On Factor Maps that Send Markov Measures to Gibbs Measures

Let X and Y be mixing shifts of finite type. Let π be a factor map from X to Y that is fiber-mixing, i.e., given \(x,\bar{x}\in X\) with \(\pi(x)=\pi(\bar{x})=y\in Y\), there is z∈π ^?1(y) that is left asymptotic to x and right asymptotic to \(\bar{x}\). We show that any Markov measure on X projects to a Gibbs measure on Y under π (for a Hölder continuous potential). In other words, all hidden Markov chains (i.e. sofic measures) realized by π are Gibbs measures. In 2003, Chazottes and Ugalde gave a sufficient condition for a sofic measure to be a Gibbs measure. Our sufficient condition generalizes their condition and is invariant under conjugacy and time reversal. We provide examples demonstrating our result.     

A New Set of Limiting Gibbs Measures for the Ising Model on a Cayley Tree

For the Ising model (with interaction constant J>0) on the Cayley tree of order k≥2 it is known that for the temperature T≥T _c,k =J/arctan?(1/k) the limiting Gibbs measure is unique, and for T<T _c,k there are uncountably many extreme Gibbs measures. In the Letter we show that if \(T\in(T_{c,\sqrt{k}}, T_{c,k_{0}})\), with \(\sqrt{k} then there is a new uncountable set \({\mathcal{G}}_{k,k_{0}}\) of Gibbs measures. Moreover \({\mathcal{G}}_{k,k_{0}}\ne {\mathcal{G}}_{k,k'_{0}}\), for k ₀≠k′₀. Therefore if \(T\in (T_{c,\sqrt{k}}, T_{c,\sqrt{k}+1})\), \(T_{c,\sqrt{k}+1} then the set of limiting Gibbs measures of the Ising model contains the set {known Gibbs measures}\(\cup(\bigcup_{k_{0}:\sqrt{k}.     

A study of the neutrino production of <Emphasis Type="Italic">φ</Emphasis> and <Emphasis Type="Italic">D</Emphasis><Stack><Subscript><Emphasis Type="Italic">s</Emphasis></Subscript><Superscript>+</Superscript></Stack> mesons

The charged current neutrino production of φ and D _s ⁺ mesons is studied, using the data obtained with the SKAT bubble chamber exposed to the Serpukhov accelerator neutrino beam. It is found that the φ production occurs predominantly in the forward hemisphere of the hadronic c.m.s. (at x _F > 0, x _F being the Feynman variable), with the mean yield strongly exceeding the expected yield of directly produced φ mesons and varying from 〈n _φ(x _F s 0)〉 = (0.92 ± 0.34) × 10^?2 at W > 2 GeV up to (1.23 ± 0.53) × 10^?2 at W > 2.6 GeV and (1.44 ± 0.69) × 10^?2 at W > 2.9 GeV, W being the invariant mass of the hadronic system. For the first time, the inclusive yield of leading D _s ⁺ mesons carrying more than z = 0.85 of the current c-quark energy is estimated: 〈n _{D s} ⁺ (z > 0.85, W > 2.9 GeV)〉 = (6.64 ± 1.91) × 10^?2. It is shown that the shape of measured φ meson differential spectrum on xF is reproduced by that expected from the D _s ⁺ → φX decays. An indication was obtained that this expected spectrum underestimates the measured φ yield.     

Energy and momentum losses of a magnetized plasma via familon emission

Familon emission from a dense magnetized plasma in the processes e^? → e^?φ and e^? → μ^?φ is investigated. The contribution of these processes to the energy losses of a supernova remnant is calculated. It is shown that, at a late stage of the cooling of a supernova remnant, the energy loss of a plasma via familon emission may become commensurate with the loss via neutrino emission. It is found that, because of asymmetry of familon emission in the process e^? → gm^?φ, there arises a force acting on the plasma.     

Coordinate asymptotic behavior of the radial three-particle wave function for a bound state involving two charged particles

The asymptotic expression for the radial component of the wave function for a three-particle bound state involving two charged particles is derived in an explicit form. This expression contains a three-particle asymptotic normalization factor C(φ), where φ is a hyperangle in the six-dimensional space of intrinsic coordinates of the three-particle system. The resulting expressions are used to analyze the asymptotic behavior of the wave functions for the ⁹Be nucleus that were calculated within the α + α + n three-particle model for various forms of the an potential. A comparison of the asymptotic expression derived here and the asymptotic expressions for model wave functions makes it possible to extract C(φ) values, which turned out to be sensitive to the form of αn interaction. This permits deducing information about two-particle interaction from a comparison of the theoretical values of C(α) with their phenomenological counterparts found from an analysis of experimental differential cross sections for relevant nuclear reactions.     

Local Geometry of the <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript> Moduli Space

We consider deformations of torsion-free G ₂ structures, defined by the G ₂-invariant 3-form φ and compute the expansion of \({\ast \varphi }\) to fourth order in the deformations of φ. By considering M-theory compactified on a G ₂ manifold, the G ₂ moduli space is naturally complexified, and we get a Kähler metric on it. Using the expansion of \({\ast \varphi }\), we work out the full curvature of this metric and relate it to the Yukawa coupling.     

Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas

We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a ₀ ? l _P (where l _P is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n _F ) to energy density ε(n _F ) dependent on the number density of fermions n _F . As the early Universe expands, the dimensionless quantity ν(n _F ) = P(n _F )/ε(n _F ) decreases with decreasing n _F from its maximum value ν_max = 1 for n _F → ∞ to zero for n _F → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n _F )–ε(n _F )–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R _c =–μ²/ξ and radius a _c ? a ₀. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G _N .     

The Generalization of Chern-Simons Current and the Topological Tensor Current of <Emphasis Type="Italic">p</Emphasis>-Branes

To make the gauge field theory foundation of the topological current of p-branes introduced in our previous work, we present a novel topological tensor current in SO(N) gauge field theory. This non-Abelian gauge field tensor current is the straightforward generalization of the Chern-Simons topological current of strings. By making use of the SO(N) gauge potential decomposition theory and the φ-mapping topological current theory, it is proved that the p-brane is created at every isolated zero of the Clifford vector field \(\overrightarrow{\phi }(x)\) and the charges carried by p-branes are topologically quantized and labelled by the winding number of the φ-mapping.     

Quantum Fisher Information for <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(2) Atomic Coherent States and <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(1, 1) Coherent States

We investigate quantum Fisher information (QFI) for s u(2) atomic coherent states and s u(1, 1) coherent states. In this work, we find that for s u(2) atomic coherent states, the QFI with respect to \(\vartheta ~(\mathcal {F}_{\vartheta })\) is independent of φ, the QFI with respect to \(\varphi (\mathcal {F}_{\varphi })\) is governed by ??. Analogously, for s u(1,1) coherent states, \(\mathcal {F}_{\tau }\) is independent of φ, and \(\mathcal {F}_{\varphi }\) is determined by τ. Particularly, our results show that \(\mathcal {F}_{\varphi }\) is symmetric with respect to ?? = π/2 for s u(2) atomic coherent states. And for s u(1,1) coherent states, \(\mathcal {F}_{\varphi }\) also possesses symmetry with respect to τ = 0.     

Description of Some Ground States by Puiseux Techniques

Let \((\Sigma^{+}_{G}, \sigma)\) be a one-sided transitive subshift of finite type, where symbols are given by a finite spin set S, and admissible transitions are represented by an irreducible directed graph G?S×S. Let \(H : \Sigma^{+}_{G}\to\mathbb{R}\) be a locally constant function (that corresponds with a local observable which makes finite-range interactions). Given β>0, let μ _βH be the Gibbs-equilibrium probability measure associated with the observable ?βH. It is known, by using abstract considerations, that {μ _βH } _β>0 converges as β→+∞ to a H-minimizing probability measure \(\mu_{\min}^{H}\) called zero-temperature Gibbs measure. For weighted graphs with a small number of vertices, we describe here an algorithm (similar to the Puiseux algorithm) that gives the explicit form of \(\mu_{\min}^{H}\) on the set of ground-state configurations.     

Studying the effect of biaxial anisotropy on nonlinear magnetization oscillations accompanying the 90° pulsed magnetization process in ferrite–garnet films with easy-plane anisotropy

Time dependences of the azimuthal component of the torque T _φ(t) acting on magnetization are calculated to understand the nature of the delayed magnetization acceleration effect observed during the 90° pulsed magnetization of real ferrite–garnet films, in which biaxial anisotropy exists alongside with in-plane anisotropy. A calculation technique based on analyzing an operating point trajectory is used. Calculations show that if the effective anisotropy field H _K2 is comparable to the magnetizing pulse amplitude H _ma, abruptly ascending regions at characteristic times t* in curves T _φ(t) arise, in the limit of which nonlinear magnetization oscillations formed. The shape of these regions depends weakly on the magnetizing pulse front duration τ_f. This explains the reason of the weak dependence of the nonlinear magnetization oscillations on duration of the magnetizing pulse front. Calculations also show that the main features of the delayed acceleration effect are less clear upon an increase of the pulse amplitude: the behavior of curves T _φ(t) becomes smoother near times t*, and an increase in the pulse front duration is accompanied by a stronger drop in the intensity of magnetization oscillations.     

On the asymptotical normality of statistical solutions for wave equations coupled to a particle

We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein–Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function which has some mixing properties. We study the distribution μ _t of the random solution at time moments t ∈ R. The main result is the convergence of μ _t to a Gaussian probability measure as t→∞. The application to the case of Gibbs initial measures is given.     

Description of composite systems in the spectral integration technique: The gauge invariance and analyticity constraints for the radiative decay amplitudes

The constraints following from gauge invariance and analyticity are considered for the amplitudes of radiative transitions of composite systems, when composite systems are treated in terms of spectral integrals. We discuss gauge-invariant amplitudes for the transitions S → γS and V → γS, with scalar S and vector V mesons being two-particle composite systems of scalar (or pseudoscalar) constituents, and we demonstrate the mechanism of cancellation of false kinematical singularities. Furthermore, we explain how to generalize this consideration for quark-antiquark systems, in particular, for the reaction φ(1020) → γf₀(980). Here, we also consider in more detail the quark-model nonrelativistic approach for this reaction.     

A new look at the KLOE data on the decay <Emphasis Type="Italic">φ</Emphasis>→<Emphasis Type="Italic">ηπ</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">γ</Emphasis>

We present an analysis of recent high-statistical KLOE data on φ → ηπ⁰γ decay. This decay mainly goes through the a₀γ intermediate state, which makes it possible to investigate properties of the a₀. It is shown that KLOE data prefer a higher a0 mass and a considerably larger a0 coupling to the K\(\bar K\) than those obtained in the analysis of the KLOE group.     

Schrödinger’s Equation with Gauge Coupling Derived from a Continuity Equation

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ? S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out.     

On Julia Set and Chaos in <Emphasis Type="Italic">p</Emphasis>-adic Ising Model on the Cayley Tree

In this paper, we study the chaotic behavior of the p-adic Ising-Potts mapping associated with the p-adic Ising model on the Cayley tree. As an application of this result, we are able to show the existence of periodic (with any period) p-adic quasi Gibbs measures for the model.     

Relative yield of charged and neutral heavy meson pairs in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation near threshold

The subject of the charged-to-neutral yield ratio for \(B\bar B\) and \(D\bar D\) pairs near their respective thresholds in e⁺e^? annihilation is revisited. As previously argued for the B mesons, this ratio should exhibit a substantial variation across the ?(4S) resonance due to interference of the resonance scattering phase with the Coulomb interaction between the charged mesons. A simple alternative derivation of the expression describing this effect is presented here, and the analysis is extended to include the D-meson production in the region of the ψ(3770) resonance. The available data on kaon production at the φ(1020) resonance are also discussed in connection with the expected variation of the charged-to-neutral yield ratio.     

The big bang as a result of the first-order phase transition driven by a change of the scalar curvature in an expanding early Universe: The “hyperinflation” scenario

We suggest that the Big Bang could be a result of the first-order phase transition driven by a change in the scalar curvature of the 4D spacetime in an expanding cold Universe filled with a nonlinear scalar field φ and neutral matter with an equation of state p = νε (where p and ε are the pressure and energy density of the matter, respectively). We consider the Lagrangian of a scalar field with nonlinearity φ⁴ in a curved spacetime that, along with the term–ξR|φ|² quadratic in φ (where ξ is the interaction constant between the scalar and gravitational fields and R is the scalar curvature), contains the term ξRφ₀(φ + φ⁺) linear in φ, where φ₀ is the vacuum mean of the scalar field amplitude. As a consequence, the condition for the existence of extrema of the scalar-field potential energy is reduced to an equation cubic in φ. Provided that ν > 1/3, the scalar curvature R = [κ(3ν–1)ε–4Λ] (where κ and Λ are Einstein’s gravitational and cosmological constants, respectively) decreases with decreasing ε as the Universe expands, and a first-order phase transition in variable “external field” parameter proportional to R occurs at some critical value R _c < 0. Under certain conditions, the critical radius of the early Universe at the point of the first-order phase transition can reach an arbitrary large value, so that this scenario of unrestricted “inflation” of the Universe may be called “hyperinflation.” After the passage through the phase-transition point, the scalar-field potential energy should be rapidly released, which must lead to strong heating of the Universe, playing the role of the Big Bang.     

Computability of Brolin-Lyubich Measure

Brolin-Lyubich measure λ _R of a rational endomorphism \({R:{\hat{\mathbb {C}}}\to {\hat{\mathbb {C}}}}\) with deg R ≥ 2 is the unique invariant measure of maximal entropy \({h_{\lambda_R}=h_{{\rm top}}(R)=\log d}\) . Its support is the Julia set J(R). We demonstrate that λ _R is always computable by an algorithm which has access to coefficients of R, even when J(R) is not computable. In the case when R is a polynomial, the Brolin-Lyubich measure coincides with the harmonic measure of the basin of infinity. We find a sufficient condition for computability of the harmonic measure of a domain, which holds for the basin of infinity of a polynomial mapping, and show that computability may fail for a general domain.     

One-Sided Continuity Properties for the Schonmann Projection

We consider the plus-phase of the two-dimensional Ising model below the critical temperature. In 1989 Schonmann proved that the projection of this measure onto a one-dimensional line is not a Gibbs measure. After many years of continued research which have revealed further properties of this measure, the question whether or not it is a Gibbs measure in an almost sure sense remains open. In this paper we study the same measure by interpreting it as a temporal process. One of our main results is that the Schonmann projection is almost surely a regular g-measure. That is, it does possess the corresponding one-sided notion of almost Gibbsianness. We further deduce strong one-sided mixing properties which are of independent interest. Our proofs make use of classical coupling techniques and some monotonicity properties which are known to hold for one-sided, but not two-sided conditioning for FKG measures.