Nonlocal quark model beyond mean field

The nonlocal chiral quark model is extended beyond mean field using a strict 1/N _c expansion scheme. The nonlocal interaction has the advantage that all diagrams are finite and leads to unique evaluation of the 1/N _c corrections. Parameters of the nonlocal model are refitted making use of the physical values of the pion mass and the weak pion decay constant. The size of the 1/N _c correction to the quark condensate is carefully studied in nonlocal and local Nambu-Jona-Lasinio models. It is found that even the sign of the corrections can be different.     

QGP susceptibilities from PNJL model

An improved version of the PNJL model is used to calculate various thermodynamical quantities including Quark Number Susceptibility, Isospin susceptibility, specific heat, speed of sound and conformal measure. Comparison with Lattice data is found to be encouraging.     

Thermodynamics of the PNJL model

QCD thermodynamics is investigated by means of the Polyakov-loop-extended Nambu–Jona–Lasinio (PNJL) model, in which quarks couple simultaneously to the chiral condensate and to a background temporal gauge field representing Polyakov loop dynamics. The behaviour of the Polyakov loop as a function of temperature is obtained by minimising the thermodynamic potential of the system. A Taylor series expansion of the pressure is performed. Pressure difference and quark number density are then evaluated up to sixth order in the quark chemical potential and compared to the corresponding lattice data. The validity of the Taylor expansion is discussed within our model through a comparison between the full results and the truncated ones. PACS 12.38.Aw; 12.38.Mh     

Nonlocal stochastic model for the free scalar field theory

The free scalar field is investigated within the framework of the Davidson stochastic model and of the hypothesis on space-time stochasticity. It is shown that the resulting Markov field obtained by averaging in this space-time is equivalent to a nonlocal Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter. Our result generalizes Guerra and Ruggiero's procedure of stochastic quantization of scalar fields. On the basis of the assumption about unobservability of in quantum field theory, the Efimov nonlocal theory is obtained from Euclidean Markov field with form factors of the class of entire analytical functions.     

Bose-Einstein condensates beyond mean field theory: quantum backreaction as decoherence

We propose an experiment to measure the slow log(N) convergence to mean field theory (MFT) around a dynamical instability. Using a density matrix formalism instead of the standard macroscopic wave function approach, we derive equations of motion which go beyond MFT and provide accurate predictions for the quantum break time. The leading quantum corrections appear as decoherence of the reduced single-particle quantum state.     

Discussion of thermodynamic features within the PNJL model

We discuss some thermodynamical features of a QCD system within the two-flavor Polyakov loop extended Nambu–Jona-Lasinio(PNJL) model. Several thermodynamical quantities of interest(pressure, energy density,specific heat, speed of sound, etc.) are investigated and discussed in detail with two different forms of Polyakov loop potential. The effective coupling strength G incorporating a quark feedback(quark condensate) through operator product expansion is also discussed, as well as the relationship between color deconfinement and chiral phase crossover.We find that some thermodynamical quantities have quite different behavior for different Polyakov loop potentials.By changing the characteristic temperature T_0 of the pure Yang-Mills field, we find that when T_0 becomes small,color deconfinement might happen earlier than chiral phase crossover, while their relationship can be determined via some thermodynamical quantities. Furthermore, the behavior of the thermodynamical quantities is quite different in the two different forms of Polyakov loop potential studied. Especially, one of the potentials, specific heat, has two peaks, which correspond to color deconfinement and chiral phase crossover respectively. This interesting phenomenon may shed some light on whether the inflection points of the chiral condensate and deconfinement transitions happen at the same temperature or not for lattice QCD and experimental studies.     

Dynamic mean field in the Hubbard model

In the framework of the one-impurity problem formulated for the nondegenerate Hubbard Hamiltonian, general expressions are derived for all its principal correlation functions, as well as its retarded and advanced thermodynamic (Matsubara) Green functions. These results are analyzed for the case of zero temperature.     

Hyperon--hyperon interaction in relativistic mean field model

By using the new experimental data of \Lambda\Lambda potential, this paper has performed a full calculation for strange hadronic matter with different strangeness contents as well as its consequences on the global properties of neutron star matter in relativistic mean field model. It finds that the new weak hyperon--hyperon interaction makes the equations of state much stiffer than the result of the previous strong hyperon--hyperon interaction, and even stiffer than the result without consideration of hyperon--hyperon interaction. This new hyperon--hyperon interaction results in a maximum mass of 1.75M_{\odot} (where M_{\odot} stands for the mass of the Sun), about 0.2--0.5M_{\odot} larger than the previous prediction with the presence of hyperons. After examining carefully the onset densities of kaon condensation it finds that this new weak version of hyperon--hyperon interaction favours the occurrence of kaons in comparison with the strong one.     

Crystalline boson phases in harmonic traps: beyond the Gross-Pitaevskii mean field

Strongly-interacting bosons in two-dimensional harmonic traps are described through breaking of rotational symmetry at the Hartree-Fock level and subsequent symmetry restoration via projection techniques, thus incorporating correlations beyond the Gross-Pitaevskii (GP) solution. The bosons localize and form polygonal-ringlike crystalline patterns, both for a repulsive contact potential and a Coulomb interaction, as revealed via conditional-probability-distribution analysis. For neutral bosons, the total energy of the crystalline phase saturates in contrast to the GP solution, and its spatial extent becomes smaller than that of the GP condensate. For charged bosons, the total energy and dimensions approach the values of classical pointlike charges in their equilibrium configuration.     

Neutron star matter in a modified PNJL model

We discuss a three-flavor Nambu-Jona-Lasinio model for the quark matter equation of state with scalar diquark interaction, isoscalar vector interaction and Kobayashi-Maskawa-??t Hooft interaction. We adopt a phenomenological scheme to include possible effects of a change in the gluon pressure at finite baryon density by including a parametric dependence of the Polyakov-loop potential on the chemical potential. We discuss the results for the mass-radius relationships for hybrid neutron stars constructed on the basis of our model EoS in the context of the constraint from the recently measured mass of (1.97 ± 0.04) M _?? for the pulsar PSR J1614-2230.     

Metastability in the Hamiltonian mean field model and Kuramoto model

We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian mean field (HMF) model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi-stationary states (QSS) observed in the model and the connections to Tsallis statistics and glassy dynamics. We also present new results on the existence of metastable states in the Kuramoto model and discuss the similarities with those found in the HMF model. The existence of metastability seems to be quite a common phenomenon in fully coupled systems, whose origin could be also interpreted as a dynamical mechanism preventing or hindering synchronization.     

Quark number susceptibilities: Lattice QCD versus PNJL model

Quark number susceptibilities at finite quark chemical potential are investigated in the framework of the Polyakov-loop-extended Nambu–Jona-Lasinio (PNJL) model. A detailed comparison is performed between the available lattice data, extrapolated using a Taylor expansion around vanishing chemical potential, and PNJL results consistently obtained from a Taylor series truncated at the same order. The validity of the Taylor expansion is then examined through a comparison between the full and truncated PNJL model calculations.     

Diffusion-limited aggregation: A continuum mean field model

Mean field theory is used as a basis for a new approach to analyzing fractal pattern formation by diffusion-limited aggregation. A coarse time scale is introduced to take into account the discrete nature of DLA clusters. A system of equations is derived and solved numerically to determine the fractal dimension and density of a cluster as a function of distance from its center. The results obtained are in good agreement with direct numerical simulations.     

Relativistic chiral mean field model for finite nuclei

We present a method for proper treatment of pion-exchange interaction in the nuclear many-body problem in a relativistic chiral mean field (RCMF) model. The pionic correlation is expressed in 2-particle 2-hole (2p–2h) states in addition to the standard mean field state, to describe the full strength of pionic correlations. The effect of the short-range repulsion is included by way of the unitary correlation operator method (UCOM) for the central part of the pion-exchange interaction. We apply the RCMF model to ¹²C and ¹⁶O. The convergence of pionic energy contributions is realized with pionic quantum number Jπ$J^{\pi }$ up to 10⁻ for ¹²C and 11⁺ for ¹⁶O. The pion-exchange interaction gives the dominant contribution to the binding energy. The pion plays an important role in the formation of the jj  -magic shell effect by way of the Pauli-blocking mechanism of the pion-exchange interaction. The lower pionic quantum numbers Jπ?³⁺$J^{\pi }?3^{+}$ are the dominant components of the nuclear surface structure.     

Saddle point mean field calculation in the Hubbard model

Using functional techniques, the Hubbard model consisting of self-coupled lattice fermions is transformed into a bosonic functional integral. In this form it is treated by a mean field approximation in its modern version as a systematic expansion around a saddle point. The method is generalized to the extended Hubbard model.     

Parametric smoothness and self-scaling of the statistical properties of a minimal climate model: What beyond the mean field theories?

A quasi-geostrophic intermediate complexity model of the mid-latitude atmospheric circulation is considered, featuring simplified baroclinic conversion and barotropic convergence processes. The model undergoes baroclinic forcing towards a given latitudinal temperature profile controlled by the forced equator-to-pole temperature difference T_E. As T_E increases, a transition takes place from a stationary regime-Hadley equilibrium-to a periodic regime, and eventually to a chaotic regime where evolution takes place on a strange attractor. The attractor dimension, metric entropy, and bounding box volume in phase space have a smooth dependence on T_E, which results in power-law scaling properties. Power-law scalings with respect to T_E are detected also for the statistical properties of global physical observables — the total energy of the system and the averaged zonal wind. The scaling laws, which constitute the main novel result of the present work, can be thought to result from the presence of a statistical process of baroclinic adjustment, which tends to decrease the equator-to-pole temperature difference and determines the properties of the attractor of the system. The self-similarity could be of great help in setting up a theory for the overall statistical properties of the general circulation of the atmosphere and in guiding-on a heuristic basis-both data analysis and realistic simulations, going beyond the unsatisfactory mean field theories and brute force approaches. A leading example for this would be the possibility of estimating the sensitivity of the output of the system with respect to changes in the parameters.     

The mean field theory of the three-dimensional ANNNI model

The mean field equations of the simple cubic or tetragonal ANNNI model are studied on finite lattices. Structure combination branching processes are found which allow us to considerably refine previous mean field calculations on the model.