Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.

Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks

The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks.A real space complete condensation phase transition in the stationary state may occur.We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks.By means of grand canonical ensemble method,we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state.We further explore the relaxation dynamics of the condensation phase transition.By applying the hierarchical evolution and scaling ansatz,a scaling law for the relaxation dynamics is predicted.Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.

A Model-Independent Discussion of Quark Number Density and Quark Condensate at Zero Temperature and Finite Quark Chemical Potential

Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.

A novel SMC-PHD filter based on particle compensation

As a typical implementation of the probability hypothesis density(PHD) filter, sequential Monte Carlo PHD(SMC-PHD) is widely employed in highly nonlinear systems. However, the particle impoverishment problem introduced by the resampling step, together with the high computational burden problem, may lead to performance degradation and restrain the use of SMC-PHD filter in practical applications. In this work, a novel SMC-PHD filter based on particle compensation is proposed to solve above problems. Firstly, according to a comprehensive analysis on the particle impoverishment problem, a new particle generating mechanism is developed to compensate the particles. Then, all the particles are integrated into the SMC-PHD filter framework. Simulation results demonstrate that, in comparison with the SMC-PHD filter, proposed PC-SMC-PHD filter is capable of overcoming the particle impoverishment problem, as well as improving the processing rate for a certain tracking accuracy in different scenarios.

A novel variable-lag probability hypothesis density smoother for multi-target tracking

It is understood that the forward-backward probability hypothesis density （PHD） smoothing algorithms proposed recently can significantly improve state estimation of targets. However, our analyses in this paper show that they cannot give a good cardinality （i.e., the number of targets） estimate. This is because backward smoothing ignores the effect of temporary track drop- ping caused by forward filtering and/or anomalous smoothing resulted from deaths of targets. To cope with such a problem, a novel PHD smoothing algorithm, called the variable-lag PHD smoother, in which a detection process used to identify whether the filtered cardinality varies within the smooth lag is added before backward smoothing, is developed here. The analytical results show that the proposed smoother can almost eliminate the influences of temporary track dropping and anomalous smoothing, while both the cardinality and the state estimations can significantly be improved. Simulation results on two multi-target tracking scenarios verify the effectiveness of the proposed smoother.

Self-consistent mean field approximation and application in three-flavor NJL model

In this study,we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio(NJL)model and compare it with the two-flavor NJL model.The self-consistent mean field approximation introduces a new parameter,α,that cannot be fixed in advance by the mean field approach itself.Due to the lack of experimental data,the parameter,α,is undetermined.Hence,it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation.αaffects numerous properties of the chiral phase transitions,such as the position of the phase transition point and the order of phase transition.Additionally,increasingαwill decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero.Finally,we observed thatαaffects the equation of state(EOS)of the quark matter,and the sound velocity can be calculated to determine the stiffness of the EOS,which provides a good basis for studying the neutron star mass-radius relationship.

Holographic Duals of Quark Gluon Plasmas with Unquenched Flavors

We review the construction of gravitational solutions holographically dual to N=1 quiver gauge theories with dynamical flavor multiplets.We focus on the D3-D7 construction and consider the finite temperature,finite quark chemical potential case where there is a charged black hole in the dual solution.Discussed physical outputs of the model include its thermodynamics (with susceptibilities) and general hydrodynamic properties.

Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram

We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors N_(f) and colors N_(c) using the Nambu-Jona-Lasinio(NJL) model of quarks in the Schwinger-Dyson equation framework,dressed with a color-flavor dependence of effective coupling.For fixed N_(f)=2 and varying N_(c),we observe that the dynamical chiral symmetry is broken when N_(c) exceeds its critical value N_(c)^(c)≈2.2.For a fixed N_(c)=3 and varying N_(f),we observe that the dynamical chiral symmetry is restored when Nf reaches its critical value N_r^(c)≈8.Strong interplay is observed between N_(c) and N_(f),i.e.,larger values of N_(c) tend to strengthen the dynamical generated quark mass and quark-antiquark condensate,while higher values of N_(f) suppress both parameters.We further sketch the quantum chromodynamics(QCD) phase diagram at a finite temperature T and quark chemical potential μ for various N_(c) and N_(f).At finite T and μ,we observe that the critical number of colors N_(c)^(c) is enhanced,whereas the critical number of flavors N_(f)^(c) is suppressed as T and μ increase.Consequently,the critical temperature T_(c),μ_(c),and co-ordinates of the critical endpoint(T_(c)^(E),μ_(c)^(E)) in the QCD phase diagram are enhanced as N_(c) increases and suppressed when N_(f) increases.Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions.