Mean-field theory of critical phenomenon for mutually repelling particles in complex plasmas

A mean-field theory of criticality for charged particles in complex plasmas is proposed. It is shown that the existence of the critical point and the liquid-vapor coexistence is fully consistent with a purely repulsive potential between particles; the cohesive field due to the plasma background drives these. The critical exponents, calculated by expanding the free energy near the critical point, are found to be classical. The phase coexistence curve, obtained by minimizing Gibbs potential, is similar to that of other mean-field models, e.g., van der Waals fluids, ionic fluids, etc. These results lend support to the concept of "universality" in widely different systems.     

Mean-field kinetic theory of a classical electron gas in a periodic potential. I. Formal solution of the Vlasov equation

We study the static and dynamic behavior of a classical electron gas in the periodic potential created by an ionic lattice. Using the well-known Vlasov approximation, we derive a mean-field kinetic equation for the density-response function of the electrons. This equation is formally solved in terms of the trajectories of one electron in the mean-field equilibrium potential which determines the local electronic density. The mean-field expressions of the static and dynamic structure factors are then obtained through the fluctuation-dissipation theorem. These expressions are used to show that within the mean-field approximation the system is a conductor at all temperatures and for all dimensions.     

Effects of the Fluctuations on Thermodynamic Properties of the Mixed Valence Compounds

Based on the SU(Nd) Anderson lattice mode1 in the slave boson formalism, westudy the effect of fluctuations around the saddle-point approximation on the thermodynamic properties for mixed valence lattice systems. The fluctuation component of slave boson field is explicitly introduced and its interactions with electrons are studied. By using the Green's function technique we obtain modified self-consistent equations of mean-field parameters and free energy. The fluctuation correction to the pseudophase transition temperature is obtained, and the validity of the mean-field approximation is examined. In the limit of low energy and small moment um transfer, a fluctuation correction to the specific heat proportional to T3 lnT at low temperature is extracted. The chemical potential shift is also studied. In order to describe the thermodynamic properties correctly, it is important to determine the chemical potential shift properly.     

Local magnetic moment in the two-dimensional reduced p-d model

A two-dimensional reduced p-d model describing CuO₂ sheets in high-T_c oxides is studied by use of the composite operator approach. A set of self-consistent equations for the Green function is derived in a generalized mean-field approximation for the paramagnetic state. The results show a good agreement with the exact results obtained by numerical simulations on finite size lattices.     

Density dependence of the single-particle potential in nuclear matter

The single-particle potential in infinite nuclear matter is computed as a function of density and energy in a variety of relativistic mean-field models of nuclear matter. A comparison of this potential is made with that computed by Friedman and Pandharipande using the variational method. We also show that the self-consistent mean-field Hartree approximation satisfies the Hugenholtz-van Hove theorem. High-density behavior of the single-particle potential is considered.     

Mean-Field Dynamics of a Two-Mode Bose-Einstein Condensate Subject to Decoherence

We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherenee （or particle loss）. Starting from the full many-body dynamics described by the master equation, an effective Gross- Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.     

Phase diagram of the fcc(1 1 0) surfaces with adsorbate-induced missing-row reconstructions

The phase diagram of the fcc(1 1 0) surfaces with missing-row reconstructions induced by adatoms, is calculated by use of the Blume–Emmery–Griffiths model. In the model, we introduce adatom–adatom interactions to determine surface structures and dipole–dipole interactions to describe the effect of zigzag adsorption. The interactions between nearest-neighbor (NN) and next-nearest-neighbor (NNN) rows are considered. The calculation of the temperature versus adatom chemical potential phase diagram is performed using mean-field approximation. It is indicated that if NN and NNN interactions are competitive, there appear either dipole or coverage modulated (incommensurate) phases at high temperatures for a wide range of the interactions.     

On the independent particle approximation of gauge theories

In this work the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1+1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed.     

Quark matter properties and fluctuations of conserved charges in (2+1)-flavored quark model

In this study, the susceptibilities of conserved charges, baryon number, charge number, and strangeness number at zero and low values of chemical potential are presented. Taylor series expansion was used to obtain results for the three-flavor Polyakov quark meson (PQM) model and the Polyakov loop extended chiral quark mean-field (PCQMF) model. Mean-field approximation was used to study quark matter with the inclusion of the isospin chemical potential, as well as the vector interactions. The effects of isospin chemical potential and vector-interactions on phase diagrams were analyzed. A comparative analysis of the two models was completed. Fluctuations of the conserved charges were enhanced in the transition temperature regime and hence provided information about the critical end point (CEP). Susceptibilities of conserved quantities were calculated by using the Taylor series method. Enhancement of fluctuations in the transition temperature neighborhood provided a clear signature of a quantum chromodynamics (QCD) critical-point.     

An Approximation for the Density Matrix in Calculations of the Mean-Field Potential of the Interaction of Nuclei

An approximation has been proposed for the nucleus single-particle density matrix in calculating the exchange component of the mean-field potential in the double-folding model. The method is based on the pseudo-oscillator representation of the density matrix and makes it possible to separate single-particle and internucleon variables, which greatly simplifies and accelerates the process of calculating the mean-field potential. Test calculations based on examples of alpha-particle interactions with ¹²C, ¹⁶O, and ⁴⁰Ca nuclei have shown the adequacy of the proposed approximation.     

Mean-field theory of the three-state chiral clock model

The phase diagram of the three-state chiral clock model, which is known to exhibit commensurate and incommensurate ordered modulated structures, is investigated in the mean-field approximation. First a numerical analysis of the mean-field equations is presented. It is based in the main on the observation that these equations define a non-linear mapping in a four dimensional space. This method of analyzing the mean-field theory proves particularly useful in the determination of the pinning transition of the incommensurate structures. Next the phase diagram is investigated analytically by means of a Landau expansion modified such as to include domain walls. It is found that in the vicinity of the order-disorder transition most features of the phase diagram can be explained quantitatively by this expansion. Finally we present a systematic lowtemperature expansion of the mean-field theory, showing that the low-temperature phase diagram obtained in the mean-field approximation is different from that of the full model.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Phase transitions and ordering of confined dipolar fluids

We apply a modified mean-field density functional theory to determine the phase behavior of Stockmayer fluids in slit-like pores formed by two walls with identical substrate potentials. Based on the Carnahan-Starling equation of state, a fundamental-measure theory is employed to incorporate the effects of short-ranged hard-sphere-like correlations while the long-ranged contributions to the fluid interaction potential are treated perturbatively. The liquid-vapor, ferromagnetic-liquid-vapor, and ferromagnetic-liquid-isotropic-liquid first-order phase separations are investigated. The local orientational structure of the anisotropic and inhomogeneous ferromagnetic liquid phase is also studied. We discuss how the phase diagrams are shifted and distorted upon varying the pore width.     

Slave-Boson Mean-Field Theory of Spin- and Orbital- Ordered States in the Degenerate Hubbard Model

The mean-field theory with the use of the slave-boson functional method has been generalized to take account of the spin- and/or orbital-ordered state in the doubly degenerate Hubbard model. Numerical calculations are presented of the antiferromagnetic orbital-ordered state in the half-filled simple-cubic model. The orbital order in the present theory is much reduced compared with that in the Hartree–Fock approximation because of the large orbital fluctuations. From a comparison of the ground-state energy, the antiferromagnetic orbital state is shown to be unstable against the antiferromagnetic spin state, although the situation becomes reversed when the exchange interaction is negative.     

Phase separation in a lattice model of a superconductor with pair hopping

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have a possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d = 1) in the ground state. Moreover, at T = 0 some results derived within the random phase approximation (and the spin-wave approximation) for d = 2 and 3 lattices and within the low-density expansions for d = 3 lattices are presented. Our investigation of the general case (as a function of the electron concentration n and as a function of the chemical potential μ) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases, superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.     

Analytic Approximations for the Velocity of Field-Driven Ising Interfaces

We present analytic approximations for the field, temperature, and orientation dependences of the interface velocity in a two-dimensional kinetic Ising model in a nonzero field. The model, which has nonconserved order parameter, is useful for ferromagnets, ferroelectrics, and other systems undergoing order–disorder phase transformations driven by a bulk free-energy difference. The solid-on-solid (SOS) approximation for the microscopic surface structure is used to estimate mean spin-class populations, from which the mean interface velocity can be obtained for any specific single-spin-flip dynamic. This linear-response approximation remains accurate for higher temperatures than the single-step and polynuclear growth models, while it reduces to these in the appropriate low-temperature limits. The equilibrium SOS approximation is generalized by mean-field arguments to obtain field-dependent spin-class populations for moving interfaces, and thereby a nonlinear-response approximation for the velocity. The analytic results for the interface velocity and the spin-class populations are compared with Monte Carlo simulations. Excellent agreement is found in a wide range of field, temperature, and interface orientation.     

Magnetic hysteresis in the generalized mean-field model for Ising system

Magnetic hysteresis and demagnetization of a simple cubic lattice of Ising spins is studied in the framework of the generalized mean-field approximation taking into account spatial fluctuations of the local magnetic field. The existence of a dynamic phase transition is demonstrated.     

Heterogenous mean-field analysis of a generalized voter-like model on networks

We propose a generalized framework for the study of voter models in complex networks at the heterogeneous mean-field (HMF) level that (i) yields a unified picture for existing copy/invasion processes and (ii) allows for the introduction of further heterogeneity through degree-selectivity rules. In the context of the HMF approximation, our model is capable of providing straightforward estimates for central quantities such as the exit probability and the consensus/fixation time, based on the statistical properties of the complex network alone. The HMF approach has the advantage of being readily applicable also in those cases in which exact solutions are difficult to work out. Finally, the unified formalism allows one to understand previously proposed voter-like processes as simple limits of the generalized model.     

两味LOFF态下的色超导

自从色超导理论被提出以来, 通常考虑的是参与配对的夸克的化学势不相等时的情形。 当化学势的差别达到某一合适值时, 库柏对就有非零的总动量, 这就是Larkin Ovchinnikov Fulde Ferre(LOFF)态。 这种形式的夸克凝聚自发破坏了平移不变性和旋转不变性, 导致能隙以晶格的形式周期性变化。 在中等重子数密度区的基础上, 从SU（2） NJL模型出发描述两味LOFF态, 并通过平均场近似, 引用N G基底、 傅立叶变换和频率求和等方法得到热力学势, 进而通过热力学势对序参量求偏导得到耦合的Gap方程, 并使用数值法解耦合方程找到LOFF态的窗口。 Ever since the theory of color superconductivity was issued, it is likely to involve pairing between species of quarks with differing chemical potentials. For suitable values of the differences between chemical potentials, Cooper pairs with non zero total momentum are favored, as was first realized by Larkin, Ovchinnikov, Fulde and Ferrell (LOFF). Condensates of this sort spontaneously break translational and rotational invariance, leading to gaps which vary periodically in a crystalline pattern. This article focuses on the two flavor color superconducting phase at moderate baryon density. LOFF state is described through SU(2) NJL model. By using the mean field approximation, N G basis, fourier transformation, frequency summation, the thermodynamic potential and Gap equation are obtained. Finally, the window of LOFF state is found by the numerical method.     

Multistability of impact, utility and threshold concepts of binary choice models

The decision making problem in the context of binary choice is considered by means of impact function, utility function and threshold model approaches. The properties of generalized impact function and utility function are examined; it is shown that these two approaches are equivalent. Their relation to the threshold model is studied and the correspondence between respective cumulative distribution functions is displayed. The stationary state corresponding to the thermodynamic equilibrium is determined within mean field approximation. Multistability of the stationary state is expressed in terms of the distribution function of the random variable of impact/utility function. The correspondence with statistical physics predictions for Ising model is discussed: logistic distribution leads to the mean-field result, i.e. Curie-Weiss approximation. Variations of the distribution functions and/or other model parameters, of social character, self-support, nonlinearity of social interactions, etc., would break the direct correspondence to statistical physics of Ising model, leading in particular cases to richer structure of the multistability.