Relationship between Oxygen Chemical Potential and Steel Cleanliness

To investigate inclusion formation in each step during steel making process, several samples were taken in different steps of the production of steel at Mobarakeh Steel Co of Esfahan to measure the oxygen chemical potential of the molten steel in each stage. The chemical compositions of the inclusions in samples were investigated by scanning electron microscope. The chemical composition of the slag was analyzed. With the use of thermodnamic calculations and chemical analysis of the melt, at the working temperature, the relationship between dissolved oxygen and other elements were determined. Finally, it was found that there is a close relationship between inclusions formed in each step with the oxygen partial pressure.

A Modified Approach for Calculating Dressed Quark Propagator at Finite Chemical Potential

Based on the rainbow approximation of Dyson-Schwinger equation and the assumption that the full inverse quark propagator at finite chemical potential is analytic in the neighborhood of μ = 1, it is proved that the dressed quark propagator at finite chemical potential μ can be written as G0^-1 [μ] =iγ·p↑-A（p↑-^2） ＋B（p↑-^2） with p↑-μ= （p↑-p4 ＋iμ）. From the dressed quark propagator at finite chemical potential in Munczek model the bag constant of a baryon and the scalar quark condensate are evaluated. A comparison with previous results is given.

Shear Viscosity of Hot QED at Finite Chemical Potential from Kubo Formula

Within the framework of finite temperature field theory this paper discusses the shear viscosity of hot QED plasma through Kubo formula at one-loop skeleton diagram level with a finite chemical potential The effective widths (damping rates) are introduced to regulate the pinch singularities and then gives a reliable estimation of the shear viscous coefficient.The finite chemical potential contributes positively compared to the pure temperature case. The result agrees with that from the kinetics theory qualitatively.

Effect of strong magnetic field on chemical potential and electron capture in magnetar

The chemical potential of electrons in a strong magnetic field is investigated. It is shown that the magnetic field has only a slight effect on electron chemical potential when B 〈 10^11 T, but electron chemical potential will decrease greatly when B 〉 10^11 T. The effects of a strong magnetic field on electron capture rates for ^60Fe are discussed, and the result shows that the electron capture sharply decreases because of the strong magnetic field.

Influence of Finite Chemical Potential on Critical Boson Mass in QED3

Using the coupled Dyson-Schwinger equation for the fermion propagator at finite chemical potential μ, we investigate the fermion chiral condensate when the gauge boson mass is nonzero in QED3. We show that the chiral symmetry restores when the boson mass is large enough, and the critical boson mass depends little on μ.

Analytic Method to Study Influence of Finite Chemical Potential in QED_3~*

Adopting the approximation to the first order of chemical potential μ, we resolve rigidly the influence on fermion condensate from μ in QED3. We show that this condensate does not respond linear expression to μ. Moreover, the influence on fermion chiral condensate from chemieal potential is investigated.

Renormalization of the chemical potential due to multiphonon effects at the surface of metals

We study the relation between renormalization of the chemical potential due to multiphonon effects at the surface of Be（0001） and doping by solving the strong-coupling self-consistent equations of a two-dimensional（2D） electron-phonon interaction system.We present the quasiparticle dispersions and inverse lifetimes of a 2D electron system interacting with Einstein phonons under the different dopings（corresponding to chemical potentials）.We find that the effect of electron-phonon interaction on electron structure is strongest at the half filling,but it has no effect on the chemical potential.However,the chemical potential shows distinct renormalization effects away from half filling due to the electron-phonon interaction.

Fermion-Boson Vertex at Finite Chemical Potential

Based on the Ward-Takahashi identity at finite chemical potential and Lorentz structure analyms, we generalize the Ball-Chiu vertex to the case of nonzero chemical potential and obtain the general form of the frmionboson vertex in QED at finite chemical potential.

Critical Number of Fermion Flavors at Finite Chemical Potential in QED3

We propose a new method for calculating the dressed fermion propagator at finite chemical potential in QED3 under the rainbow approximation of Dyson-Schwinger equation. In the above approximation, we show that the dressed fermion propagator at finite chemical potential # has the form S（p） = iγ.p^-A（p^-2） ＋ B（ p^-2） with p^-μ= （p^-1p3 ＋ iμ）. Using this form of fermion propagator at nonzero chemical potential, we investigate the Dyson-Schwinger equation for the dressed fermion propagator at finite chemical potential and study the effects of the chemical potential on the critical number of the fermion flavors.

Linear Chemical Potential Dependence of Two-Quark Condensate

By differentiating the inverse dressed quark propagator at finite chemical potential μ with respect to μ, the linear response of the dressed quark propagato r to the chemical potential can be obtained, From this we extract a modelindependent formula for the linear chemical potential dependence of the in-medium two-quark condensate and show by two independent methods （explicit calculation and Lorentz covariance arguments） that the first-order contribution in μ to the in-medium two-quark condensate vanishes identically. Therefore if one wants to study the in-medium two-quark condensate one should expand to at/east the second order in the chemical potential μ.

Dyson-Schwinger Equations of Chiral Chemical Potential

We discuss the chiral phase transition of quantum chromodynamics （QCD） with a chiral chemical potential μ5 as an additional scale. Within the framework of Dyson-Schwinger equations, we focus particularly on the behavior of the widely accepted as well as interesting critical end point （CEP）, using a separable gluon propagator and a Gaussian gluon propagator. We find that there may be no CEP5 in the T-μ5 plane, and the phase transition in the T μ5 plane might be totally crossover. Our results have apparent consistency with the Lattice QCD calculation. On the other hand, our study may also provide some useful hints to some other studies related to μ5.

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.

Chemical Potential Dependence of Vertices

Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the fermion-boson vertex in the neighborhood of zero chemical potential （μ = 0） and neglecting the #-dependence of the dressed gluon propagator, we apply the method in [Phys. Rev. C 71 （2005） 015205] of studying the dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ can also be obtained from the one at μ = 0 by a simple shift of variables. Using this result we extend the results of [Phys. Lett. B 420 （1998） 267] to the situation of finite chemical potential and show that under the approximations we have taken, the Gell-Mann Oakes-Renner relation also holds at finite chemical potential

Minimum-Modified Debye-Hückel Theory for Size-Asymmetric Electrolyte Solutions with Moderate Concentrations

A minimum-modified Debye-Hückel(DH)theory for electrolytes with size asymmetry is developed.Com-pared with the conventional DH theory,the minimum-modified DH theory only introduces an extra surface charge density to capture the electrostatic effect of the size asymmetry of the electrolytes and hence facilitates a boundary element method for electrostatic potential calculation.This theory can distinguish the electrostat-ic energies and excess chemical potentials of ions with the same sizes but opposite charges,and is applied to a binary primitive electrolyte solution with moderate electrostatic coupling.Compared with the hyper-netted chain theory,the validity of this modified DH theory demonstrates significant improvement over the conventional DH theory.

A Dynamical Approach to the Explanation of the Upper Critical Field Data of Compressed H3S

Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (Hc2(T)) data of H3S reported by Mozaffari et al. [Nature Communications 10, 2522 (2019)] by employing four alternative phenomenological models, each of which invoked two or more properties from its sample-specific set S1 = {Tc, gap, coherence length, penetration depth, jump in sp.ht.} and a single value of the effective mass (m*) of an electron. Based on the premise that the variation of Hc2(T) is due to the variation of the chemical potential μ(T), we report here fits to the same data by employing a T-, μ- and m*-dependent equation for Hc2(T) and three models of μ(T), viz. the linear, the parabolic and the concave-upward model. For temperatures up to which the data are available, each of these provides a good fit. However, for lower values of T, their predictions differ. Notably, the predicted values of Hc2(0) are much higher than in any of the models dealt with by Talantsev. In sum, we show here that the addressed data are explicable in a framework comprising the set S2 = {μ, m*, interaction parameter λm, Landau index NL}, which is altogether different from S1.

Compressed H3S: Fits to the Empirical Hc2(T) Data and a Discussion of the Meissner Effect

Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field Hc2(T), where μ, T and H denote the chemical potential, temperature and the applied field, respectively, we provide in this paper fits to the empirical Hc2(T) data of H3S reported by Mozaffari, et al. (2019) and deal with the issue of whether or not H3S exhibits the Meissner effect. Employing a variant of the template given by Dogan and Cohen (2021), we examine in detail the results of Hirsch and Marsiglio (2022) who have claimed that H3S does not exhibit the Meissner effect and Minkov, et al. (2023) who have claimed that it does. We are thus led to suggest that monitoring the chemical potential (equivalently, the number density of Cooper pairs Ns at T = Tc) should shed new light on the issue being addressed.

On the Role of Chemical Potential in Determining the Temperature Dependent Critical Magnetic Field and the Penetration Depth of Superconductors

Dealing with both elemental and high-Tc superconductors (SCs) - Sn, Nb and Pb belonging to the former category, and MgB2 and different samples of YBCO to the latter - we show that the difference in the values of their critical magnetic field Hc1,c2 and the penetration depth λL(0) is, remarkably, attributable predominantly to the difference in the values of a single parameter, viz., the chemical potential (μ) close to their critical temperatures (Tcs). Based directly on the dynamics of pairing in a magnetic field and the corresponding number equation, our approach relates Hc1,c2 of an SC with the following set of its properties: S1 = {μ, Tc, Debye temperature, effective mass of the electron, magnetic interaction parameter, Landau index}. Hence, it provides an alternative to the approach followed by Talantsev [Mod. Phys. Lett. B 33, 1950195 (2019)] who has shown by ingeniously combining the results of various well-established theories that Hc2 of an SC can be calculated via four different equations, each of which invokes two or more properties from its sample-specific set S2 = {Tc, gap, coherence length, λL(0), jump in sp. ht.}, which is radically different from S1.

Ion adsorption components in liquid/solid systems

Experiments on Zn^2＋ and Cd^2＋ adsorptions on vermiculite in aqueous solutions were conducted to investigate the widely observed adsorbent concentration effect on the traditionally defined adsorption isotherm in the adsorbate range 25--500 mg/L and adsorbent range 10--150 g/L. The results showed that the equilibrium ion adsorption density did not correspond to a unique equilibrium ion concentration in liquid phase. Three adsorbate/adsorbent ratios, the equilibrium adsorption density, the ratio of equilibrium adsorbate concentration in liquid phase to adsorbent concentration, and the ratio of initial adsorbate concentration to adsorbent concentration, were found to be related with unique values in the tested range. Based on the assumption that the equilibrium state of a liquid/solid adsorption system is determined by four mutually related components： adsorbate in liquid phase, adsorbate in solid phase, uncovered adsorption site and covered adsorption site, and that the equilibrium chemical potentials of these components should be equalized, a new model was presented for describing ion adsorption isotherm in liquid/solid systems. The proposed model fit well the experimental data obtained from the examined samples.

Hawking Radiation of Charged Particles in Reissner-Nordstrm Black Hole

We extend the method that Banerjee and Majhi have used to discuss Hawking radiation. Under the condition that the total energy and electrical charge of spacetime are conserved, we investigate Hawking radiation of the charged black hole by a new Tortoise coordinate transformation. Taking the reaction of the radiation of the particle to the spacetime into consideration, we not only derive the radiation spectrum that satisfies the unitary principle in quantum mechanics but also show that the contribution of ingoing particles is equal to the one of outgoing particles on the similar chemical potential term in radiation spectrum caused by charged particles.

Statistical Thermodynamic Properties of Linear Protein Solutions

The thermodynamic properties of linear protein solutions are discussed by a statistical me-chanics theory with a lattice model. The numerical results show that the Gibbs function of the solution decreases, and the protein chemical potential is enhanced with increase of the protein concentration for dilute solutions. The influences of chain length and temperature on the Gibbs function of the solution as well as the protein chemical potential are analyzed.As an application of the theory, the chemical potentials of some mutants of type I antifreeze proteins are computed and discussed.