Entropy for Zero-Temperature Limits of Gibbs-Equilibrium States for Countable-Alphabet Subshifts of Finite Type

Let Σ _A be a finitely primitive subshift of finite type over a countable alphabet. For suitable potentials f : Σ _A → ℝ we can associate an invariant Gibbs equilibrium state μ _tf to the potential tf for each t ≥ 1. In this note, we show that the entropy h(μ _tf ) converges in the limit t→ ∞ to the maximum entropy of those invariant measures which maximize ∫ f dμ. We further show that every weak-* accumulation point of the family of measures μ _tf has entropy equal to this value. This answers a pair of questions posed by O. Jenkinson, R. D. Mauldin and M. Urbański.     

Relaxation of finite, closed systems

On a semi-finite W^*-algebra together with a faithful normal semi-finite trace τ and a one-parameter group of trace preserving ^*-automorphism α_t, we study the limit as t → ∞ of α^*_tψ of a normal state ψ. It is shown that the existence of this limit in the weak sense is determined by the spectral properties of the evolution operator. These results are specialized to finite classical and quantum mechanical systems.     

Comment on Vub from exclusive semileptonic B and D decays

The prospects for determining |V_ub| from exclusive B semileptonic decay are discussed. The double ratio of form factors (f^(B→ρ)/f^(B→K*))/(f^(D→ρ)/f^(D→K*)) is calculated using chiral perturbation theory. Its deviation from unity due to contributions that are non-analytic in the symmetry breaking parameters is very small. Combining experimental data obtainable from , and can lead to a model independent determination of |V_ub| with an uncertainty from theory of about 10%.     

Resonances in at rest

Data on at rest show two resonant processes: (a) f₀(1370)η,f₀(1370)→σσ and ρρ, (b) η(1440)σ, η(1440)→ηπ⁺π⁻. The branching ratio BR[f₀(1370)→ρρ]/BR[f₀(1370)→σσ]=0.98±0.25 in the mass range available here. Using data on , the ratio Γ_4π/Γ_2π5 for f₀(1370). The effects of the strongly s-dependent width of f₀(1370) are discussed in some detail.The η(1440) is observed decaying to ησ and a₀(980)π, with strong destructive interference between them. In its decay to a₀(980)π, a narrow peak appears in the ηπ mass spectrum, but 30–50 MeV above that usually attributed to a₀(980) and significantly above the KK threshold. This effect is explained naturally by a two-step process: η(1440)→K^*(890)K followed by rescattering of the two kaons through a₀(980) to ηπ above the KK threshold.     

Looking for double beta decay of Nd to excited states of Sm by gamma ray spectroscopy

We have measured the gamma ray activity of a sample of 6189 grams of metallic Neodimium with a germanium detector. From the gamma energy spectrum recorded during almost 6500 hours we extract lower limits for the halflife of the inclusive (0ν + 2ν) ββ decay of ¹⁵⁰Nd to the first excited states of ¹⁵⁰Sm : t_1/2(0⁺ → 0₁⁺ > 1.0·10²⁰, t_1/2(O⁺ → 0₂⁺) > 2.0 · 10²⁾, t_1/2(0⁺ → 2₁⁺) > 9.1 · 10¹⁹.     

Zero Temperature Limits of Gibbs Equilibrium States for Countable Markov Shifts

We prove that, given a uniformly locally constant potential f on a countable state Markov shift and suitable conditions which guarantee the existence of the equilibrium states μ _tf for all t, the measures μ _tf converge in the weak star topology as t tends to infinity.     

Asymptotic behavior of orbits of C 0-semigroups and solutions of linear and semilinear abstract differential equations

In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t ⁿ f(t, u(t)), where A is the generator of a C ₀-semigroup (or group) T(·), f(·, x) ∈ A for each x ∈ X, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each x ∈ X; and the semilinear case when T(·) is an asymptotically stable C ₀-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S ^p-A defined similarly to the case of S ^p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A _u:= A ∩ BUC(ℝ, X) if n = 0 and to t ⁿ A _u ⊕ w _n C ₀ (ℝ, X) if n ∈ ℕ, where w _n(t) = (1 + |t|)ⁿ. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0. Dedicated to the memory of B. M. Levitan     

New Crystalline Lasers on the Base of Monoclinic KR(W04)2:Ln3+ Tungstates (R=Y and Ln)

Monoclinic KY(WO₄)₂:Pr₃₊, Tm₃₊:KY(WO₄)₂:Er₃₊, Yb₃₊ single crystals are grown by low-gradient Czochralski technique. Stimulated emission at 1.0223μm wavelength in the new lasing ¹D₂→³F₃ channel of Pr³⁺ ions in KY(WO₄)₂ at room temperature under Xe-flashlamp pumping is excited. Full sets of Stark-level energies for Pr₃₊ ions in KY(WO₄)2 and KGd(WO₄)₂ crystals at 77 K are determined. 4f²-4f² intensity-transitions for the KY(WO₄)₂:Pr³⁺ are analyzed preliminarily. All observed at present and earlier one-micron Pr³⁺-ion, induced transitions in the ¹D₂→³F₃ and ¹D₂→³F₄ channels are identified. In yttrium and gadolinium sensitized-tungstates a two-micron (³H₄→³H₆) low-threshold generation of Tm³⁺ ions at cryogenic temperatures is achieved.All authors cooperate with the Joint Open Laboratory for Laser Crystals and Precise Laser Systems at the Institute of Crystallography and Institute of Laser Physics, Russian Academy of Sciences.     

Study of in flight

An analysis of data on is presented at beam momenta 600 to 1940 MeV/c. There is evidence for an I=1, J^PC=2⁻⁺ resonance in ηηπ⁰ with mass M=1880±20 MeV and width 255±45 MeV, decaying strongly to a₂(1320)η; it is too strong to be explained as the high mass tail of π₂(1670)→a₂(1320)η. There is tentative evidence also for weak decays to f₀(1500)π. It makes a natural partner to the η₂(1860).     

Extreme compression behaviour of equations of state

The extreme compression (P→∞) behaviour of various equations of state with K′_∞>0 yields (P/K)_∞=1/K′_∞, an algebraic identity found by Stacey. Here P is the pressure, K the bulk modulus, K^′=dK/dP, and K′_∞, the value of K^′ at P→∞. We use this result to demonstrate further that there exists an algebraic identity also between the higher pressure derivatives of bulk modulus which is satisfied at extreme compression by different types of equations of state such as the Birch–Murnaghan equation, Poirier–Tarantola logarithmic equation, generalized Rydberg equation, Keane's equation and the Stacey reciprocal K-primed equation. The identity has been used to find a relationship between λ_∞, the third-order Grüneisen parameter at P→∞, and pressure derivatives of bulk modulus with the help of the free-volume formulation without assuming any specific form of equation of state.     

Study of the process ee→ππγ in c.m. energy range 600–970 MeV at CMD-2

The cross section of the process e⁺e⁻→π⁰π⁰γ has been measured in the c.m. energy range 600–970 MeV with the CMD-2 detector. The following branching ratios have been determined:

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and

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. Evidence for the ρ⁰→f₀(600)γ decay has been obtained:

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. From a search for the process e⁺e⁻→ηπ⁰γ the following upper limit has been obtained: at 90% CL.     

Differentiating the Absolutely Continuous Invariant Measure of an Interval Map <Emphasis Type="Italic">f</Emphasis> with Respect to <Emphasis Type="Italic">f</Emphasis>

Let the map f:[−1,1]→[−1,1] have a.c.i.m. ρ (absolutely continuous f-invariant measure with respect to Lebesgue). Let δρ be the change of ρ corresponding to a perturbation X=δf○f⁻¹ of f. Formally we have, for differentiable A,but this expression does not converge in general. For f real-analytic and Markovian in the sense of covering (−1,1) m times, and assuming an analytic expanding condition, we show thatis meromorphic in C, and has no pole at λ=1. We can thus formally write δρ(A)=Ψ(1).     

Enhancement of the Debye frequency due to a charged-boson exchange model of high temperature superconductors

A simple model of 1-2-3 superconductors in which electrons (holes) in CuO₂ planes interact via exchange with two kinds of bosons is considered. Namely, via one-phonon exchange (weak coupling-Cooper pairing), and via paired holes on oxygen O⁰ from Cu-O chains. The mechanisms of paired holes exchange (“charged bosons”-“O⁰” exchange) considered here in strong coupling leads to the enhancement of the Fröhlich constant g_f (g²_F→Kg²F), and as a consequence to the enhancement of the Debye frequency ω_D^K=f^Kω_D, f^K 1. In the proposed model the exact expression for the constant K is derived.     

Unparticle effects on top quark rare decays

In this work we study the flavor changing neutral current (FCNC) decays of the top quark, t→cγ and t→cg, in the framework of the unparticle physics. The Standard Model predictions for the branching ratios of these decays are about 5×10⁻¹⁴, and 1×10⁻¹², respectively. The parameter space of λ, Λ, and d is obtained by taking into account the SM predictions and the results of the simulation performed by the ATLAS Collaboration for the branching ratios of t→cγ and t→cg decays.     

On a Measure on the Inductive Limit of Projection Logics

The aim of the paper is to measure the logic of J-projections from inductive limit of W J-algebras studied. The main result isTheorem. Let А be a W^∗ J-factor of countable type (type of А is different from I₂) and let А be the inductive limit of W^∗ J-factors А_α different from I₂. If (1) А be a W^∗ P-factor or (2) А and all А_α are W^∗ K-factors, then any indefinite measure ν : ∪_αА^h_α→ R can be unique by the strong operator topology extended to an indefinite measure on A^h.     

The emission spectrum of HgI

The ultraviolet emission systems of HgI—C → X, D → X, F₃ → X, G → X, and H → X—are photographed and analyzed using tesla-discharge sources containing isotopically pure ²⁰⁰Hg. The previous assignment for F₃ → X is revised, the main change being a decrease by 3 units in the v″ numbering. Results for the other systems corroborate the existing interpretations, except that for C → X there are prominent intensity gaps in the unresolved rotational structure of the bands, not reported previously for “natural” HgI spectra. These gaps are attributed to perturbations of the C state by high levels (v ≈ 90) of the B state. The data for these systems are combined with existing B → X data for ²⁰⁰Hg¹²⁷I and ²⁰⁰Hg¹²⁹I and fitted simultaneously to yield optimal vibrational parameters for all states. In this analysis the X state is fitted to a mixed representation—a polynomial in ( ) for v ≤ 20 and a near-dissociation expansion for v ≥ 20, with G_v and its first derivative constrained to be continuous at v = 20. The revised estimate of _e for X is 2800 ± 40 cm⁻¹. The recommended vibrational parameters (cm⁻¹) for v ≤ 20 are ω_e = 125.41, ω_ex_e = 1.009, ω_ey_e = −0.0159.     

Smoothness of Invariant Manifolds for Nonautonomous Equations

For semiflows generated by ordinary differential equations v’=A(t)v admitting a nonuniform exponential dichotomy, we show that for any sufficiently small perturbation f there exist smooth stable and unstable manifolds for the perturbed equation v’=A(t)v+f(t,v). As an application, we establish the existence of invariant manifolds for the nonuniformly hyperbolic trajectories of a semiflow. In particular, we obtain smooth invariant manifolds for a class of vector fields that need not be C^1+α for any α ∈ (0,1). To the best of our knowledge no similar statement was obtained before in the nonuniformly hyperbolic setting. We emphasize that we do not need to assume the existence of an exponential dichotomy, but only the existence of a nonuniform exponential dichotomy, with sufficiently small nonuniformity when compared to the Lyapunov exponents of the original linear equation. Furthermore, for example in the case of stable manifolds, we only need to assume that there exist negative Lyapunov exponents, while we also allow zero exponents. Our proof of the smoothness of the invariant manifolds is based on the construction of an invariant family of cones.Supported by the Center for Mathematical Analysis, Geometry, and Dynamical Systems, and through Fundação para a Ciência e a Tecnologia by Program POCTI/FEDER, Program POSI, and the grant SFRH/BPD/14404/2003.     

Scale transformations for renormalized field operators: Discussion of the soluble model

We discuss the operator formulation of the Zachariasen-Thirring model, describing the chain approximation to the propagator (the sum of three-particle massless bubbles) in massless λ⁴ theory. Such a model is formally scale-invariant and explicitly soluble. All intermediate steps of conventional renormalization procedure, regularization, introduction of appropriate counterterms, and cut-off free limit, are explicitly performed. In every step the scaling properties are discussed and respective dilatation currents are written down. After the proper choice of scale transformations for the renormalized field operator, we obtain the nonlocal dilatation current, defining the renormalized dilatation generator D_Λ^R(t). In the cut-off free limit Λ → ∞ the ET commutator of D_Λ^R(t) with renormalized field operators reproduces the Callan-Symanzik modification of “naive” canonical scale transformations. The renormalized scale transformations coincide in the cut-off free limit with renormalized dimensional transformations and define the exact symmetry of the renormalized theory.     

Nonlinear kinematic response of premixed flames to harmonic velocity disturbances

This paper analyzes the nonlinear dynamics of premixed flames responding to harmonic velocity disturbances. These nonlinear dynamics were studied by solving a constant flame speed front tracking equation for the flame’s response to harmonically oscillating velocity disturbances. The solution to these equations is used to quantify the transfer function relating the ratio of the normalized flame area to velocity fluctuations, G = (A′/A_o)/(u′/u_o), upon the amplitude of velocity oscillations, ε = u′/u_o. Due to nonlinearities, the amplitude of this transfer function relative to its linear value decreases with increasing amplitude of velocity oscillation, u′/u_o. In contrast, the transfer function phase exhibits almost no amplitude dependence. The velocity amplitude where transfer function nonlinearities become significant depends strongly upon three parameters: a Strouhal number, St = ωL_f/u_o (where L_f is the flame length), the ratio of the flame length to width, β = L_f/R, and the flame shape in the absence of perturbations (i.e., conical, inverted wedge, etc.). In the linear case, the transfer function, G, depends only upon an algebraic combination of the first two parameters, given by St₂ = St (1 + β²)/β². In general, however, G exhibits a distinct dependence upon both parameters St and β. In particular, we show that the nonlinear response of G is an intrinsically dynamic phenomenon; i.e., its quasi-steady response (St 1) is purely linear. As such, nonlinearity is enhanced with increasing Strouhal numbers. In contrast, nonlinearity is suppressed at large β values; as such, the response of a long flame remains quite similar to its linear value, even at large ε values where the flame front exhibits substantial corrugation and cusping. Finally, we show that the response of conical flames remains much more linear at comparable disturbance amplitudes than for “V” or wedge-shaped flames. These predictions are shown to be consistent with available experimental data.     

Spectral characterization and energy levels of Cr:Sc2(MoO4)3 crystal

This paper reports the spectral properties and energy levels of Cr³⁺:Sc₂(MoO₄)₃ crystal. The crystal field strength Dq, Racah parameter B and C were calculated to be 1408 cm⁻¹, 608 cm⁻¹ and 3054 cm⁻¹, respectively. The absorption cross sections σ_α of ⁴A₂→⁴T₁ and ⁴A₂→⁴T₂ transitions were 3.74×10⁻¹⁹ cm² at 499 nm and 3.21×10⁻¹⁹ cm² at 710 nm, respectively. The emission cross section σ_e was 375×10⁻²⁰ cm² at 880 nm. Cr³⁺:Sc₂(MoO₄)₃ crystal has a broad emission band with a broad FWHM of 176 nm (2179 cm⁻¹). Therefore, Cr³⁺:Sc₂(MoO₄)₃ crystal may be regarded as a potential tunable laser gain medium.