions
Kittel, E W
2004-01-01
Soft multiparticle production in hadron-hadron collisions is reviewed with particular emphasis on its role as a standard for heavy-ion collisions at SPS and RHIC energies and as a bridge interpolating between the most simple e **+e**- and the most complex AA collisions.
Fractality and geometry in ultra-relativistic nuclear collisions
Zborovský, I
2002-01-01
Assuming fractality of hadronic constituents, we argue that asymmetry of space-time can be induced in the ultra-relativistic interactions of hadrons and nuclei. The asymmetry is expressed in terms of the anomalous fractal dimensions of the colliding objects. Besides state of motion, the relativistic principle is applied to the state of asymmetry as well. Such realization of relativity concerns scale dependence of physical laws emerging at small distances. We show that induced asymmetries of space-time are a priori not excluded by the Michelson's experiment even at large scales.
Optimized $\\delta$ expansion for relativistic nuclear models
Krein, G I; Peres-Menezes, D; Nielsen, M; Pinto, M B
1998-01-01
The optimized $\\delta$-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the $\\lambda \\phi^4$ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the $\\delta$ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.
CMS Central Hadron Calorimeter
Budd, Howard S.
2001-01-01
We present a description of the CMS central hadron calorimeter. We describe the production of the 1996 CMS hadron testbeam module. We show the results of the quality control tests of the testbeam module. We present some results of the 1995 CMS hadron testbeam.
2003-01-01
Hall 180 work on Hadronic Calorimeter The ATLAS hadronic tile calorimeter The Tile Calorimeter, which constitutes the central section of the ATLAS hadronic calorimeter, is a non-compensating sampling device made of iron and scintillating tiles. (IEEE Trans. Nucl. Sci. 53 (2006) 1275-81)
Investigation of Properties of Exotic Nuclei in Non-relativistic and Relativistic Models
2001-01-01
Properties of exotic nuclei are described by non-relativistic and relativistic models. The relativistic mean field theory predicts one proton halo in 26,27,28P and two proton halos in 27,28,29S, recently, one proton halo in 26,27,28P has been found experimentally in MSU lab. The relativistic Hartree-Fock theory has been used to investigate the contribution of Fock term and isovector mesons to the properties of exotic nuclei. It turns out that the influence of the Fock term and isovector mesons on the properties of neutron extremely rich nuclei is very different from that of near stable nuclei. Meanwhile, the deformed Hartree-Fock-Bogoliubov theory has been employed to describe the ground state properties of the isotopes for some light nuclei.
Novel Perspectives for Hadron Physics
Brodsky, Stanley J.; /SLAC
2012-03-09
I discuss several novel and unexpected aspects of quantum chromodynamics. These include: (a) the nonperturbative origin of intrinsic strange, charm and bottom quarks in the nucleon at large x; the breakdown of pQCD factorization theorems due to the lensing effects of initial- and final-state interactions; (b) important corrections to pQCD scaling for inclusive reactions due to processes in which hadrons are created at high transverse momentum directly in the hard processes and their relation to the baryon anomaly in high-centrality heavy-ion collisions; and (c) the nonuniversality of quark distributions in nuclei. I also discuss some novel theoretical perspectives in QCD: (a) light-front holography - a relativistic color-confining first approximation to QCD based on the AdS/CFT correspondence principle; (b) the principle of maximum conformality - a method which determines the renormalization scale at finite order in perturbation theory yielding scheme independent results; (c) the replacement of quark and gluon vacuum condensates by 'in-hadron condensates' and how this helps to resolve the conflict between QCD vacuum and the cosmological constant.
The Common Elements of Atomic and Hadronic Physics
Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States)
2015-02-26
Atomic physics and hadronic physics are both governed by the Yang Mills gauge theory Lagrangian; in fact, Abelian quantum electrodynamics can be regarded as the zero-color limit of quantum chromodynamics. I review a number of areas where the techniques of atomic physics can provide important insight into hadronic eigenstates in QCD. For example, the Dirac-Coulomb equation, which predicts the spectroscopy and structure of hydrogenic atoms, has an analog in hadron physics in the form of frame-independent light-front relativistic equations of motion consistent with light-front holography which give a remarkable first approximation to the spectroscopy, dynamics, and structure of light hadrons. The production of antihydrogen in flight can provide important insight into the dynamics of hadron production in QCD at the amplitude level. The renormalization scale for the running coupling is unambiguously set in QED; an analogous procedure sets the renormalization scales in QCD, leading to scheme-independent scale-fixed predictions. Conversely, many techniques which have been developed for hadron physics, such as scaling laws, evolution equations, the quark-interchange process and light-front quantization have important applicants for atomic physics and photon science, especially in the relativistic domain.
Amplitude pattern synthesis for conformal array antennas using mean-field neural networks
Castaldi, G.; Gerini, G.
2001-01-01
In this paper, we deal with the synthesis problem of conformai array antennas using a mean-field neural network. We applied a discrete version of mean-field neural network proposed by Vidyasagar [1], This technique is used to find the global minimum of the objective function, which represents the sq
Rigorous mean-field dynamics of lattice bosons: quenches from the Mott insulator
M. Snoek
2011-01-01
We provide a rigorous derivation of Gutzwiller mean-field dynamics for lattice bosons, showing that it is exact on fully connected lattices. We apply this formalism to quenches in the interaction parameter from the Mott insulator to the superfluid state. Although within mean-field the Mott insulator
On Mean-Field Theory of Quantum Phase Transition in Granular Superconductors
Simkin, M V
1996-01-01
In previous work on quantum phase transition in granular superconductors, where mean-field theory was used, an assumption was made that the order parameter as a function of the mean field is a convex up function. Though this is not always the case in phase transitions, this assumption must be verified, what is done in this article.
Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field
Häggström, O.; Külske, C.
2004-01-01
We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do
Mean-field theory of random-site q-state Potts models
van Enter, Aernout; Hemmen, Jan Leonard van; Pospiech, C.
1988-01-01
A class of random-site mean-field Potts models is introduced and solved exactly. The bifurcation properties of the resulting mean-field equations are analysed in detail. Particular emphasis is put on the relation between the solutions and the underlying symmetries of the model. It turns out that, in
Hadron Colliders and Hadron Collider Physics Symposium
Denisov D.
2013-05-01
Full Text Available This article summarizes main developments of the hadron colliders and physics results obtained since their inception around forty years ago. The increase in the collision energy of over two orders of magnitude and even larger increases in luminosity provided experiments with unique data samples. Developments of full acceptance detectors, particle identification and analysis methods provided fundamental discoveries and ultra-precise measurements which culminated in the completion and in depth verification of the Standard Model. Hadron Collider Physics symposium provided opportunities for those working at hadron colliders to share results of their research since 1979 and helped greatly to develop the field of particle physics.
Energy and Centrality Dependences of Charged Multiplicity Density in Relativistic Nuclear Collisions
SA; Ben-hao; Bonasera; A; TAI; An
2002-01-01
Using a hadron and string cascade model, JPCIAE, the energy and centrality dependences of chargedparticle pseudo rapidity density in relativistic nuclear collisions were studied. Within the framework ofthis model, both the relativistic p + p experimental data and the PHOBOS and PHENIX Au + Au data at
Relativistic and non-relativistic geodesic equations
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Charm-Hadron Production at Hadron Colliders
Watson, Miriam; The ATLAS collaboration
2016-01-01
Recent results on charm hadron production are presented, using data recorded in proton-proton collisions at the Large Hadron Collider and in proton-antiproton collisions at the Tevatron. These results include the production of charmonium and of open charm mesons, and their comparison with theoretical predictions. Measurements of the associated production of hidden or open charm mesons with additional quarkonium states are also presented.
Hadron multiplicity in pp and AA collisions at LHC from the color glass condensate
Levin, Eugene; Rezaeian, Amir H.
2010-09-01
We provide quantitative predictions for the rapidity, centrality and energy dependencies of inclusive charged-hadron productions for the forthcoming LHC measurements in nucleus-nucleus collisions based on the idea of gluon saturation in the color-glass condensate framework. Our formulation gives very good descriptions of the first data from the LHC for the inclusive charged-hadron production in proton-proton collisions, the deep inelastic scattering at the Hadron-Elektron-Ring-Anlage at small Bjorken x, and the hadron multiplicities in nucleus-nucleus collisions at the Relativistic Heavy Ion Collider.
Relativistic Pseudospin Symmetry as a Supersymmetric Pattern in Nuclei
Leviatan, A
2004-01-01
Shell-model states involving several pseudospin doublets and ``intruder'' levels in nuclei, are combined into larger multiplets. The corresponding single-particle spectrum exhibits a supersymmetric pattern whose origin can be traced to the relativistic pseudospin symmetry of a nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.
Dual mean field search for large scale linear and quadratic knapsack problems
Banda, Juan; Velasco, Jonás; Berrones, Arturo
2017-07-01
An implementation of mean field annealing to deal with large scale linear and non linear binary optimization problems is given. Mean field annealing is based on the analogy between combinatorial optimization and interacting physical systems at thermal equilibrium. Specifically, a mean field approximation of the Boltzmann distribution given by a Lagrangian that encompass the objective function and the constraints is calculated. The original discrete task is in this way transformed into a continuous variational problem. In our version of mean field annealing, no temperature parameter is used, but a good starting point in the dual space is given by a ;thermodynamic limit; argument. The method is tested in linear and quadratic knapsack problems with sizes that are considerably larger than those used in previous studies of mean field annealing. Dual mean field annealing is capable to find high quality solutions in running times that are orders of magnitude shorter than state of the art algorithms. Moreover, as may be expected for a mean field theory, the solutions tend to be more accurate as the number of variables grow.
Conserved charge fluctuations are not conserved during the hadronic phase
Steinheimer, J; Aichelin, J; Bleicher, M; Stöcker, H
2016-01-01
We study the correlation between the distributions of the net-charge, net-kaon, net-baryon and net-proton number at hadronization and after the final hadronic decoupling by simulating ultra relativistic heavy ion collisions with the hybrid version of the ultrarelativistic quantum molecular dynamics (UrQMD) model. We find that due to the hadronic rescattering these distributions are not strongly correlated. The calculated change of the correlation, during the hadronic expansion stage, does not support the recent paradigm, namely that the measured final moments of the experimentally observed distributions do give directly the values of those distributions at earlier times, when the system had been closer to the QCD crossover.
Fast Equilibration of Hadrons in an Expanding Fireball
Noronha-Hostler, J; Shovkovy, I A
2007-01-01
Due to long chemical equilibration times within standard hadronic reactions during the hadron gas phase in relativistic heavy ion collisions it has been suggested that the hadrons are "born" into equilibrium after the quark gluon plasma phase. Here we develop a dynamical scheme in which possible Hagedorn states contribute to fast chemical equilibration times of baryon anti-baryon pairs (as well as kaon anti-kaon pairs) inside a hadron gas and just below the critical temperature. Within this scheme, we use master equations and derive various analytical estimates for the chemical equilibration times. Applying a Bjorken picture to the expanding fireball, the kaons and baryons as well as the bath of pions and Hagedorn resonances can indeed quickly chemically equilibrate for both an initial overpopulation or underpopulation of Hagedorn resonances. Moreover, a comparison of our results to $(B+\\bar{B})/\\pi^{+}$ and $K/\\pi^{+}$ ratios at RHIC, indeed, shows a close match.
Aspects of thermal and chemical equilibration of hadronic matter
Bratkovskaya, E L; Greiner, C; Effenberger, M; Mosel, U; Sibirtsev, A A
2000-01-01
We study thermal and chemical equilibration in 'infinite' hadron matter as well as in finite size relativistic nucleus-nucleus collisions using a BUU cascade transport model that contains resonance and string degrees-of-freedom. The 'infinite' hadron matter is simulated within a cubic box with periodic boundary conditions. The various equilibration times depend on baryon density and energy density and are much shorter for particles consisting of light quarks then for particles including strangeness. For kaons and antikaons the chemical equilibration time is found to be larger than $\\simeq$ 40 fm/c for all baryon and energy densities considered. The inclusion of continuum excitations, i.e. hadron 'strings', leads to a limiting temperature of $T_s\\simeq$ 150 MeV. We, furthermore, study the expansion of a hadronic fireball after equilibration. The slope parameters of the particles after expansion increase with their mass; the pions leave the fireball much faster then nucleons and accelerate subsequently heavier ...
Photons from quark gluon plasma and hot hadronic matter
Jan-E Alam
2003-04-01
The productions of real photons from quark gluon plasma and hot hadronic matter formed after the nucleus–nucleus collisions at ultra-relativistic energies are discussed. The effects of the spectral shift of the hadrons at ﬁnite temperature on the production of photons are investigated. On the basis of the present analysis it is shown that the photon spectra measured by WA98 collaboration in Pb + Pb collisions at CERN SPS energies can be explained by both QGP as well as hadronic initial states if the spectral shift of hadrons at ﬁnite temperature is taken into account. Several other works on the analysis of WA98 photon data have also been brieﬂy discussed.
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Leardini, Fabrice
2013-01-01
This manuscript presents a problem on special relativity theory (SRT) which embodies an apparent paradox relying on the concept of simultaneity. The problem is represented in the framework of Greek epic poetry and structured in a didactic way. Owing to the characteristic properties of Lorenz transformations, three events which are simultaneous in a given inertial reference system, occur at different times in the other two reference frames. In contrast to the famous twin paradox, in the present case there are three, not two, different inertial observers. This feature provides a better framework to expose some of the main characteristics of SRT, in particular, the concept of velocity and the relativistic rule of addition of velocities.
From infinity to one: The reduction of some mean field games to a global control problem
Guéant, Olivier
2011-01-01
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced by J.M. Lasry and P.L. Lions and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation, from which the MFG equations can be deduced. Then, this Master equation can be reinterpreted using a global control problem inducing the same behaviors as in the non-cooperative initial mean field game.
MODEL STUDY OF THE SIGN PROBLEM IN A MEAN-FIELD APPROXIMATION.
HIDAKA,Y.
2007-07-30
We study the sign problem of the fermion determinant at nonzero baryon chemical potential. For this purpose we apply a simple model derived from Quantum Chromodynamics, in the limit of large chemical potential and mass. For SU(2) color, there is no sign problem and the mean-field approximation is similar to data from the lattice. For SU(3) color the sign problem is unavoidable, even in a mean-field approximation. We apply a phase-reweighting method, combined with the mean-field approximation, to estimate thermodynamic quantities. We also investigate the meanfield free energy using a saddle-point approximation [1].
Unraveling hadron structure with generalized parton distributions
Andrei Belitsky; Anatoly Radyushkin
2004-10-01
The recently introduced generalized parton distributions have emerged as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom. They combine the features of form factors, parton densities and distribution amplitudes - the functions used for a long time in studies of hadronic structure. Generalized parton distributions are analogous to the phase-space Wigner quasi-probability function of non-relativistic quantum mechanics which encodes full information on a quantum-mechanical system. We give an extensive review of main achievements in the development of this formalism. We discuss physical interpretation and basic properties of generalized parton distributions, their modeling and QCD evolution in the leading and next-to-leading orders. We describe how these functions enter a wide class of exclusive reactions, such as electro- and photo-production of photons, lepton pairs, or mesons.
Relativistic Symmetry Suppresses Quark Spin-Orbit Splitting
Page, P R; Ginocchio, J N; Page, Philip R.; Goldman, Terry; Ginocchio, Joseph. N.
2001-01-01
Experimental data indicate small spin-orbit splittings in hadrons. Forheavy-light mesons we identify a relativistic symmetry that suppresses thesesplittings. We suggest an experimental test in electron-positron annihilation.Furthermore, we argue that the dynamics necessary for this symmetry arepossible in QCD.
Hadronic Transport Coefficients from Effective Field Theories
Torres-Rincon, Juan M
2012-01-01
This dissertation focuses on the calculation of transport coefficients in the matter created in a relativistic heavy-ion collision after the chemical freeze-out. This matter can be well approximated by a pion gas out of equilibrium. We describe the theoretical framework to obtain the shear and bulk viscosities, the thermal and electrical conductivities and the flavor diffusion coefficients of a meson gas at low temperatures. To describe the interactions of the degrees of freedom, we use effective field theories with chiral and heavy quark symmetries. We introduce the unitarization methods in order to obtain a scattering amplitude that satisfies the unitarity condition exactly. We perform the calculation of the transport properties of the low temperature phase of quantum chromodynamics -the hadronic medium- that can be used in the hydrodynamic simulations of a relativistic heavy-ion collision and its subsequent evolution. We show that the shear viscosity over entropy density exhibits a minimum in a phase trans...
U Mosel
2006-04-01
In these lectures I first give the motivation for investigations of in-medium properties of hadrons. I discuss the relevant symmetries of QCD and how they might affect the observed hadron properties. I then discuss at length the observable consequences of in-medium changes of hadronic properties in reactions with elementary probes, and in particular photons, on nuclei. Here I put an emphasis on new experiments on changes of the - and -mesons in medium.
Leptonic and Hadronic Modeling of Fermi-Detected Blazars
Böttcher Markus
2013-12-01
Full Text Available We describe new implementations of leptonic and hadronic models for the broadband emission from relativistic jets in AGN in a temporary steady state. The new model implementations are used to fit snap-shot spectral energy distributions of a representative set of Fermi-LAT detected blazars from the first LAT AGN catalogue. We find that the leptonic model is capable of producing acceptable fits to the SEDs of almost all blazars with reasonable parameters close to equipartition between the magnetic field and the relativistic electron population. If charge neutrality in leptonic models is provided by cold protons, our fits indicate that the kinetic energy carried by the jet should be dominated by protons. We also find satisfactory representations of the snapshot SEDs of most blazars in our sample with the hadronic model presented here. All of our hadronic model fits require powers in relativistic protons in the range 1047 – 1049 erg/s. As a potential way to distinguish between the leptonic and hadronic high-energy emission models considered here, we suggest diagnostics based on the predicted X-ray and γ-ray polarization, which are drastically different for the two types of models.
Mean-field dynamos: the old concept and some recent developments
Rädler, K -H
2014-01-01
This article reproduces the Karl Schwarzschild lecture 2013. Some of the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids are explained. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of $\\alpha^2$ and $\\alpha$ $\\Omega$ type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force t...
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.
2014-04-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
Mean-field approximation for spacing distribution functions in classical systems
González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.
2012-01-01
We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.
Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials
Vollhardt, Dieter
2010-11-01
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott-Hubbard metal-insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean-field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many-body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean-field theory for correlated fermions, the dynamical mean-field theory (DMFT), (v) derive the DMFT self-consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.
Parity Violating Electron Scattering in the Relativistic Eikonal Approximation
DONG Tie-Kuang; REN Zhong-Zhou
2008-01-01
The parity violating electron scattering is investigated in the relativistic Eikonal approximation. The parity violating asymmetry parameters for many isotopes are calculated. In calculations the proton and neutron densities are obtained from the relativistic mean-field theory. We take Ni isotopes as examples to analyse the behaviour of the parity violating asymmetry parameters. The results show that the parity violating asymmetry parameter is sensitive to the difference between the proton and neutron densities. The amplitude of the parity violating asymmetry parameter increases with the distance between the minima of proton and neutron form factors. Our results are useful for future parity violating electron scattering experiments. By comparing our results with experimental data one can test the validity of the relativistic mean-field theory in calculating the neutron densities of nuclei.
On the mean-field theory of the Karlsruhe Dynamo Experiment
K.-H. Rädler
2002-01-01
Full Text Available In the Forschungszentrum Karlsruhe an experiment has been constructed which demonstrates a homogeneous dynamo as is expected to exist in the Earth's interior. This experiment is discussed within the framework of mean-field dynamo theory. The main predictions of this theory are explained and compared with the experimental results. Key words. Dynamo, geodynamo, dynamo experiment, mean-field dynamo theory, a-effect
Can realistic interaction be useful for nuclear mean-field approaches?
Nakada, H.; Sugiura, K. [Chiba University, Department of Physics, Graduate School of Science, Inage, Chiba (Japan); Inakura, T. [Chiba University, Department of Physics, Graduate School of Science, Inage, Chiba (Japan); Kyoto University, Yukawa Institute of Theoretical Physics, Sakyo, Kyoto (Japan); Niigata University, Department of Physics, Niigata (Japan); Margueron, J. [Universite de Lyon 1, CNRS/IN2P3, Institut de Physique Nucleaire de Lyon, Villeurbanne (France)
2016-07-15
Recent applications of the M3Y-type semi-realistic interaction to the nuclear mean-field approaches are presented: (i) Prediction of magic numbers and (ii) isotope shifts of nuclei with magic proton numbers. The results exemplify that the realistic interaction, which is derived from the bare 2N and 3N interaction, furnishes a new theoretical instrument for advancing nuclear mean-field approaches. (orig.)
Crowd-Averse Cyber-Physical Systems: The Paradigm of Robust Mean Field Games
Bauso, D.; Tembine, H.
2015-01-01
For a networked controlled system we illustrate the paradigm of robust mean-field games. This is a modeling framework at the interface of differential game theory, mathematical physics, and H1-optimal control that tries to capture the mutual influence between a crowd and its individuals. First, we establish a mean-field system for such games including the effects of adversarial disturbances. Second, we identify the optimal response of the individuals for a given population behavior. Third, we...
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem
2015-02-24
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng\\'s type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
Fast Dynamical Evolution of Hadron Resonance Gas via Hagedorn States
Beitel, M.; Gallmeister, K.; Greiner, C.
2017-01-01
Hagedorn states (HS) are a tool to model the hadronization process which occurs in the phase transition region between the quark gluon plasma (QGP) and the hadron resonance gas (HRG). These states are believed to appear near the Hagedorn temperature TH which in our understanding equals the critical temperature Tc . A covariantly formulated bootstrap equation is solved to generate the zoo of these particles characterized baryon number B, strangeness S and electric charge Q. These hadron-like resonances are characterized by being very massive and by not being limited to quantum numbers of known hadrons. All hadronic properties like masses, spectral functions etc. are taken from the hadronic transport model Ultra Relativistic Quantum Molecular Dynamics (UrQMD). Decay chains of single Hagedorn states provide a well description of experimentally observed multiplicity ratios of strange and multi-strange particles as the Ξ0- and the Ω‑-baryon. In addition, the final energy spectra of resulting hadrons show a thermal-like distribution with the characteristic Hagedorn temperature TH . Box calculations including these Hagedorn states are performed. Indeed, the time scales leading to equilibration of the system are drastically reduced down to 2. . . 5 fm/c.
Equilibration of hadrons in HICs via Hagedorn States
Beitel, M.; Gallmeister, K.; Greiner, C.
2016-08-01
Hagedorn states (HS) are a tool to model the hadronization process which occurs in the phase transition region between the quark gluon plasma (QGP) and the hadron resonance gas (HRG). These states are believed to appear near the Hagedorn temperature TH which in our understanding equals the critical temperature Tc. A covariantly formulated bootstrap equation is solved to generate the zoo of these particles characterized baryon number B, strangeness S and electric charge Q. These hadron-like resonances are characterized by being very massive and by not being limited to quantum numbers of known hadrons. All hadronic properties like masses, spectral functions etc. are taken from the hadronic transport model Ultra Relativistic Quantum Molecular Dynamics (UrQMD). Decay chains of single Hagedorn states provide a well description of experimentally observed multiplicity ratios of strange and multi-strange particles. In addition, the final energy spectra of resulting hadrons show a thermal-like distribution with the characteristic Hagedorn temperature TH. Box calculations including these Hagedorn states are performed. Indeed, the time scales leading to equilibration of the system are drastically reduced down to 2... 5fm/c.
Quark-hadron phase transition and strangeness conservation constraints
Saeed-Uddin
1999-01-01
The implications of the strangeness conservation in a hadronic resonance gas (HRG) on the expected phase transition to the quark gluon plasma (QGP) are investigated. It is assumed that under favourable conditions a first order hadron-quark matter phase transition may occur in the hot hadronic matter such as those produced in the ultra-relativistic heavy-ion collisions at CERN and BNL. It is however shown that the criteria of strict strangeness conservation in the HRG may not permit the occurrence of a strict first order equilibrium quark-hadron phase transition unlike a previous study. This emerges as a consequence of the application of a realistic equation of state (EOS) for the HRG and QGP phases, which account for the finite-size effect arising from the short range hard-core hadronic repulsion in the HRG phase and the perturbative QCD interactions in the QGP phase. For a first order hadron-quark matter phase transition to occur one will therefore require large fluctuations in the critical thermal parameters, which might arise due to superheating, supercooling or other nonequlibrium effects. We also discuss a scenario proposed earlier, leading to a possible strangeness separation process during hadronization.
Statistical Hadronization and Holography
Bechi, Jacopo
2009-01-01
In this paper we consider some issues about the statistical model of the hadronization in a holographic approach. We introduce a Rindler like horizon in the bulk and we understand the string breaking as a tunneling event under this horizon. We calculate the hadron spectrum and we get a thermal......, and so statistical, shape for it....
Toponium at hadronic colliders
Finjord, J. (Bern Univ. (Switzerland)); Girardi, G.; Sorba, P. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules); Mery, P. (European Organization for Nuclear Research, Geneva (Switzerland))
1982-05-27
We calculate hadronic toponium production by specific diagrams obeying colour conservation and charge conjugation. The resulting rates, though lower than those calculated using semi-local duality arguments are encouraging and may allow for toponium discovery at hadronic colliders currently in development.
Evaporation/Hadronization Correspondence
Allahbakhshi, Davood
2016-01-01
A holographic duality is proposed between black hole evaporation in the bulk and hadronization (confinement) in dual field theory. Information paradox is discussed in this duality. We also propose that the recently introduced semi black brane solution is holographically dual to a mixed plasma of quarks, gluons and hadrons in global equilibrium.
Fragmentation and Hadronization
Webber, B. R.
1999-01-01
Experimental data, theoretical ideas and models concerning jet fragmentation and the hadronization process are reviewed, concentrating on the following topics: factorization and small-x resummation of fragmentation functions, hadronization models, single-particle yields and spectra in Z decay, comparisons between quark and gluon jets, current and target fragmentation in deep inelastic scattering, heavy quark fragmentation, Bose-Einstein correlations and WW fragmentation.
Finite-size and correlation-induced effects in Mean-field Dynamics
Touboul, Jonathan
2010-01-01
The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon a recent approach that includes correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of...
Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows
Rädler, Karl-Heinz; Del Sordo, Fabio; Rheinhardt, Matthias
2011-01-01
Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the P\\'eclet or magnetic Reynolds numbers are not too large and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic case several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented as well as numerical results obtained by the test-field method, which applies independently of this a...
Rädler, K.-H.
This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α2 and α Ω type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.
Leptonic and Hadronic Modeling of Fermi-Detected Blazars
Boettcher, M; Sweeney, K; Prakash, A
2013-01-01
We describe new implementations of leptonic and hadronic models for the broadband emission from relativistic jets in AGN in a temporary steady state. For the leptonic model, a temporary equilibrium between particle injection/acceleration, radiative cooling, and escape from a spherical emission region is evaluated, and the self-consistent radiative output is calculated. For the hadronic model, a temporary equilibrium between particle injection/acceleration, radiative and adiabatic cooling, and escape is evaluated for both primary electrons and protons. A new, semi-analytical method to evaluate the radiative output from cascades initiated by internal gamma-gamma pair production is presented. We use our codes to fit snap-shot spectral energy distributions of a representative set of Fermi-LAT detected blazars. We find that the leptonic model provides acceptable fits to the SEDs of almost all blazars with parameters close to equipartition between the magnetic field and the relativistic electron population. However...
Lerchner, A; Hertz, J; Ahmadi, M
2004-01-01
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the description: Irregular firing with statistics close to -- but not restricted to -- Poisson statistics; an almost linear gain function (firing frequency as a function of stimulus contrast) of the neurons within the network; and a contrast-invariant tuning width of the neuronal firing. We find that the irregularity in firing depends sensitively on synaptic strengths. If Fano factors are bigger than 1, then they are so for all stim...
Exact mean field dynamics for epidemic-like processes on heterogeneous networks
Lucas, Andrew
2012-01-01
We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a solution in terms of an integral over functions dependent on the degree distribution of the network, and reconstructing all mean field functions of interest from this integral. Irreversibility of the SIR epidemic is crucial for the solution. We also find exact solutions to the sexually transmitted disease SI epidemic on bipartite graphs, to a simplified rumor spreading model, and to a new model for recommendation spreading, via similar techniques. Numerical simulations of these processes on scale free networks demonstrate the qualitative validity of mean field theory in most regimes.
Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs
Ruimin Xu
2014-01-01
Full Text Available We obtain the existence and uniqueness result of the mild solutions to mean-field backward stochastic evolution equations (BSEEs in Hilbert spaces under a weaker condition than the Lipschitz one. As an intermediate step, the existence and uniqueness result for the mild solutions of mean-field BSEEs under Lipschitz condition is also established. And then a maximum principle for optimal control problems governed by backward stochastic partial differential equations (BSPDEs of mean-field type is presented. In this control system, the control domain need not to be convex and the coefficients, both in the state equation and in the cost functional, depend on the law of the BSPDE as well as the state and the control. Finally, a linear-quadratic optimal control problem is given to explain our theoretical results.
Mean field theories and dual variation mathematical structures of the mesoscopic model
Suzuki, Takashi
2015-01-01
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
Simplified method for including spatial correlations in mean-field approximations
Markham, Deborah C.; Simpson, Matthew J.; Baker, Ruth E.
2013-06-01
Biological systems involving proliferation, migration, and death are observed across all scales. For example, they govern cellular processes such as wound healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration, and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behavior. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pairwise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplification in the form of a partial differential equation description for the evolution of pairwise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behavior in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before and find our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.
Noisy mean field game model for malware propagation in opportunistic networks
Tembine, Hamidou
2012-01-01
In this paper we present analytical mean field techniques that can be used to better understand the behavior of malware propagation in opportunistic large networks. We develop a modeling methodology based on stochastic mean field optimal control that is able to capture many aspects of the problem, especially the impact of the control and heterogeneity of the system on the spreading characteristics of malware. The stochastic large process characterizing the evolution of the total number of infected nodes is examined with a noisy mean field limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realistic for such types of networks. By introducing control strategies, we show that the fraction of infected nodes can be maintained below some threshold. In contrast to most of the existing results on mean field propagation models which focus on deterministic equations, we show that the mean field limit is stochastic if the second moment of the number of object transitions per time slot is unbounded with the size of the system. This allows us to compare one path of the fraction of infected nodes with the stochastic trajectory of its mean field limit. In order to take into account the heterogeneity of opportunistic networks, the analysis is extended to multiple types of nodes. Our numerical results show that the heterogeneity can help to stabilize the system. We verify the results through simulation showing how to obtain useful approximations in the case of very large systems. © 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering.
Hadron multiplicities at COMPASS
Du Fresne Von Hohenesche, Nicolas
2014-01-01
Quark fragmentation functions (FF) D h q ( z ; Q 2 ) describe final-state hadronisation of quarks q into hadrons h . The FFs can be extracted from hadron multiplicities produced in semi-inclusive deep inelastic scattering. The COMPASS collaboration has recently measured charged hadron multiplicities for identified pions and kaons using a 160 GeV/c muon beam impinging on an isoscalar LiD target. The data cover a large kinematical range and provide an important input for global QCD analyses of world data at NLO, aiming at the determination of FFs. The latest results from COMPASS on pion multiplicities and pion fragmentation functions will be discussed.
Deppman, Airton
2016-01-01
The non extensive aspects of $p_T$ distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of self-similarity in both theoretical and experimental works in High Energy and in Hadron Physics are discussed, to show that the idea of fractal structure of hadrons and fireballs have being under discussion for decades. The non extensive self-consistent thermodynamics and the thermofractal structure allow one to connect non extensivity to intermittence and possibly to parton distribution functions in a single theoretical framework.
Streamlined mean field variational Bayes for longitudinal and multilevel data analysis.
Lee, Cathy Yuen Yi; Wand, Matt P
2016-07-01
Streamlined mean field variational Bayes algorithms for efficient fitting and inference in large models for longitudinal and multilevel data analysis are obtained. The number of operations is linear in the number of groups at each level, which represents a two orders of magnitude improvement over the naïve approach. Storage requirements are also lessened considerably. We treat models for the Gaussian and binary response situations. Our algorithms allow the fastest ever approximate Bayesian analyses of arbitrarily large longitudinal and multilevel datasets, with little degradation in accuracy compared with Markov chain Monte Carlo. The modularity of mean field variational Bayes allows relatively simple extension to more complicated scenarios.
Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses
Bressloff, P. C.
1999-08-01
We analyze the effects of synaptic depression or facilitation on the existence and stability of the splay or asynchronous state in a population of all-to-all, pulse-coupled neural oscillators. We use mean-field techniques to derive conditions for the local stability of the splay state and determine how stability depends on the degree of synaptic depression or facilitation. We also consider the effects of noise. Extensions of the mean-field results to finite networks are developed in terms of the nonlinear firing time map.
Another mean field treatment in the strong coupling limit of lattice QCD
Ohnishi, Akira; Miura, Kohtaroh; Nakano, Takashi Z.
2011-01-01
We discuss the QCD phase diagram in the strong coupling limit of lattice QCD by using a new type of mean field coming from the next-to-leading order of the large dimensional expansion. The QCD phase diagram in the strong coupling limit recently obtained by using the monomer-dimer-polymer (MDP) algorithm has some differences in the phase boundary shape from that in the mean field results. As one of the origin to explain the difference, we consider another type of auxiliary field, which corresp...
Frank, T. D.; Daffertshofer, A.; Beek, P. J.
2001-01-01
We study the transient and stationary behavior of many-particle systems in terms of multivariate Ornstein-Uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-field approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing.
Skyrme mean-field studies of nuclei far from the stability line
Heenen, P H; Cwiok, S; Nazarewicz, W; Valor, A
1999-01-01
Two applications of mean-field calculations based on 3D coordinate-space techniques are presented. The first concerns the structure of odd-N superheavy elements that have been recently observed experimentally and shows the ability of the method to describe, in a self-consistent way, very heavy odd-mass nuclei. Our results are consistent with the experimental data. The second application concerns the introduction of correlations beyond a mean-field approach by means of projection techniques and configuration mixing. Results for Mg isotopes demonstrate that the restoration of rotational symmetry plays a crucial role in the description of 32Mg.
Dynamical mean field theory-based electronic structure calculations for correlated materials.
Biermann, Silke
2014-01-01
We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.
Time-Dependent Mean-Field Games in the Subquadratic Case
Gomes, Diogo A.
2014-10-14
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.
Mean-field approximation for the potts model of a diluted magnet in the external field
Semkin, S. V.; Smagin, V. P.
2016-07-01
The Potts model of a diluted magnet with an arbitrary number of states placed in the external field has been considered. Phase transitions of this model have been studied in the mean-field approximation, the dependence of the critical temperature on the external field and the density of magnetic atoms has been found, and the magnetic susceptibility has been calculated. An improved mean-field technique has been proposed, which provides more accurate account of the effects associated with nonmagnetic dilution. The influence of dilution on the first-order phase transition curve and the magnetization jump at the phase transition has been studied by this technique.
On the convergence of finite state mean-field games through Γ-convergence
Ferreira, Rita C.
2014-10-01
In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.
Non-mean-field effects in systems with long-range forces in competition.
Bachelard, R; Staniscia, F
2012-11-01
We investigate the canonical equilibrium of systems with long-range forces in competition. These forces create a modulation in the interaction potential and modulated phases appear at the system scale. The structure of these phases differentiate this system from monotonic potentials, where only the mean-field and disordered phases exist. With increasing temperature, the system switches from one ordered phase to another through a first-order phase transition. Both mean-field and modulated phases may be stable, even at zero temperature, and the long-range nature of the interaction will lead to metastability characterized by extremely long time scales.
Weibull model of Multiplicity Distribution in hadron-hadron collisions
Dash, Sadhana
2014-01-01
We introduce the Weibull distribution as a simple parametrization of charged particle multiplicities in hadron-hadron collisions at all available energies, ranging from ISR energies to the most recent LHC energies. In statistics, the Weibull distribution has wide applicability in natural processes involving fragmentation processes. This gives a natural connection to the available state-of-the-art models for multi-particle production in hadron hadron collisions involving QCD parton fragmentation and hadronization.
Detailed comparison between parton cascade and hadronic cascade at SPS and RHIC
Nara, Y; Longacre, R S
1999-01-01
We study the importance of the partonic phase produced in relativistic heavy ion collision by comparing the parton cascade model and the hadronic cascade model. Hadron yield, baryon stopping and transverse momentum distribution are calculated with JAM and discussions are given comparing with VNI. Both of these models give good description of experimental data. We also discuss the strangeness production mechanism and the directed transverse flow. (21 refs).
Hadronic "flow" in p--Pb collisions at the Large Hadron Collider?
Zhou, You; Li, Pengfei; Song, Huichao
2015-01-01
Using the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, we investigate azimuthal correlations in p--Pb collisions at $\\sqrt{s_{_{\\rm NN}}}=5.02$ TeV. Comparison with the experimental data shows that UrQMD can not reproduce the multiplicity dependence of 2- and 4-particle cumulants, especially the transition from positive to negative values of $c_{2}\\{4\\}$ in high multiplicity events, which has been taken as experimental evidence of collectivity in p--Pb collisions. Meanwhile, UrQMD can not qualitatively describe the differential elliptic flow, $v_{2}(p_{\\rm T})$, of all charged hadrons at various multiplicity classes. These discrepancies show that the simulated hadronic p--Pb systems can not generate enough collective flow as observed in experiment, the associated hadron emissions are largely influenced by non-flow effects. However, the characteristic $v_{2}(p_{\\rm T})$ mass-ordering of pions, kaons and protons is observed in UrQMD, which is the consequence of hadronic interactions and not nece...
Cattaneo, Carlo
2011-01-01
This title includes: Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste; A. Lichnerowicz: Ondes de choc, ondes infinitesimales et rayons en hydrodynamique et magnetohydrodynamique relativistes; A.H. Taub: Variational principles in general relativity; J. Ehlers: General relativistic kinetic theory of gases; K. Marathe: Abstract Minkowski spaces as fibre bundles; and, G. Boillat: Sur la propagation de la chaleur en relativite.
Inelastic quarkonium photoproduction in hadron-hadron interactions at LHC energies
Goncalves, V.P. [Universidade Federal de Pelotas, Instituto de Fisica e Matematica, Pelotas, RS (Brazil); Machado, M.M. [Ciencia e Tecnologia, IF - Farroupilha, Instituto Federal de Educacao, Sao Borja, RS (Brazil)
2014-04-15
In this paper we study the inelastic quarkonium photoproduction in coherent pp/p Pb/PbPb interactions. Considering the ultra-relativistic hadrons as a source of photons, we estimate the total h{sub 1}+h{sub 2} → h x V+X (V=J/Ψ and Υ) cross sections and rapidity distributions at LHC energies. Our results demonstrate that the experimental analysis of this process can be used to understand the underlying mechanism governing heavy quarkonium production. (orig.)
Gluon saturation and pseudo-rapidity distributions of charged hadrons at RHIC energy regions
WEI Xin-Bing; FENG Sheng-Qin
2012-01-01
We modified the gluon saturation model by rescaling the momentum fraction according to saturation momentum and introduced Cooper-Frye hydrodynamic evolution to systematically study the pseudorapidity distributions of final charged hadrons at different energies and different centralities for Au-Au collisions in relativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC).The features of both gluon saturation and hydrodynamic evolution at different energies and different centralities for Au-Au collisions are investigated in this paper.
Moreau, Pierre; Palmese, Alessia; Bratkovskaya, Elena
2016-01-01
We study the production of hadrons in nucleus-nucleus collisions within the Parton-Hadron-String Dynamics (PHSD) transport approach that is extended to incorporate essentials aspects of chiral symmetry restoration (CSR) in the hadronic sector (via the Schwinger mechanism) on top of the deconfinement phase transition as implemented in PHSD. The essential impact of CSR is found in the Schwinger mechanism (for string decay) which fixes the ratio of strange to light quark production in the hadronic medium. Our studies provide a microscopic explanation for the maximum in the $K^+/\\pi^+$ ratio at about 30 A GeV which only shows up if in addition to CSR a deconfinement transition to partonic degrees-of-freedom is incorporated in the reaction dynamics.
Swanson, E S
2009-01-01
A brief review of theoretical progress in hadron spectroscopy and nonperturbative QCD is presented. Attention is focussed on recent lattice gauge theory, the Dyson-Schwinger formalism, unquenching constituent models, and some beyond the Standard Model physics.
Tang, Alfred [Univ. of Wiscon, Milwaukee, WI (United States)
2002-08-01
Hadron production cross sections are calculated in the perturbative QCD frame work. Parton distribution functions are obtained from a strip-soliton model. The fragmentation functions are derived from the Lund model of string breaking.
Test of Relativistic Eigenfunctions for Pseudospin Symmetry
Ginocchio, Joseph N.
2001-10-01
Pseudospin symmetry has been shown to be a relativistic symmetry of the Dirac Hamiltonian [1] and the generators of this symmetry have been determined [2]. Although the measured energy splittings between pseudospin doublets are small, the eigenfunctions of the doublets have been examined only recently [3]. We show to what extent the pseudospin partners of realistic relativistic mean field eigenfunctions [4] are themselves eigenfunctions of the same Dirac Hamiltonian. 1) J. N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997). 2) J. N. Ginocchio and A. Leviatan, Phys. Lett. B 425, 1 (1998). 3) J. N. Ginocchio and A. Leviatan, to be published in Phys. Rev. Lett. (2001). 4) J. N. Ginocchio and D. G. Madland, Phys. Rev. C 57, 1167 (1998).
Melting Hadrons, Boiling Quarks
Rafelski, Johann
2015-01-01
In the context of the Hagedorn temperature half-centenary I describe our understanding of the hot phases of hadronic matter both below and above the Hagedorn temperature. The first part of the review addresses many frequently posed questions about properties of hadronic matter in different phases, phase transition and the exploration of quark-gluon plasma (QGP). The historical context of the discovery of QGP is shown and the role of strangeness and strange antibaryon signature of QGP illustra...
The Mesozoic Era of relativistic heavy ion physics and beyond
Harris, J.W.
1994-03-01
In order to understand how matter 15 billion years ago in the form of quarks, gluons and leptons at a temperature of 2 {times} 10{sup 12} {degrees}K evolved to become today`s Universe, the goal of relativistic and ultra-relativistic heavy ion physics is to understand the equation of state of nuclear, hadronic and partonic matter. This quest is of cross-disciplinary interest. The phase transition from partonic matter to hadronic matter tens of micro-seconds after the beginning of the universe is of interest to cosmology. Fluctuations during this phase transition would influence nucleosynthesis and the understanding of baryonic inhomogeneities in the universe. The nuclear matter equation of state, which describes the incompressibility of nuclear matter, governs neutron star stability. It determines the possible existence of strange quark matter stars and the dynamics of supernova expansion in astrophysics. The existence of collective nuclear phenomena in nuclear physics is also determined by the nuclear equation of state. In relativistic heavy ion collisions collective nuclear flow has been observed and is being studied extensively to obtain a better understanding of the incompressibility of nuclear matter. In high energy nuclear and particle physics, production and excitations of hadronic final states have been studied in detail and are important to an overall understanding of the equation of state of nuclear matter at finite temperature. The possibility in ultra-relativistic heavy ion collisions to create and study highly excited hadronic and partonic degrees of freedom provides a unique opportunity for understanding the behavior of nuclear, hadronic and partonic matter. Study of the QCD vacuum, of particular interest in particle physics, would provide a better understanding of symmetry-breaking mechanisms and the origins of the masses of the various quarks and particles.
Mean field dynamics of networks of delay-coupled noisy excitable units
Franović, Igor, E-mail: franovic@ipb.ac.rs [Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Todorović, Kristina; Burić, Nikola [Department of Physics and Mathematics, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, Belgrade (Serbia); Vasović, Nebojša [Department of Applied Mathematics, Faculty of Mining and Geology, University of Belgrade, PO Box 162, Belgrade (Serbia)
2016-06-08
We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.
Mean-field Approach to the Derivation of Baryon Superpotential from Matrix Model
Suzuki, H
2003-01-01
We discuss how to obtain the superpotential of the baryons and mesons for SU(N) gauge theories with N flavour matter fields from matrix integral. We apply the mean-field approximation for the matrix integral. Assuming the planar limit of the self-consistency equation, we show that the result almost agrees with the field theoretical result.
A simplified BBGKY hierarchy for correlated fermionic systems from a Stochastic Mean-Field approach
Lacroix, Denis; Ayik, Sakir; Yilmaz, Bulent
2015-01-01
The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here, that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-, ..., N-body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for sho...
A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet
Boualem Djehiche
2014-01-01
a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.
Another mean field treatment in the strong coupling limit of lattice QCD
Ohnishi, Akira; Nakano, Takashi Z
2010-01-01
We discuss the QCD phase diagram in the strong coupling limit of lattice QCD by using a new type of mean field coming from the next-to-leading order of the large dimensional expansion. The QCD phase diagram in the strong coupling limit recently obtained by using the monomer-dimer-polymer (MDP) algorithm has some differences in the phase boundary shape from that in the mean field results. As one of the origin to explain the difference, we consider another type of auxiliary field, which corresponds to the point-splitting mesonic composite. Fermion determinant with this mean field under the anti-periodic boundary condition gives rise to a term which interpolates the effective potentials in the previously proposed zero and finite temperature mean field treatments. While the shift of the transition temperature at zero chemical potential is in the desirable direction and the phase boundary shape is improved, we find that the effects are too large to be compatible with the MDP simulation results.
Mean Field Theory, Ginzburg Criterion, and Marginal Dimensionality of Phase-Transitions
Als-Nielsen, Jens Aage; Birgenau, R. J.
1977-01-01
By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges...
Explicit solutions of one-dimensional, first-order, stationary mean-field games with congestion
Gomes, Diogo A.
2017-01-05
Here, we consider one-dimensional first-order stationary mean-field games with congestion. These games arise when crowds face difficulty moving in high-density regions. We look at both monotone decreasing and increasing interactions and construct explicit solutions using the current formulation. We observe new phenomena such as discontinuities, unhappiness traps and the non-existence of solutions.
Phase behaviour of colloids suspended in a near-critical solvent : A mean-field approach
Edison, John R.; Belli, Simone; Evans, Robert; Van Roij, René; Dijkstra, Marjolein
2015-01-01
Colloids suspended in a binary solvent may, under suitable thermodynamic conditions, experience a wide variety of solvent-mediated interactions that can lead to colloidal phase transitions and aggregation phenomena. We present a simple mean-field theory, based on free-volume arguments, that describe
Going Beyond a Mean-field Model for the Learning Cortex: Second-Order Statistics
Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Sleigh, J. W.
2008-01-01
Mean-field models of the cortex have been used successfully to interpret the origin of features on the electroencephalogram under situations such as sleep, anesthesia, and seizures. In a mean-field scheme, dynamic changes in synaptic weights can be considered through fluctuation-based Hebbian learning rules. However, because such implementations deal with population-averaged properties, they are not well suited to memory and learning applications where individual synaptic weights can be important. We demonstrate that, through an extended system of equations, the mean-field models can be developed further to look at higher-order statistics, in particular, the distribution of synaptic weights within a cortical column. This allows us to make some general conclusions on memory through a mean-field scheme. Specifically, we expect large changes in the standard deviation of the distribution of synaptic weights when fluctuation in the mean soma potentials are large, such as during the transitions between the “up” and “down” states of slow-wave sleep. Moreover, a cortex that has low structure in its neuronal connections is most likely to decrease its standard deviation in the weights of excitatory to excitatory synapses, relative to the square of the mean, whereas a cortex with strongly patterned connections is most likely to increase this measure. This suggests that fluctuations are used to condense the coding of strong (presumably useful) memories into fewer, but dynamic, neuron connections, while at the same time removing weaker (less useful) memories. PMID:19669541
Iacobelli, Giulio; Kuelske, Christof
We consider a general class of disordered mean-field models where both the spin variables and disorder variables eta take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate describing the probabilities to find a large system close to a
Mean-field description of the structure and tension of curved fluid interfaces
Kuipers, Joris
2009-01-01
This thesis described the interfacial properties of curved fluid interfaces mainly employing mean-field models. Investigations of Tolman's length in simple systems and systems in contact with a hard wall are presented. Both the interfacial properties as well as the wetting behavior of phase-separate
Van Mieghem, P.F.A.; Van de Bovenkamp, R.
2015-01-01
Mean-field approximations (MFAs) are frequently used in physics. When a process (such as an epidemic or a synchronization) on a network is approximated by MFA, a major hurdle is the determination of those graphs for which MFA is reasonably accurate. Here, we present an accuracy criterion for Markovi
Ground state correlations and mean field using the exp(S) method
Heisenberg, J H; Heisenberg, Jochen H.; Mihaila, Bogdan
1999-01-01
This document gives a detailed account of the terms used in the computation of the ground state mean field and the ground state correlations. While the general approach to this description is given in a separate paper (nucl-th/9802029) we give here the explicite expressions used.
Analytically Solvable Mean-Field Potential for Stable and Exotic Nuclei
Stoitsov, M. V.; S. S. Dimitrova(INRNE, Sofia); Pittel, S.; Van Isacker, P.(GANIL, CEA/DSM–CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5, France); Frank, A
1997-01-01
Slater determinants built from the single-particle wave functions of the analytically solvable Ginocchio potential are used to approximate the self-consistent Hartree-Fock solutions for the ground states of nuclei. The results indicate that the Ginocchio potential provides a good parametrization of the nuclear mean field for a wide range of nuclei, including those at the limit of particle stability.
Automating the mean-field method for large dynamic gossip networks
Bakhshi, Rena; Endrullis, Jörg; Endrullis, Stefan; Fokkink, Wan; Haverkort, Boudewijn
2010-01-01
We investigate an abstraction method, called mean- field method, for the performance evaluation of dynamic net- works with pairwise communication between nodes. It allows us to evaluate systems with very large numbers of nodes, that is, systems of a size where traditional performance evaluation meth
A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach
Lacroix, Denis; Tanimura, Yusuke [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France); Ayik, Sakir [Tennessee Technological University, Physics Department, Cookeville, TN (United States); Yilmaz, Bulent [Ankara University, Physics Department, Faculty of Sciences, Ankara (Turkey)
2016-04-15
The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-,.., N -body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for short time evolution. In that case, it gives information on the evolution time-scale close to a saddle point associated to a quantum phase-transition. For long time evolution and strong coupling, we observed that the simplified BBGKY hierarchy cannot be truncated and only the full SMF with initial sampling leads to reasonable results. (orig.)
New a priori estimates for mean-field games with congestion
Evangelista, David
2016-01-06
We present recent developments in crowd dynamics models (e.g. pedestrian flow problems). Our formulation is given by a mean-field game (MFG) with congestion. We start by reviewing earlier models and results. Next, we develop our model. We establish new a priori estimates that give partial regularity of the solutions. Finally, we discuss numerical results.
Chaotic time series prediction using mean-field theory for support vector machine
Cui Wan-Zhao; Zhu Chang-Chun; Bao Wen-Xing; Liu Jun-Hua
2005-01-01
This paper presents a novel method for predicting chaotic time series which is based on the support vector machines approach, and it uses the mean-field theory for developing an easy and efficient learning procedure for the support vector machine. The proposed method approximates the distribution of the support vector machine parameters to a Gaussian process and uses the mean-field theory to estimate these parameters easily, and select the weights of the mixture of kernels used in the support vector machine estimation more accurately and faster than traditional quadratic programming-based algorithms. Finally, relationships between the embedding dimension and the predicting performance of this method are discussed, and the Mackey-Glass equation is applied to test this method. The stimulations show that the mean-field theory for support vector machine can predict chaotic time series accurately, and even if the embedding dimension is unknown, the predicted results are still satisfactory. This result implies that the mean-field theory for support vector machine is a good tool for studying chaotic time series.
Mean field limit for bosons and infinite dimensional phase-space analysis
Zied, Ammari
2007-01-01
This article proposes the construction of Wigner measures in the infinite dimensional bosonic quantum field theory, with applications to the derivation of the mean field dynamics. Once these asymptotic objects are well defined, it is shown how they can be used to make connections between different kinds of results or to prove new ones.
Mott-Hubbard and Anderson transitions in dynamical mean-field theory
Byczuk, Krzysztof [Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, PL-00-681 Warsaw (Poland)]. E-mail: byczuk@fuw.edu.pl; Hofstetter, Walter [Condensed Matter Theory Group, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Vollhardt, Dieter [Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute for Physics, University of Augsburg, D-86135 Augsburg (Germany)
2005-04-30
The Anderson-Hubbard Hamiltonian at half-filling is investigated within dynamical mean-field theory at zero temperature. The local density of states is calculated by taking the geometric and arithmetic mean, respectively. The non-magnetic ground state phase diagrams obtained within the different averaging schemes are compared.
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion
de Andrade, L Garcia
2009-01-01
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion}} Previous attempts for building a cosmic dynamo including preheating in inflationary universes [Bassett et al Phys Rev (2001)] has not included mean field or turbulent dynamos. In this paper a mean field dynamo in cosmic scales on a Riemannian spatial cosmological section background, is set up. When magnetic fields and flow velocities are parallel propagated along the Riemannian space dynamo action is obtained. Turbulent diffusivity ${\\beta}$ is coupled with the Ricci magnetic curvature, as in Marklund and Clarkson [MNRAS (2005)], GR-MHD dynamo equation. Mean electric field possesses an extra term where Ricci tensor couples with magnetic vector potential in Ohm's law. In Goedel universe induces a mean field dynamo growth rate ${\\gamma}=2{\\omega}^{2}{\\beta}$. In this frame kinetic helicity vanishes. In radiation era this yields ${\\gamma}\\approx{2{\\beta}{\\times}10^{-12}s^{-1}}$. In non-comoving the magnetic field is expressed as $B\\ap...
Mean field dynamics of networks of delay-coupled noisy excitable units
Franović, Igor; Todorović, Kristina; Vasović, Nebojša; Burić, Nikola
2016-06-01
We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.
Holography inspired stringy hadrons
Sonnenschein, Jacob
2017-01-01
Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons and glueballs as strings in flat four dimensional space-time. The models are based on a "map" from stringy hadrons of holographic confining backgrounds. In this note we review the "derivation" of the models. We start with a brief reminder of the passage from the AdS5 ×S5 string theory to certain flavored confining holographic models. We then describe the string configurations in holographic backgrounds that correspond to a Wilson line, a meson, a baryon and a glueball. The key ingredients of the four dimensional picture of hadrons are the "string endpoint mass" and the "baryonic string vertex". We determine the classical trajectories of the HISH. We review the current understanding of the quantization of the hadronic strings. We end with a summary of the comparison of the outcome of the HISH models with the PDG data about mesons and baryons. We extract the values of the tension, masses and intercepts from best fits, write down certain predictions for higher excited hadrons and present attempts to identify glueballs.
Recent results on relativistic heavy ion collisions
Munhoz, Marcelo [Universidade de Sao Paulo (IF/USP), Sao Paulo, SP (Brazil). Inst. de Fisica
2013-07-01
Full text: The study of relativistic heavy ion collisions is a very important tool in order to understand the strong interaction described by QCD. The formation of the Quark-Gluon Plasma and the study of its properties is a very challenging quest. The Large Hadron Collider (LHC) from CERN (European Organization for Nuclear Research) generates ultra-relativistic Pb + Pb collisions at the TeV scale inaugurating a new era for such studies. Three experiments, ATLAS, CMS and ALICE are able to measure the products of such collisions. In special, the ALICE experiment was designed specifically for the study of heavy ion collisions. In this presentation, I'll discuss the latest results that shed light in the QGP understanding. (author)
Nonlinear waves in strongly interacting relativistic fluids
Fogaça, D A; Filho, L G Ferreira
2013-01-01
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of hadronic matter but also fluids of quarks and gluons. Part of the physics program of these machines is the observation of waves in this strongly interacting medium. From the theoretical point of view, these waves are often treated with li-nearized hydrodynamics. In this text we review the attempts to go beyond linearization. We show how to use the Reductive Perturbation Method to expand the equations of (ideal and viscous) relativistic hydrodynamics to obtain nonlinear wave equations. These nonlinear wave equations govern the evolution of energy density perturbations (in hot quark gluon plasma) or baryon density perturbations (in cold quark gluon plasma and nuclear matter). Different nonlinear wave equations, such as the breaking wave, Korteweg-de Vries and Burgers equations, are...
Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
Machado Velho, Roberto
2017-09-10
In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).
Introduction to the relativistic string theory
Barbashov, B M
1990-01-01
This book presents a systematic and detailed account of the classical and quantum theory of the relativistic string and some of its modifications. Main attention is paid to the first-quantized string theory with possible applications to the string models of hadrons as well as to the superstring approach to unifications of all the fundamental interactions in the elementary particle physics and to the "cosmic" strings. Some new aspects are provided such as the consideration of the string in an external electromagnetic field and in the space-time of constant curvature (the de Sitter universe), th
Relativistic radiative transfer in relativistic spherical flows
Fukue, Jun
2017-02-01
Relativistic radiative transfer in relativistic spherical flows is numerically examined under the fully special relativistic treatment. We first derive relativistic formal solutions for the relativistic radiative transfer equation in relativistic spherical flows. We then iteratively solve the relativistic radiative transfer equation, using an impact parameter method/tangent ray method, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities, and the Eddington factor. We consider several cases; a scattering wind with a luminous central core, an isothermal wind without a core, a scattering accretion on to a luminous core, and an adiabatic accretion on to a dark core. In the typical wind case with a luminous core, the emergent intensity is enhanced at the center due to the Doppler boost, while it reduces at the outskirts due to the transverse Doppler effect. In contrast to the plane-parallel case, the behavior of the Eddington factor is rather complicated in each case, since the Eddington factor depends on the optical depth, the flow velocity, and other parameters.
Thermophoretic Flow in Relativistic Heavy-Ion Collisions
Thoma, M H
2001-01-01
If a quark-gluon plasma is formed in relativistic heavy-ion collisions, there might be a mixed phase of quarks and gluons and hadronic clusters when the critical temperature is reached in the expansion of the fireball. If there is a temperature gradient in the fireball, the hadronic clusters, embedded in the heat bath of quarks and gluons, are subjected to a thermophoretic force. It is shown that even for small temperature gradients and short lifetimes of the mixed phase thermophoresis leads to a strong flow.
Agakishiev, H.; Aggarwal, M.M.; Braidot, E; Mischke, A.; Peitzmann, T.; Zoulkarneeva, Y.
2011-01-01
We report first results from an analysis based on a new multi-hadron correlation technique, exploring jet-medium interactions and di-jet surface emission bias at the BNL Relativistic Heavy Ion Collider (RHIC). Pairs of back-to-back high-transverse-momentum hadrons are used for triggers to study asso
Search for Exotic Strange Dibaryon in Relativistic Heavy Ion Collisions
GAOChong-Shou
2003-01-01
The exotic strange dibaryon particle (ΩΩ)0+ with S = -6 can be produced in relativistic heavy ion collisions. The yields of this kind of exotic strange dibaryon particles can increase signitlcantly soon as the formation of QGP does exhibit after the collision. If there is no phase transition after the collision, the upper bound of the production of this diomega can be estimated from the free hadronic gas model for nuclear matter. The relative yield ratio of diomega to deuteron is less than 0.000205, this means that if there is no QGP creation it is difficult to observe the production of diomega in relativistic heavy ion collisions.
Search for Exotic Strange Dibaryon in Relativistic Heavy Ion Collisions
GAO Chong-Shou
2003-01-01
The exotic strange dibaryon particle (ΩΩ)0+ with S = -6 can be produced in relativistic heavyioncollisions. The yields of this kind of exotic strange dibaryon particles can increase significantly soon as the formation ofQGP does exhibit after the collision. If there is no phase transition after the collision, the upper bound of the productionof this diomega can be estimated from the free hadronic gas model for nuclear matter. The relative yield ratio of diomegato deuteron is less than 0.000205, this means that if there is no QGP creation it is difficult to observe the production ofdiomega in relativistic heavy ion collisions.
The description for the spin polarizabilities of hadrons based on the covariant Lagrangian
Belousova, S A
2000-01-01
On the basis of the correspondence principle between the relativistic moving medium electrodynamics and relativistic quantum field theory the covariant Lagrangian of the electromagnetic field interaction with the polarized spin particles have been obtained. This Lagrangian satisfies the main relativistic quantum field theory requirements and contains four independent covariant spin structures, which have particular physical meaning. It is shown that the spin polarizabilities give the contribution to the amplitude for Compton scattering on the spin-1/2 hadron in the ${\\cal O}(\\omega^3)$.
Study of highly-excited string states at the Large Hadron Collider
Gingrich, Douglas M
2008-01-01
In TeV-scale gravity scenarios with large extra dimensions, black holes may be produced at future colliders. Good arguments have been made for why general relativistic black holes may be just out of reach of the Large Hadron Collider (LHC). However, in weakly-coupled string theory, highly excited string states - string balls - could be produced at the LHC with high rates and decay thermally, not unlike general relativistic black holes. In this paper, we simulate and study string ball production and decay at the LHC. We specifically emphasize the experimentally-detectable similarities and differences between string balls and general relativistic black holes at a TeV scale.
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
ERL-BASED LEPTON-HADRON COLLIDERS: eRHIC AND LHeC
Zimmermann, F
2013-01-01
Two hadron-ERL colliders are being proposed. The Large Hadron electron Collider (LHeC) plans to collide the high-energy protons and heavy ions in the Large Hadron Collider (LHC) at CERN with 60-GeV polarized electrons or positrons. The baseline scheme for this facility adds to the LHC a separate recirculating superconducting (SC) lepton linac with energy recovery, delivering a lepton current of 6.4mA. The electron-hadron collider project eRHIC aims to collide polarized (and unpolarized) electrons with a current of 50 (220) mA and energies in the range 5–30 GeV with a variety of hadron beams— heavy ions as well as polarized light ions— stored in the existing Relativistic Heavy Ion Collider (RHIC) at BNL. The eRHIC electron beam will be generated in an energy recovery linac (ERL) installed inside the RHIC tunnel.
2009-01-01
The CERN Dragon Boat team – the Hadron Dragons – achieved a fantastic result at the "Paddle for Cancer" Dragon Boat Festival at Lac de Joux on 6 September. CERN Hadron Dragons heading for the start line.Under blue skies and on a clear lake, the Hadron Dragons won 2nd place in a hard-fought final, following top times in the previous heats. In a close and dramatic race – neck-and-neck until the final 50 metres – the local Lac-de-Joux team managed to inch ahead at the last moment. The Hadron Dragons were delighted to take part in this festival. No one would turn down a day out in such a friendly and fun atmosphere, but the Dragons were also giving their support to cancer awareness and fund-raising in association with ESCA (English-Speaking Cancer Association of Geneva). Riding on their great success in recent competitions, the Hadron Dragons plan to enter the last Dragon Boat festival of 2009 in Annecy on 17-18 October. This will coincide with t...
Mean-field dynamics of a population of stochastic map neurons
Franović, Igor; Maslennikov, Oleg V.; Bačić, Iva; Nekorkin, Vladimir I.
2017-07-01
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking, and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series. The effective model is further shown to reproduce with sufficient accuracy the phase response curves of the exact system and the assembly's response to external stimulation of finite amplitude and duration.
Beyond the mean field in the particle-vibration coupling scheme
Baldo, M; Colo', G; Rizzo, D; Sciacchitano, L
2015-01-01
The Energy Density Functional theory is one of the most used methods developed in nuclear structure. It is based on the assumption that the energy of the ground state is a functional only of the density profile. The method is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other bulk properties along the whole mass table. Although the Density Functional is in this case represented formally as the Hartree-Fock mean field of an effective force, the corresponding single-particle states in general do not reproduce the phenomenology particularly well. To overcome this difficulty, a strategy has been developed where the effective force is adjusted to reproduce directly the single particle energies, trying to keep the ground state energy sufficiently well reproduced. An alternative route, that has been developed along several years, for solving this problem is to introduce the mean field fluctuations, as represented by t...
Mean field theory for Lyapunov exponents and KS entropy in Lorentz lattice gases
Ernst, M H; Nix, R; Jacobs, D; Ernst, M H; Dorfman, J R; Nix, R; Jacobs, D
1994-01-01
automata lattice gases are useful systems for systematically exploring the connections between non-equilibrium statistical mechanics and dynamical systems theory. Here the chaotic properties of a Lorentz lattice gas are studied analytically and by means of computer simulations. The escape-rates, Lyapunov exponents, and KS entropies are estimated for a one- dimensional example using a mean field theory. The results are compared with simulations for a range of densities and scattering parameters of the lattice gas. The computer results show a distribution of values for the dynamical quantities with average values that are in good agreement with the mean field theory and consistent with the escape-rate formalism for the coefficient of diffusion.
Mean-Field Limit and Phase Transitions for Nematic Liquid Crystals in the Continuum
Bachmann, Sven; Genoud, François
2017-08-01
We discuss thermotropic nematic liquid crystals in the mean-field regime. In the first part of this article, we rigorously carry out the mean-field limit of a system of N rod-like particles as N→ ∞, which yields an effective `one-body' free energy functional. In the second part, we focus on spatially homogeneous systems, for which we study the associated Euler-Lagrange equation, with a focus on phase transitions for general axisymmetric potentials. We prove that the system is isotropic at high temperature, while anisotropic distributions appear through a transcritical bifurcation as the temperature is lowered. Finally, as the temperature goes to zero we also prove, in the concrete case of the Maier-Saupe potential, that the system converges to perfect nematic order.
Mean-field analysis of phase transitions in the emergence of hierarchical society
Okubo, Tsuyoshi; Odagaki, Takashi
2007-09-01
Emergence of hierarchical society is analyzed by use of a simple agent-based model. We extend the mean-field model of Bonabeau [Physica A 217, 373 (1995)] to societies obeying complex diffusion rules where each individual selects a moving direction following their power rankings. We apply this mean-field analysis to the pacifist society model recently investigated by use of Monte Carlo simulation [Physica A 367, 435 (2006)]. We show analytically that the self-organization of hierarchies occurs in two steps as the individual density is increased and there are three phases: one egalitarian and two hierarchical states. We also highlight that the transition from the egalitarian phase to the first hierarchical phase is a continuous change in the order parameter and the second transition causes a discontinuous jump in the order parameter.
State-of-the-art of beyond mean field theories with nuclear density functionals
Egido, J Luis
2016-01-01
We present an overview of beyond mean field theories (BMFT) based on the generator coordinate method (GCM) and the recovery of symmetries used in nuclear physics with effective forces. After a reminder of the Hartree-Fock-Bogoliubov (HFB) theory a discussion of the shortcomings of any mean field approximation (MFA) is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. The lack of fluctuations around the average values of the MFA is a shortcoming of this approach. To build in correlations in BMFT one selects the relevant degrees of freedom: quadrupole, octupole and the pairing vibrations as well as the single particle ones. In the GCM the operators representing these degrees of f...
On the dynamics of mean-field equations for stochastic neural fields with delays
Touboul, Jonathan
2011-01-01
The cortex is composed of large-scale cell assemblies sharing the same individual properties and receiving the same input, in charge of certain functions, and subject to noise. Such assemblies are characterized by specific space locations and space-dependent delayed interactions. The mean-field equations for such systems were rigorously derived in a recent paper for general models, under mild assumptions on the network, using probabilistic methods. We summarize and investigate general implications of this result. We then address the dynamics of these stochastic neural field equations in the case of firing-rate neurons. This is a unique case where the very complex stochastic mean-field equations exactly reduce to a set of delayed differential or integro-differential equations on the two first moments of the solutions, this reduction being possible due to the Gaussian nature of the solutions. The obtained equations differ from more customary approaches in that it incorporates intrinsic noise levels nonlinearly ...
Spectral properties of the one-dimensional Hubbard model: cluster dynamical mean-field approaches
Go, Ara; Jeon, Gun Sang
2011-03-01
We investigate static and dynamic properties of the one-dimensional Hubbard model using cluster extensions of the dynamical mean-field theory. It is shown that the two different extensions, the cellular dynamical mean-field theory and the dynamic cluster approximation, yield the ground-state properties which are qualitatively in good agreement with each other. We compare the results with the Bethe ansatz results to check the accuracy of the calculation with finite sizes of clusters. We also analyze the spectral properties of the model with the focus on the spin-charge separation and discuss the dependency on the cluster size in the two approaches. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2010-0010937).
Analytical slave-spin mean-field approach to orbital selective Mott insulators
Komijani, Yashar; Kotliar, Gabriel
2017-09-01
We use the slave-spin mean-field approach to study particle-hole symmetric one- and two-band Hubbard models in the presence of Hund's coupling interaction. By analytical analysis of the Hamiltonian, we show that the locking of the two orbitals vs orbital selective Mott transition can be formulated within a Landau-Ginzburg framework. By applying the slave-spin mean field to impurity problems, we are able to make a correspondence between impurity and lattice. We also consider the stability of the orbital selective Mott phase to the hybridization between the orbitals and study the limitations of the slave-spin method for treating interorbital tunnelings in the case of multiorbital Bethe lattices with particle-hole symmetry.
Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.
Szabó-Solticzky, András; Berthouze, Luc; Kiss, Istvan Z; Simon, Péter L
2016-04-01
An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models.
Heterogeneous mean field for neural networks with short-term plasticity
di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro
2014-08-01
We report about the main dynamical features of a model of leaky integrate-and-fire excitatory neurons with short-term plasticity defined on random massive networks. We investigate the dynamics by use of a heterogeneous mean-field formulation of the model that is able to reproduce dynamical phases characterized by the presence of quasisynchronous events. This formulation allows one to solve also the inverse problem of reconstructing the in-degree distribution for different network topologies from the knowledge of the global activity field. We study the robustness of this inversion procedure by providing numerical evidence that the in-degree distribution can be recovered also in the presence of noise and disorder in the external currents. Finally, we discuss the validity of the heterogeneous mean-field approach for sparse networks with a sufficiently large average in-degree.
Nonuniversal behavior for aperiodic interactions within a mean-field approximation.
Faria, Maicon S; Branco, N S; Tragtenberg, M H R
2008-04-01
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta . For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.
Macroscopic and large scale phenomena coarse graining, mean field limits and ergodicity
Rademacher, Jens; Zagaris, Antonios
2016-01-01
This book is the offspring of a summer school school “Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity”, which was held in 2012 at the University of Twente, the Netherlands. The focus lies on mathematically rigorous methods for multiscale problems of physical origins. Each of the four book chapters is based on a set of lectures delivered at the school, yet all authors have expanded and refined their contributions. Francois Golse delivers a chapter on the dynamics of large particle systems in the mean field limit and surveys the most significant tools and methods to establish such limits with mathematical rigor. Golse discusses in depth a variety of examples, including Vlasov--Poisson and Vlasov--Maxwell systems. Lucia Scardia focuses on the rigorous derivation of macroscopic models using $\\Gamma$-convergence, a more recent variational method, which has proved very powerful for problems in material science. Scardia illustrates this by various basic examples and a mor...
Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling
Opper, Manfred; Winther, Ole
2001-01-01
We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics. which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge of the d......We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics. which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge...... distributions in the thermodynamic limit. On the other hand, simulations on a real data model demonstrate that the method achieves more accurate predictions as compared to conventional TAP approaches....
Beyond-mean-field approach to low-lying spectra of $\\Lambda$ hypernuclei
Hagino, K; Yao, J M; Motoba, T
2015-01-01
Taking the hypernucleus $^{13}_{~\\Lambda}$C as an example, we illustrate the miscroscopic particle-rotor model for low-lying spectra of hypernuclei. This approach is based on the beyond-mean-field method, with the particle number and angular momentum projections. The quantum fluctuation of the mean-field is also taken into account for the core nucleus using the generator coordinate method. We show that the impurity effect of $\\Lambda$ hyperon, such as a change in $B(E2)$, is well described with this model. Our calculation indicates that the most important impurity effect in $sd$-shell hypernuclei is a change in a deformation parameter rather than in a nuclear size.
A. Sadeghi
2007-03-01
Full Text Available Using both mean field renormalization group (MFRG and Surface-Bulk MFRG (SBMFRG, we study the critical behavior of the classical Heisenberg and XY models on a simple cubic lattice. Critical temperatures as well as critical exponents, characteristic the universality classes of these two models were calculated, analytically for1, 2, 3 and 4 spin clusters. The results are in good agreement with higher accurate methods such as Monte Carlo and High- temperature series.
Universal mean-field phase diagram for biaxial nematics obtained from a minimax principle.
Bisi, Fulvio; Virga, Epifanio G; Gartland, Eugene C; De Matteis, Giovanni; Sonnet, André M; Durand, Georges E
2006-05-01
We study a class of quadratic Hamiltonians which describe both fully attractive and partly repulsive molecular interactions, characteristic of biaxial liquid crystal molecules. To treat the partly repulsive interactions we establish a minimax principle for the associated mean-field free energy. We show that the phase diagram described by Sonnet [Phys. Rev. E 67, 061701 (2003)] is universal. Our predictions are in good agreement with the recent observations on both V-shaped and tetrapodal molecules.