Nucleon propagator at finite temperature

We study the nucleon propagator at finite temperature in the framework of finite energy QCD sum rules. We find that the nucleon mass is approximately constant over a wide range of temperature, increasing sharply near the critical temperature for deconfinementT _c . The coupling of the nucleon to quarks is a monotonically decreasing function ofT, vanishing atT=T _c .     

QCD sum rule determination of the axial-vector coupling of the nucleon at finite temperature

A thermal QCD Finite Energy Sum Rule (FESR) is used to obtain the temperature dependence of the axial-vector coupling of the nucleon, g_A(T). We find that g_A(T) is essentially independent of T, in the very wide range 0≤T≤0.9 T_c, where T_c is the critical temperature. While g_A at T=0 is q²-independent, it develops a q² dependence at finite temperature. We then obtain the mean square radius associated with g_A and find that it diverges at T=T_c, thus signalling quark deconfinement. As a byproduct, we study the temperature dependence of the Goldberger-Treiman relation.     

Free Energies of Dilute Bose Gases: Upper Bound

We derive an upper bound on the free energy of a Bose gas at density ϱ and temperature T. In combination with the lower bound derived previously by Seiringer (Commun. Math. Phys. 279(3): 595–636, 2008), our result proves that in the low density limit, i.e., when a ³ ϱ≪1, where a denotes the scattering length of the pair-interaction potential, the leading term of Δf, the free energy difference per volume between interacting and ideal Bose gases, is equal to 4pa(2r²-[r-r_c]²₊)4\pi a(2\varrho^{2}-[\varrho-\varrho_{c}]^{2}_{+}). Here, ϱ _c (T) denotes the critical density for Bose–Einstein condensation (for the ideal Bose gas), and [⋅]₊=max {⋅,0} denotes the positive part.     

Production of the P-wave excited Bc-states through the Z0 boson decays

In Deng et al. (Eur. Phys. J. C 70:113, 2010), we have dealt with the production of the two color-singlet S-wave (c[`(b)])(c\bar{b})-quarkonium states B<sub>c</sub>(|(c[`(b)])₁[¹S₀]?)B_{c}(|(c\bar {b})_{\mathbf{1}}[^{1}S_{0}]\rangle) and B^*_c(|(c[`(b)])<sub>1</sub>[<sup>3</sup>S<sub>1</sub>]?)B^{*}_{c}(|(c\bar{b})_{\mathbf{1}}[^{3}S_{1}]\rangle) through the Z <sup>0</sup> boson decays. As an important sequential work, we make a further discussion on the production of the more complicated P-wave excited (c[`(b)])(c\bar{b})-quarkonium states, i.e. |(c[`(b)])<sub>1</sub>[<sup>1</sup>P<sub>1</sub>]?|(c\bar{b})_{\mathbf{1}}[^{1}P_{1}]\rangle and |(c[`(b)])₁[³P_J]?|(c\bar{b})_{\mathbf{1}}[^{3}P_{J}]\rangle (with J=(1,2,3)). More over, we also calculate the channel with the two color-octet quarkonium states |(c[`(b)])<sub>8</sub>[<sup>1</sup>S<sub>0</sub>]g?|(c\bar{b})_{\mathbf{8}}[^{1}S_{0}]g\rangle and |(c[`(b)])₈[³S₁]g?|(c\bar{b})_{\mathbf{8}}[^{3}S_{1}]g\rangle, whose contributions to the decay width maybe at the same order of magnitude as that of the color-singlet P-wave states according to the naive nonrelativistic quantum chromodynamics scaling rules. The P-wave states shall provide sizable contributions to the B _c production, whose decay width is about 20% of the total decay width \varGamma _{Z⁰? Bc}\varGamma _{Z^{0}\to B_{c}}. After summing up all the mentioned (c[`(b)])(c\bar {b})-quarkonium states’ contributions, we obtain \varGamma _{Z⁰? Bc}=235.9^+352.8_-122.0\varGamma _{Z^{0}\to B_{c}}=235.9^{+352.8}_{-122.0} KeV, where the errors are caused by the main sources of uncertainty.     

CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds

In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures, in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every h ? [-1,-\frac2?{n-1}n)h\in[-1,-\frac{2\sqrt{n-1}}{n}) can be realized as the constant curvature of a complete immersion of S₁^n-1×\mathbbRS_1^{n-1}\times \mathbb{R} in the (n + 1)-dimensional de Sitter space S₁ⁿ⁺¹\hbox{\bf S}_1^{n+1}. We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and 5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that can be extended to closed hypersurfaces.     

Magnetoelastic instability in the XXZ rings with next-nearest neighbour coupling

This paper numerically investigates the magnetoelastic instability in the S = 1/2 {XXZ} rings containing finite spins N with antiferromagnetic nearest-neighbour ({NN}) and next-nearest neighbour ({NNN}) coupling. It finds that, as the {NN} anisotropy Δ₁ equals the {NNN} anisotropy \varDelta₂, there exists a critical {NNN} coupling strength J₂^c(≈0.5), at which the systems always locate in dimerized phase for arbitrary large spring constant. As Δ₁ \ne Δ₂, the values of J₂^{\rm c} are dependent on N and the difference of (Δ₁-\varDelta₂).     

Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces

In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and B^{-\frac12,\frac12}₄{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS _ν ) has a unique global solution with initial data u₀ = (u₀^h, u₀³){u_0 = (u_0^h, u_0^3)} which satisfies ||u₀^h||_B exp(\fracCn⁴ ||u₀³||_B⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or ||u₀^h||_{B^{-\frac12,\frac12}4} exp(\fracCn⁴ ||u₀³||_{B^{-\frac12,\frac12}4}⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c ₀ sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner type spaces, [(L^p_t)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L²_{t, f})\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L ¹ function f(t).     

Upper Bounds for Coarsening for the Deep Quench Obstacle Problem

The deep quench obstacle problem models phase separation at low temperatures. During phase separation, domains of high and low concentration are formed, then coarsen or grow in average size. Of interest is the time dependence of the dominant length scales of the system. Relying on recent results by Novick-Cohen and Shishkov (Discrete Contin. Dyn. Syst. B 25:251–272, 2009), we demonstrate upper bounds for coarsening for the deep quench obstacle problem, with either constant or degenerate mobility. For the case of constant mobility, we obtain upper bounds of the form t ^1/3 at early times as well as at times t for which E(t) ￡ \frac(1-[`(u)]<sup>2</sup>)4E(t)\le\frac{(1-\overline{u}^{2})}{4}, where E(t) denotes the free energy. For the case of degenerate mobility, we get upper bounds of the form t <sup>1/3</sup> or t <sup>1/4</sup> at early times, depending on the value of E(0), as well as bounds of the form t <sup>1/4</sup> whenever E(t) ￡ \frac(1-[`(u)]²)4E(t)\le\frac{(1-\overline{u}^{2})}{4}.     

Correction of Cosmological Expansion to Angular Deflection of Light and Radar Echo Delay

The angular deflection of light and radar echo delay are famous results predicted by general relativity. The gravitational lensing problems depend on the deviation of light from its straight line path in its basic equation. Using the Robertson-McVittie spacetime metric, which coincides thoroughly with the Schwarzschild metric in the isotropic coordinate and the FLRW metric for curvature parameter k=0 when M=0, we discuss the correction of cosmological expansion to the angular deviation of light path and the radar echo delay. The deviation terms arising from the expansion of universe are found to be simply -\frac4GMr_minc²(\fracH₀²2c²r_min²)-\frac{4GM}{r_{\mathit{min}}c^{2}}(\frac{H_{0}^{2}}{2c^{2}}r_{\mathit{min}}^{2}) for angular deviation and \frac2H₀²3c³(r_A³+r_B³)\frac{2H_{0}^{2}}{3c^{3}}(r_{A}^{3}+r_{B}^{3}) for radar echo delay.     

MD simulation of concentrated polymer solutions: Structural relaxation near the glass transition

We examine by molecular dynamics simulations the relaxation of polymer-solvent mixtures close to the glass transition. The simulations employ a coarse-grained model in which polymers are represented by bead-spring chains and solvent particles by monomers. The interaction parameters between polymer and solvent are adjusted such that mixing is favored. We find that the mixtures have one glass transition temperature T _g or critical temperature T _c of mode-coupling theory (MCT). Both T _g and T _c (> T _g decrease with increasing solvent concentration . The decrease is linear for the concentrations studied (up to = 25%. Above T _c we explore the structure and relaxation of the polymer-solvent mixtures on cooling. We find that, if the polymer solution is compared to the pure polymer melt at the same T, local spatial correlations on the length scale of the first peak of the static structure factor S(q) are reduced. This difference between melt and solution is largely removed when comparing the S(q) of both systems at similar distance to the respective T _c. Near T _c we investigate dynamic correlation functions, such as the incoherent intermediate scattering function (t), mean-square displacements of the monomers and solvent particles, two non-Gaussian parameters, and the probability distribution P(ln r;t) of the logarithm of single-particle displacements. In accordance with MCT we find, for instance, that (t) obeys the time-temperature superposition principle and has relaxation times which are compatible with a power law increase close (but not too close) to T _c. In divergence to MCT, however, the increase of depends on the wavelength q, small q values having weaker increase than large ones. This decoupling of local and large-length scale relaxation could be related to the emergence of dynamic heterogeneity at low T. In the time window of the relaxation an analysis of P(ln r;t) reveals a double-peak structure close to T _c. The first peak correponds to “slow” particles (monomer or solvent) which have not moved much farther than 10% of their diameter in time t, whereas the second occurs at distances of the order of the particle diameter. These “fast” particles have succeeded in leaving their nearest-neighbor cage in time t. The simulation thus demonstrates that large fluctuations in particle mobility accompany the final structural relaxation of the cold polymer solution in the vicinity of the extrapolated T _c.     

Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate correlations parallel to the layering in the diagonally layered model with periodv=2, the so-called “general square lattice” model (GS). If the model has a finite critical temperature,T _c>0, we have a spontaneous magnetization belowT _c vanishing atT _c with the Ising exponent β=1/8. AtT _c correlations decay algebraically with critical exponnet η=1/4 and exponentially forT>T _c. In the frustrated case we have oscillatory behaviour superposed on the exponential decay where the wavevector of the oscillations changes at some “disorder temperature”T _D(>T _c) from commensurate to temperature-dependent in commensurate periods. If the critical temperature vanishes,T _c=0 we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index η=1/2, i.e.T=0 is thus a critical point.     

Laser-induced optical activity in range of Rydberg autoionizing states of xenon

Optical activity of xenon atoms in the vacuum UV range induced by circularly polarized laser light is studied theoretically. The optical activity arises in the vicinity of the autoionizing state 5p ⁵(² P _1/2)8s′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 as a result of its coupling via the laser field with the discrete state 5p ⁵(² P _3/2)7p $ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 . Polarization variations of the vacuum UV radiation upon its propagation through the atomic medium are calculated, and the possibility of controlling this polarization is discussed. Manifestations of nonresonant coupling of the discrete state with the broad autoionizing state 5p ⁵(² P _1/2)6d′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 induced by the overlap of the Rydberg autoionizing series in xenon are studied.     

Critical Hardy–Lieb–Thirring Inequalities for Fourth-Order Operators in Low Dimensions

This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality

Theoretical studies on intervalley splittings in Si/SiO<Subscript>2</Subscript> quantum dot structures

Using the coupled cluster method we investigatespin-s J ₁-J′ ₂ Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice for the two cases where the spin quantum number s = 1 and s = $\frac{3} {2}$\frac{3} {2}. With respect to an underlying square-lattice geometry the model has antiferromagnetic (J ₁ > 0) bonds between nearest neighbours and competing (J′ ₂ > 0) bonds between next-nearest neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry, the model has two types of nearest-neighbour bonds: namely the J′ ₂ ≡ κJ ₁ bonds along parallel chains and the J ₁ bonds producing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one limit (κ = 0) and a set of decoupled chains at the other limit (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For both the spin-1 model and the spin-$\frac{3} {2}$\frac{3} {2} model we find a second-order type of quantum phase transition at κ _c = 0.615 ± 0.010 and κ _c = 0.575 ± 0.005 respectively, between a Néel antiferromagnetic state and a helically ordered state. In both cases the ground-state energy E and its first derivative dE/dκ are continuous at κ = κ _c , while the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition. The phase transition at κ = κ _c between the Néel antiferromagnetic phase and the helical phase for both the s = 1 and s = $\frac{3} {2}$\frac{3} {2} cases is analogous to that also observed in our previous work for the s = $\frac{1} {2}$\frac{1} {2} case at a value κ _c = 0.80 ± 0.01. However, for the higher spin values the transition appears to be of continuous (second-order) type, exactly as in the classical case, whereas for the s = $\frac{1} {2}$\frac{1} {2} case it appears to be weakly first-order in nature (although a second-order transition could not be ruled out entirely).     

A reanalysis of finite temperature <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

We revise the SU(N _c ), N _c =3,4,6, lattice data on pure gauge theories at finite temperature by means of a quasi-particle approach. In particular, we focus on the relation between the effective mass of the quasi-particle and the order of the deconfinement transition, the scaling of the interaction measure with N²_c -1N^{2}_{c} -1, the role of gluon condensate, and the screening mass.     

Enhancement of superconductivity by an external magnetic field in magnetic alloys

An infinite-volume limit solution of the thermodynamics of a BCS superconductor containing spin 1/2 and 7/2 magnetic impurities, obtained recently in [D. Borycki, J. Ma?kowiak, Supercond. Sci. Technol. 24, 035007 (2011)] is exploited to derive the expressions for critical magnetic field $\mathcal{H}_c$ (T). The credibility of the resulting thermodynamically limited theoretical equations, which depend on the magnetic coupling constant g and impurity concentration c, is verified on the experimental data for the following superconducting alloys: LaCe, ThGd and SmRh₄B₄. Good quantitative agreement with experimental data is found for sufficiently small values of c. The discrepancies between theoretical and experimental values of $\mathcal{H}_c$ (T) for larger values of c in case of LaCe and ThGd are reduced by introducing the concept of the effective temperature $\tilde T$ , which accounts for the Coulomb interactions between the electron gas and impurity ions. At low temperatures, the critical magnetic field is found to increase with decreasing temperature T. This enhancement of the critical magnetic field provides evidence of the Jaccarino-Peter effect, which was experimentally observed in the Kondo systems like LaCe, (La_{1 ? x} Ce _x )Al₂ and also in the pseudoternary compounds, including Sn_{1 ? x} Eu _x Mo₆S₈, Pb_{1 ? x} Eu _x Mo₆S₈ and La_{1.2 ? x} Eu _x Mo₆S₈. The effect of an external magnetic field $\mathcal{H}$ on a BCS superconductor perturbed by magnetic impurities was also studied. On these grounds, by analyzing the dependence of superconducting transition temperature T _c on $\mathcal{H}$ of (La_{1 ? x} Ce _x )Al₂, we have shown, that for certain parameter values, external magnetic field compensates the destructive effect of magnetic impurities.     

Stable multiquark states with heavy quarks in a diquark model

Based on the color–spin interaction in diquarks, we argue why some multiquark configurations could be stable against strong decay when heavy quarks are included. After showing the stability of previously discussed states we identify new possible stable states. These are the T⁰_cb(ud[`(c)][`(b)])T^{0}_{cb}(ud\bar{c}\bar{b}) tetraquark, the \varTheta _bs(udus[`(b)])\varTheta _{bs}(udus\bar{b}) pentaquark and the H _c (udusuc) dibaryon, and so forth.     

Holographic superconductor models in the non-minimal derivative coupling theory

We study a general class of holographic superconductor models via the Stu¨ckelberg mechanism in the non-minimal derivative coupling theory in which the charged scalar field is kinetically coupling to Einstein’s tensor. We explore the effects of the coupling parameter on the critical temperature, the order of phase transitions and the critical expo- nents near the second-order phase transition point. Moreover, we compute the electrical conductivity using the probe approximation and check the ratios ω g /T c for the different coupling parameters.     

Superconductivity and Peierls instability in coupled linear chain systems

We study the superconducting transition temperature (T_c) and the Peierls instability temperature (T_p) using Eliashberg type equations for both T_c and T_p self consistently with finite interchain coupling. We show that T_c > T_p below a critical electron-phonon coupling constant which depends on the bare phonon frequency. This determines an upper bound on T_c so that for higher transition temperatures T_p > T_c and superconductivity is unlikely. Higher values of T_c are possible if the interchain coupling is increased above a critical value where the Peierls instability is suppressed.