Model In Mean-field Approximation Research Articles

Thermodynamics from the quark condensate

We present a method to compute thermodynamic quantities within functional continuum frameworks that is independent of the employed truncation. As a proof of principle, we first apply it to a Nambu-Jona-Lasinio model in mean-field approximation. Then, we use the method with solutions obtained from a coupled set of truncated Dyson-Schwinger equations for the quark and gluon propagators of ($2+1$)-flavor quantum chromodynamics in Landau gauge to obtain the pressure, entropy density, energy density, and interaction measure across the phase diagram of strong-interaction matter. We also discuss the limitation of the proposed method.

Jahn–Teller Distortion in Two-Orbital Model for s±-Wave Iron-Based Superconductors

The theoretical aspects of research on the role of Jahn–Teller (JT) interactions in quasi-two-dimensional iron-based high-[Formula: see text] superconductors are analyzed. A model Hamiltonian for the JT distortion in iron-based superconductors is proposed by a tight-binding two-orbital model. We have proposed here a [Formula: see text]-wave pairing symmetry of the form [Formula: see text] in the model in mean-field approximation. The model is solved by Zubarev’s double-time Green’s function technique to find the self-consistent gap equation and is solved self-consistently. The lattice strain energy, specific heat, conduction electron density of states and energy band structure for the system are calculated.

Inhomogeneous chiral condensates in three-flavor quark matter

We investigate the effect of strange quark degrees of freedom on the formation of inhomogeneous chiral condensates in a three-flavor Nambu--Jona-Lasinio model in mean-field approximation. A Ginzburg-Landau study complemented by a stability analysis allow us to determine in a general way the location of the critical and Lifshitz points, together with the phase boundary where the (partially) chirally restored phase becomes unstable against developing inhomogeneities, without resorting to specific assumptions on the shape of the chiral condensate. We discuss the resulting phase structure and study the influence of the bare strange-quark mass $m_s$ and the axial anomaly on the size and location of the inhomogeneous phase compared to the first-order transition associated with homogeneous matter. We find that, as a consequence of the axial anomaly, critical and Lifshitz point split. For realistic strange-quark masses the effect is however very small and becomes sizeable only for small values of $m_s$.

Antiferromagnetism in two-orbital model for s ± -wave iron based superconductors

In iron based superconductors the superconducting phase occurs near the onset of antiferromagnetism order. Unconventional superconductivity has led to extensive experimental and theoretical studies on the effect of electron correlations and on the nature of magnetism in iron based superconductors. For the study of antiferromagnetism in these superconductors we have proposed a tight-binding two-orbital model Hamiltonian. We have proposed here a s±-wave pairing symmetry of the form coskx × cosky in the model in mean-field approximation. The model is solved by Zubarev’s double-time Green’s function technique to find the self-consistent gap equation and is solved self-consistently numerically. The antiferromagnetism gap, specific heat, conduction electron density of states and energy band structure for the system are calculated.

Properties of Neutron stars with hyperon cores in parametrized hydrostatic conditions

Models of neutron stars (NSs) with hyperon cores are constructed with an effective chiral model in mean-field approximation. The hyperon couplings are fixed by reproducing their experimentally determined binding energies. The impact of these couplings on population of different particles and the equation of state (EoS) are studied in this work. The global properties of NSs like gravitational mass, radius, baryonic mass and central density are calculated using parametrized Tolman–Oppenheimer–Volkoff equations (PTOVs) with special emphasis on two effects of pressure — one contributing to total mass density and the other to self-gravity of the star. We find that with PTOV solutions in static conditions, a softer EoS (including hyperons) can also lead to massive stellar configurations of NSs, which are in good agreement with the observed maximum mass bound of [Formula: see text] (PSR J0348-0432). Estimates of [Formula: see text] and [Formula: see text], obtained with the PTOV equations, are consistent with the recent findings of the same from the data analysis of gravitational waves (GW170817) observation.

Observation of Subradiant Atomic Momentum States with Bose-Einstein Condensates in a Recoil Resolving Optical Ring Resonator.

We experimentally investigate the formation of subradiant atomic momentum states in Bose-Einstein condensates inside a recoil resolving optical ring resonator according to the theoretical proposal of Cola, Bigerni, and Piovella. The atoms are pumped from the side with laser light that contains two frequency components. They resonantly drive cavity assisted Raman transitions between three discreet atomic momentum states. Within a few hundred microseconds, the system evolves into a stationary subradiant state. In this state, the condensate develops two density gratings suitable to diffract the two frequency components of the pump field into the resonator. Both components destructively interfere such that scattering is efficiently suppressed. A series of subradiant states for various amplitude ratios of the two pump components between 0 and 2.1 have been observed. The results are well explained with a three state quantum model in mean field approximation.

Enhanced antiferromagnetic transition and magnetodielectric study in cobalt and holmium co-substituted multiferroic Bi2Fe4O9

The search for new room temperature magnetoelectric materials for future multifunctional device application is the motivation behind the preparation of polycrystalline Bi2(1−x)Ho2xFe4(1−y)Co4yO9 (x = y = 0; x = 0, y = 0.02; x = 0.02, y = 0 and x = y = 0.02) ceramics. Along with substantial variation in antiferromagnetic transition (TN) in substituted samples (BFCO2, BHFO2), the co-substituted sample (BHFCO2) shows an enhanced TN at room temperature i.e. 288 K as compared to parent BFO (250 K). All the samples except BHFO2, depicts a clear irreversibility in ZFC-FCW for T < 360 K along with an opening in MH curves, thus indicating the onset of weak ferromagnetism associated with magnetic glassiness in the studied samples. The dielectric measurements reveal an unusual oppression/hump around TN, thereby providing evidence of magnetodielectric (MD) coupling, without any possibility of magnetoresistance. Moreover, a dielectric crossover at T ∼ 200 K is seen for BHFO2 and BHFCO2 while the mechanism is explained using a mean-field approximation model, thus validating the presence of isolated defects due to Ho3+. Lastly, all the samples are subjected to MD study, where the co-substituted sample exhibited ∼ −0.4% (∼7.5 times) of MD% effect at 288 K as compared to BFO (∼ −0.06%). Confirmation to the MD coupling is further established from MD% versus T plot and MD% versus H plot where later is found to obey behavior, with ‘m’ value being comparable to exponent (1-p) of thermoremanent magnetization.

Isolation and Characterization of Few-Layer Manganese Thiophosphite.

This work reports an experimental study on an antiferromagnetic honeycomb lattice of MnPS3 that couples the valley degree of freedom to a macroscopic antiferromagnetic order. The crystal structure of MnPS3 is identified by high-resolution scanning transmission electron microscopy. Layer-dependent angle-resolved polarized Raman fingerprints of the MnPS3 crystal are obtained, and the Raman peak at 383 cm-1 exhibits 100% polarity. Temperature dependences of anisotropic magnetic susceptibility of the MnPS3 crystal are measured in a superconducting quantum interference device. Anisotropic behaviors of the magnetic moment are explored on the basis of the mean field approximation model. Ambipolar electronic conducting channels in MnPS3 are realized by the liquid gating technique. The conducting channel of MnPS3 offers a platform for exploring the spin/valleytronics and magnetic orders in 2D limitation.

Effect of Holmium substitution on the magnetic and magnetodielectric properties of multiferroic Bi2Fe4O9

In the quest for deriving new multiferroics from the existing ones, we have prepared and studied polycrystalline Bi2(1-x)Ho2xFe4O9 (0 ≤ x ≤ 0.02) ceramics. A substantial increase in the Néel temperature (TN) from 250 K (x = 0, BFO) to 266 K (x = 0.02, BHFO2) is observed for Ho-substituted samples. The magnetization measurements suggest that Ho3+ goes as isolated magnetic defects and interaction among them is reflected only when the temperature goes below 70 K. Interestingly, the Néel temperature is not clearly visible in the magnetization-temperature plot due to its masking by the high moment of isolated Ho3+ ions, but TN is very clearly reflected in the dielectric plot, thus indicating a plausible coupling between the magnetic and electric order parameters. Also, a dielectric crossover at T ∼ 200 K is observed for Ho3+ substituted samples and explained using a mean-field approximation model, thereby validating the presence of isolated defects arising due to Ho3+ substitution. At the same time, an enhanced magnetodielectric (MD) effect at 200 K i.e., ∼−1.6% (∼530 times) for BHFO2 is discerned as compared to BFO. Furthermore, confirmation to this coupling is drawn from MD% versus T plot and MD% versus H plot, where the latter is found to obey ∝(H)m behaviour.

Computational Simulation of Thermal and Chemical Phenomena for Honeycomb-Structured Catalytic Reforming Reactor

A fully coupled numerical model for solid and fluid phases is developed to investigate the performance of catalytic reforming reactors. The transport of mass, momentum, energy and species in a reforming reactor are simultaneously solved using a three dimensional fully implicit unstructured finite volume approach. The nonlinear system of equations is solved by Newton’s method. Eight gas-phase species (CH4, CO2, H2O, N2, O2, CO, OH and H2) are considered for the simulation. The surface chemistry is modeled by detailed reaction mechanisms including 38 heterogeneous reactions with 20 surface-adsorbed species for rhodium catalyst and solved using the mean-field approximation model to obtain the surface convergence and reaction rates. The numerical results are compared with the experimental data and good agreement is observed. The simulation is performed for two different honeycomb-structured reactors. The governing equations for fluid and solid regions of the monolith are simultaneously solved with considering the catalytic combustion at their interface. The performance of the reforming reactor is numerically studied.

Computational Simulation of Thermal and Chemical Phenomena for a Honeycomb-Structured Catalytic Reforming Reactor

A fully coupled numerical simulation is used to investigate the catalytic partial oxidation of methane over a honeycomb-structured Rh/Al2O3 coated catalyst. The transport of mass, momentum, energy and species in a reforming reactor are simultaneously solved using a three dimensional fully implicit unstructured finite volume approach. The nonlinear system of equations is solved by Newton’s method. Eight gas-phase species (CH4, CO2, H2O, N2, O2, CO, OH and H2) are considered for the simulation. The surface chemistry is modeled by detailed reaction mechanisms including 38 heterogeneous reactions with 20 surface-adsorbed species for rhodium catalyst and solved using the mean-field approximation model to obtain the surface convergence and reaction rates. The numerical results are compared with the experimental data and good agreement is observed. The simulation is performed for a reforming reactor with a channel density of 600 cpsi (channels per square inch). The governing equations for fluid and solid regions of the monolith are simultaneously solved with considering the catalytic combustion at their interface. The performance of the reforming reactor is numerically studied. A finite element approach is used to obtain the thermal stresses based on the temperature field obtained from the solid/fluid FVM solver. Figure 1

Statistical description of the system electrons on the liquid helium surface

It is known that homogeneous distribution of particles in Coulomb-like systems can be unstable, and spatially inhomogeneous structures can be formed. A simple method for describing such inhomogeneous systems and obtaining spacial distributions of electron density is proposed and applied to the case of two-dimensional electron systems on surface of liquid helium. A free energy functional for the model in mean field approximation is obtained. Creation of various types of structures, such as long-range periodical modulation and multi-electron dimples, is predicted by minimizing this functional.

T-t'-J-U Model in Mean-Field Approximation: Coexistence of Superconductivity and Antiferromagnetism

We discuss the $t$-$J$-$U$ model in the mean-field approximation. The role of spin-exchange coupling $J$ and the second nearest hopping $t'$ are examined in the context of the coexistence of superconductivity (SC) and antiferromagnetism (AF). Stability of the phases is studied with respect to temperature. The coexistence region exists for the sufficiently large Coulomb repulsion ($U>U_{cr}$), and in the vicinity of the half-filled band (hole doping $\delta < \delta_{cr}$). The critical hole doping is relatively small ($\delta_{cr} \approx 0.006$ for $J/|t| = 1/3$) and linear with respect to $J$. The decrease of $U_{cr}$ is proportional to $J$, except the limit of small $J$ ($J/|t|< 0.03)$, where $U_{cr}$ grows rapidly with decreasing $J$. The effect of the second nearest hopping is limited -- the phase diagram does not change in a qualitative manner when the $t'$ value is changed. In the limit of $T \rightarrow 0$, SC phase is stable even for large hole-doping (such as $\delta = 0.5$). Additional paramagnetic (PM) phase appears for large $\delta$ or small $U$ at non-zero temperature. When temperature increases, both SC and AF+SC phase regions are reduced.

Dynamical diversity induced by individual responsive immunization

A voluntary vaccination allows for a healthy individual to choose vaccination according to the individual’s local information. Hence, vaccination has the potential to provide a complex negative feedback (non-infection decreases propensity for vaccination, hence increasing infection and vice versa). In this paper, we investigate a kind of SIS epidemic model with a deterministic and voluntary vaccination scheme in scale-free networks. We first study a threshold model with no historical information. By using the comparative method we confirm that under some conditions there exist two critical values of infection rates to determine three kinds of epidemic dynamical behaviors: the epidemic spread, the asymptotical decay and the exponential decay. Furthermore, a mean-field approximation model can predict the maximal infection level but cannot predict the existence of two critical infection rates. In numerical simulations, we observe a maximum in epidemic duration as a function of the model parameter. A similar phenomenon has been found in the model with historical information. Finally, we study a degree-weighted model with a nonnegative exponent α where α=0 corresponds to the threshold model. We find that at the steady state the infection density increases with α, while the variation of the vaccination fraction is less straightforward.

Electronic Structure and Magnetic Properties of Doped GaAs (Zinc Blende) with Double Impurities and Defects

Using ab-initio calculations based on Korringa- Kohn-Rostoker coherent potential approximation (KKR- CPA) method in connection with the local density approx- imation (LDA), we study theoretically the electronic and magnetic properties of a system based on GaAs material. These properties have been studied, with different point de- fects in GaAs, which are Gallium interstitials (Gai), Gal- lium antisites (GaAs), Gallium vacancies (VGa), Arsenic in- terstitials (Asi) and Arsenic antisites (AsGa), Arsenic vacan- cies (VAs), and in-doped or codoped system Ga1−xCoxAs and Ga1−y−zCoyFezAs, respectively. This work presents de- tailed information about total and local density of states at different concentrations of these defects and doped ele- ments; the stability of the ferromagnetic state compared with the spin-glass state has been discussed. The result of elec- tronic properties shows that codoped GaAs material with Fe and Co become ferromagnetic, also doped GaAs with Co or Fe with a defect (hole in Ga) is stable in the ferromagnetic The Curie temperature is estimated from the total energy difference between the Disorder Local Moment (DLM) and the (FM) state by using a mapping on the Heisenberg model in mean field approximation.

Analytical derivation of critical exponents of the dynamic phase transition in the mean-field approximation

We have analyzed the dynamic phase transition of the kinetic Ising model in mean-field approximation by means of an analytical approach. Specifically, we study the evolution of the system under the simultaneous influence of time-dependent and time-independent magnetic fields. We demonstrate that within the approximate analytical treatment of our approach, the dynamic phase transition exhibits power-law dependencies for the order parameter that have the same critical exponents as the mean-field equilibrium case. Moreover we have obtained an equation of state, with which we can prove that the time-independent field component is effectively the conjugate field of the order parameter. Our analysis is limited to the parameter range, in which only second-order phase transitions occur, i.e., for small applied field amplitudes and temperatures close to the Curie point. In order to ensure the reliability of our analytical results we have corroborated them by comparison to numerical evaluations of the same model.

Freezing transition in the mean-field approximation model of pedestrian counter flow

We study the freezing transition in the counter flow of pedestrians within the channel numerically and analytically. We present the mean-field approximation (MFA) model for the pedestrian counter flow. The model is described in terms of a couple of nonlinear difference equations. The excluded-volume effect and bi-directionality are taken into account. The fundamental diagrams (current–density diagrams) are derived. When pedestrian density is higher than a critical value, the dynamical phase transition occurs from the free flow to the freezing (stopping) state. The critical density is derived by using the linear stability analysis. Also, the velocity and current (flow) at the steady state are derived analytically. The analytical result is consistent with that obtained by the numerical simulation.

Spontaneous polarization in the tetragonal, orthorhombic and rhombohedral phases of KNbO3

AbstractThe spontaneous polarization and the refractive indices in the tetragonal, orthorhombic and rhombohedral phases of KNbO3 are discussed quantitatively from the microscopic consideration. The shift of the Nb ion situated at the centre of the lattice is calculated at various temperatures from the mean field approximation model. The spontaneous polarization has been calculated by the dipole‐dipole model using the calculated values of the shift of the Nb ions, the vertical strains and the shearings. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Impact of baryon resonances on the chiral phase transition at finite temperature and density

We study the phase diagram of a generalized chiral SU(3)-flavour model in mean-field approximation. In particular, the influence of the baryon resonances, and their couplings to the scalar and vector fields, on the characteristics of the chiral phase transition as a function of temperature and baryon-chemical potential is investigated. Present and future finite-density lattice calculations might constrain the couplings of the fields to the baryons. The results are compared to recent lattice QCD calculations and it is shown that it is non-trivial to obtain, simultaneously, stable cold nuclear matter.

In Situ Dual-Beam Coincidence Second Harmonic Generation as a Probe of Spatially Resolved Dynamics at Electrochemical Interfaces

In situ dual-beam coincidence second harmonic generation was used to monitor spatially resolved dynamics at the Pt(111)/CO-saturated 0.1 M HClO4 interface. The results obtained showed that, for potential steps from 30 to about 870 mV vs RHE, the full electrooxidation of CO as evidenced from SHG occurred at different times for the two areas of the Pt(111) surface probed by the beams. On this basis, the diffusional rates of adsorbed CO cannot be assumed to be generally large enough as to render the entire surface in a homogeneous state, as invoked by the mean field approximation model.