Interpolation parameter and expansion for a three-dimensional nontrivial scalar infrared fixed point

We compute a nontrivial infraredϕ ₃ ⁴ -fixed point by means of an interpolation expansion in fixed dimension. The expansion is formulated for an infinitesimal momentum-space renormalization group. We choose a coordinate representation for the fixed-point interaction in derivative expansion, and compute its coordinates to high orders by means of computer algebra. We compute the series for the critical exponentv up to order 25 of interpolation expansion in this representation, and evaluate it using Padé, Borel-Padé, Borel-conformal-Padé, andD log -Padé resummation. The resummation returns 0.6262(13) as the value ofv. Our renormalization group uses canonical resealing, for whichη = 0     

(GL(<Emphasis Type="Italic">n</Emphasis> + 1, ℝ), GL(<Emphasis Type="Italic">n</Emphasis>, ℝ)) is a generalized Gelfand pair

Denote by G = GL(n + 1, ℝ) the group of invertible (n + 1) × (n + 1) matrices with real entries, acting on ℝ ⁿ⁺¹ in the usual way, and let H ₁ = GL(n, ℝ) be the stabilizer of the first unit vector e ₀. Let H ₀ = GL(1, ℝ) and set H = H ₀ × H ₁. It is known that the pair (G,H) is a generalized Gelfand pair. Define a character χ of H by χ(h) = χ(h ₀ h ₁) = χ0(h ₀) where χ0 is a unitary character of H ₀ (h ₀ ∈ H ₀, h ₁ ∈ H ₁). Let σ be the anti-involution on G given by σ(g) = ^t g. In this note, we show that any distribution T on G satisfying T(h ₁ gh ₂) = χ(h ₁ h ₂) T(g) (g ∈ G; h ₁, h ₂ ∈ H) is invariant under the anti-involution σ. This result implies that (G,H ₁) is a generalized Gelfand pair.     

Spin-dependent correction to the relativistic-electron mass in QED in the presence of an external electric field

A new expression is found for the spin-dependent contribution Δm _s to the self-energy of an electron moving with a transverse momentum p⊥ in an electric field. The structure of an asymptotic expansion of Δm _s (r, χ) as a function of two dynamical invariants r = γ _⊥⁻² and χ = γ _⊥|ɛ|/ɛ _c (γ _⊥² ≡ 1 + p _⊥²/m ² c ² and ɛ _c ≡ m ² c ³/|e|ℏ) is clarified with the aid of this expression. The expansion of Δm _s (r, χ) can be represented in the form of a Taylor series in r, the coefficients in this series, F ₀(χ), F ₁(χ), etc., being integrals of the Mellin type. The major coefficient F ₀(χ) is universal and, in the case of an appropriate interpretation of χ, describes well-known spin-dependent corrections to the mass in three different cases of a constant external field (for r → 0). The asymptotic properties of the function F ₁(χ) are studied in detail, but only order-of-magnitude estimates are obtained for F ₂(χ) and F ₃(χ). A comparison of these contributions revealed that, in the semiclassical region χ ≪ 1, r is indeed the parameter of the aforementioned expansion, while, for χ ≫ 1, the true parameter is rχ ² ≡ β ². In particular, the anomalous magnetic moment develops, owing to F ₁(χ), a term that grows logarithmically for χ ≫ 1, but which does not violate the hierarchy of terms in the Taylor series being considered, provided that β remains smaller than unity.     

Application of the Padé approximations to calculation of rotational energies of a triatomic linear molecule

A possibility of applying the Padé approximations to calculation of rotational-level energies of degenerate vibrational states is studied for linear molecules with various quantum numbers of the vibrational angular momentum 1. The calculations of rotational energy levels for the CO ₂ molecule show that the Padé form has a better predictability as compared to a power series. Spectroscopic constants of the Padé approximations for the vibrational states (04⁰0, 04²0, 04⁴0), (14⁰0, 14²0, 14⁴0), (15¹0, 15³0, 15⁵0), and (06⁰0, 06²0, 06⁴0, 06⁶0) for the CO ₂ molecule are determined. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 54–57, September, 2006.     

Semiempirical study of perturbations of the Landé g factors of electronic-vibrational-rotational levels of hydrogen: II. i 3 g − and j 3Δ g − states of the H2, HD,and D2 molecules

The values of the Landé g factors of the i ³Π _g ⁻ , v, N and j ³Δ _g ⁻ , v, N states of the H₂, HD, and D₂ molecules have been found semiempirically for the following vibrational and rotational quantum numbers: v≤3; N≤7 for H₂; N≤5 for HD; and N≤11 for D₂. These values were obtained in terms of the nonadiabatic model, which takes into account the interaction between the 3dπ³Π_g and 3dδ³Δ_g states with the same values of v and N in the approximation of pure precession, with the use of semiempirical values of the expansion coefficients of the wave functions in the Born-Oppenheimer basis determined by us previously and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. The results obtained for the H₂ molecule are in good agreement with the data in the literature. For the i ³Π _g ⁻ and j ³Δ _g ⁻ states of the HD and D₂ molecules, the g factors were found for the first time. This made it possible to study for the first time the role of the isotopic effect in the perturbation of the dependences of the g factors of rovibrational levels on v and N for the triplet electronic states of the hydrogen molecule. It was found that the interference effects of interaction between the 3dπ³Π_g and 3dδ³Δ_g states lead both to significant differences—up to 8, 6, and 11 times for H₂, HD, and D₂, respectively (the i ³Π _g ⁻ state), 20 times for H₂ and HD, and two orders of magnitude for D₂ (the j ³Δ _g ⁻ state)—between the nonadiabatic values of the g factors and the corresponding adiabatic values for some isotopomers of the hydrogen molecule and to significant differences—up to 9 and 1.5 times for the j ³Δ _g ⁻ and i ³Π _g ⁻ states, respectively—in the nonadiabatic values of the g factors of rovibrational levels of different isotopomers of the hydrogen molecule. __________ Translated from Optika i Spektroskopiya, Vol. 96, No. 1, 2004, pp. 42–54. Original Russian Text Copyright ? 2004 by Astashkevich.     

The K * Kπ and ρππ couplings in QCD

The light cone QCD sum rules are derived for the K ^* Kπ coupling g _K ^* Kπ and the ρππ coupling g _ρππ. The contribution from the excited states and the continuum is subtracted cleanly through the double Borel transform with respect to the two external momenta, p ₁ ², p ₂ ²= (p−q)². Our result g _K ^* Kπ= (8.7 ± 0.5) and g _ρππ= (11.5 ± 0.8) is in good agreement with the experimental value. Received: 31 July 1998 / Revised version: 20 November 1998     

Quantum chromodynamics studies at LEP2

Several studies have been made to the hadronic final states in e ⁺ e ⁻ collisions at LEP. Studies of the annihilation process at LEP2 have given rise to results on jet rate, event shape, heavy flavour production, inclusive momentum spectra, Bose-Einstein correlation and colour reconnection effects. Event shape studies have given rise to accurate determination of the strong coupling constant α _s using O (α _s ² ) with resummed leading and next-to-leading log calculation and also with power law corrections. Studies of 2-photon processes have yielded results on γγ cross-section, heavy flavour production, photon structure function and γ*γ* scattering.     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

Analysis on configuration spaces and Gibbs cluster ensembles

The distribution μ of a Gibbs cluster point process in χ = ℝ^d (with n-point clusters) is studied via the projection of an auxiliary Gibbs measure defined on the space of configurations in χ × χ ⁿ. We show that μ is quasi-invariant with respect to the group Diff₀(χ) of compactly supported diffeomorphisms of χ and prove an integration-by-parts formula for μ. The corresponding equilibrium stochastic dynamics is then constructed by using the method of Dirichlet forms. Dedicated to the memory of Vladimir Geyler Research supported in part by DFG Grant 436 RUS 113/722.     

πη scattering and the resummation of vacuum fluctuation in three-flavor χPT

We discuss various aspects of resummed chiral perturbation theory, which was developed recently in order to consistently include the possibility of large vacuum fluctuations of the s̄s pairs and the scenario with smaller value of the q̄q condensate for N_f=3. The subtleties of this approach are illustrated using a concrete example of observables connected with πη scattering. This process seems to be a suitable theoretical laboratory for this purpose due to its sensitivity to the values of the O(p⁴) LECs, namely to the values of the fluctuation parameters L₄ and L₆. We discuss several issues in detail, namely the choice of “good” observables and properties of their bare expansions, the “safe” reparametrization in terms of physical observables, the implementation of exact perturbative unitarity and exact renormalization scale independence, the role of higher order remainders and estimates of their influence. We make a detailed comparison with standard chiral perturbation theory and use generalized χPT as well as resonance chiral theory to estimate the higher order remainders.     

Multiphoton ionization of molecules under the conditions of strong field-induced perturbation of Rydberg states

Multiphonon ionization of the H₂ molecule under the action of a weak (probe) field, which provides the initial population of the low-lying (working) level, and intense monochromatic linearly polarized radiation is studied. The multiphoton ionization process occurs under the conditions of strong field perturbation of two intermediate Rydberg series, np0(¹Σ _u ⁺ and np2(¹Π_u), of the optical R(0)branch which have different ionization potentials. The series are occupied simultaneously as a result of single-photon absorption by an excited H ₂ ^* molecule in the working state 4s σH′¹Σ _g ⁺ (v=0). As a result of the irregularity in the arrangement of the intermediate levels from a large group of states that are combined in the multiphoton ionization process a sharp and irregular change occurs in the dependence of the shifts and widths Γ_n of the levels on the intensity f of the strong field in a transition from one level to another. It is shown that for field intensities f such that the level widths remain much less than the splitting between the levels (Γ_n≪/n ³) the stabilizing effect (i.e., the field-induced narrowing of the levels as f→∞) in the form Γ_n ∝ 1/f ² (as happens in atoms with a structureless core) is not observed in molecular systems. Zh. éksp. Teor. Fiz. 115, 1987–2000 (June 1999)     

Ferromagnetism of manganese compounds

It is shown on the basis of the notion of a strong electron-electron interaction in the unit cell that a ferromagnetic instability is possible in a system with hops between manganese cations and oxygen anions. The phase diagram for the existence of ferromagnetic ordering as a function of the degrees of underfilling n _p and n _t of the 2p ⁶ shell of oxygen and the 3t _g ⁶ shell of manganese, respectively, is constructed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 254–259 (25 August 1997)     

D?→Dπ and D?→Dγ decays: axial coupling and magnetic moment of D? meson

The axial coupling and the magnetic moment of D ^∗-meson or, more specifically, the couplings g_D^*Dpg_{D^{\ast}D\pi} and g_D^*Dgg_{D^{\ast}D\gamma }, encode the non-perturbative QCD effects describing the decays D ^∗→Dπ and D ^∗→Dγ. We compute these quantities by means of lattice QCD with N _f=2 dynamical quarks, by employing the Wilson (“clover”) action. On our finer lattice (a≈0.065 fm) we obtain g_D^*Dp⁺=20±2g_{D^{\ast}D\pi^{+}}=20\pm2, and g_{D^*0 D⁰g}=2.0±0.6 GeV^-1g_{D^{\ast0} D^{0}\gamma}=2.0\pm 0.6~{\rm GeV}^{-1}. This is the first determination of g_{D^*0 D⁰g}g_{D^{\ast0} D^{0}\gamma} on the lattice. We also provide a short phenomenological discussion and the comparison of our result with experiment and with the results quoted in the literature.     

Mean-field and high temperature series expansion calculations of some magnetic properties of Ising and XY antiferromagnetic thin-films

In this work,the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of N’eel temperature and thickness for layers(n = 2,3,4,5,6,and bulk(∞)) by means of a mean-field and high temperature series expansion(HTSE) combined with Pad’e approximant calculations.The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ,ν eff(mean),ratio of the critical exponents γ/ν,and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2,3,4,5,6,and bulk(∞).     

Magnetic susceptibility anisotropy and low-dimensional antiferromagnetism of CuO

The anisotropy of the magnetic susceptibility χ and the influence of oxygen vacancies in CuO single crystals on it are investigated. The temperature dependences of χ(T) along the a, b, and c axes in the range 60<T<600 K and the behavior of the field dependence of the magnetization σ(H) above and below the Néel temperature T _N are plotted for a crystal before and after heat treatment. The χ(T) curves have the form characteristic of low-dimensional systems, which become three-dimensional when the temperature is lowered. The character of the χ(T) curves remains unchanged after annealing. Oxygen vacancies have practically no influence on the a-axis magnetic susceptibility, but they alter the absolute values of the b-and c-axis susceptibilities. The significant effects of reducing the oxygen concentration include a decrease in the magnitude of the low-temperature anomaly (increase) in χ and an increase in the minimum value of χ. The results of the calculations of the exchange parameter I/k and the g factor are discussed in terms of the Heisenberg and Ising models for a one-dimensional system. Zh. éksp. Teor. Fiz. 113, 1026–1035 (March 1998)     

Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bƃ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J _PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺, 1⁺⁻ and radiative transitions ψ(2S) → γχ _c0(1P), γχ _c1(1P), γχ _c2(1P), γχ _c(1S) and χ _c0(1P), χ _c1(1P), χ _c2(1P) → γJ/ψ. The c-c levels and their wave functions are calculated for the radial excitations with n ≤ 6. Also, we determine the c-c component of the photon wave function using the e ⁺ e ⁻-annihilation data: e ⁺ e ⁻ → J/ψ(3097), ψ(3686), ψ(3770), ψ(4040), ψ(4160), ψ(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states η _c0(1S), χ _c0(1P), χ _c2(1P) → γγ and n = 2 states η _c0(2S) → γγ, χ _c0(2P) → γγ. We discuss the status of the recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either χ _c1(2P) or η _c2(1D), while Y(3941) is χ _c2(2P). The text was submitted by the authors in English.     

Thermo-optic coefficients of monoclinic KLu(WO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The three thermo-optic coefficients of the biaxial laser host KLu(WO₄)₂ are measured at 633 nm by a deflection method. Their values at 300 K amount to ∂ n _g /∂ T=−7.4×10⁻⁶ K⁻¹; ∂ n _m /∂ T=−1.6×10⁻⁶ K⁻¹ and ∂ n _p /∂ T=−10.8×10⁻⁶ K⁻¹. Nearly athermal propagation directions are found for polarizations along the N _m and N _p dielectric axes.     

Glass: Kohlrausch exponent,fragility, anharmonicity

The thermodynamical and mechanical properties of (fragile and strong) glass are modeled based on a generalised activation energy relationship log _τ = ΔG _β /RTn(T′) process of glass-forming liquids. This cooperative process involves 1/n(T′) elementary β motions of activation Gibbs energy ΔG _β dependent on the equivalent temperature T′, the temperature of the liquid in equilibrium having the volume of the glass, function of temperature and aging conditions. From this modified VFT law the relaxation of any properties (V , H , stress, creep) can be calculated and approximated by the Kohlrausch function. This model predicts consistency relationships for: a) the temperature (and aging time) variation of the Kohlrausch exponent; b) the temperature dependence of the stabilisation time domain of strong and fragile glass; c) the linear relation between the activation parameters (E ^* energy, S ^* entropy, V ^* volume) of the α and β transition. The Lawson and Keyes (LK) relations are recalled and it is shown that these relations (somewhat equivalant to the compensation law or Meyer-Neldel rule) are observed generally in glass. Morever the (macroscopic) ratios ΔH/ΔV observed during aging or after a temperature jump and the (microscopic) ratio E ^*/V ^* are found equal to κγ (κ compressibily, γ Grüneisen parameter), in agreement with the LK predictions. From various experiments and in agreement with predictions of this model we conclude that the Grüneisen parameter γ _B (pressure derivative of the bulk modulus) and the Mean Square Displacement (MSD) characterising the anharmonicity of solids (and liquids) are the main parameters which govern the relaxation properties of the glass state. Linear relations between the parameters γ _B , the fragility m, and the Kohlrausch exponent n _g at T _g are explained. These correlations underscore a strong relationship between the fragilty of glass formers and the extent of the anharmonicity in the interatomic interactions.     

Even harmonics of AC susceptibility in some sintered pellets of high temperature superconductors

The real (χ′ _n) and imaginary (χ″ _n) parts of even harmonic susceptibility (n⩽6) are measured as a function of external DC field (H _dc) in the field increasing (H↑) and decreasing (H↑) cycle. Hysteresis is observed betweenH↑ andH↓ cycles. In theH↓ cycle, at a field,H _comp=4·2G, bothχ′ andχ″ of all the even harmonics vanish indicating a true cancellation of fields in the intergrain region (H _eff≈0) caused by the balance betweenH _dc and the remanent magnetization of the grains. The position of the extrema and the zero of the various harmonics undergo a shift proportional to the remanent magnetization of the grains at that particular field.     

Experimental observation of the interference of three-and five-wave mixing processes in optical second harmonic generation in a solution of bacteriorhodopsin

The generation of a femptosecond second harmonic in a bacterior-hodopsin solution is investigated. It is shown that the behavior of the harmonic can be explained by the coherent interference of several contributions from three-and five-wave mixing processes (χ ⁽²⁾ and χ ⁽⁴⁾). The magnitude and phase of the fourth-order electronic susceptibility χ ⁽⁴⁾ of the medium with respect to χ ⁽²⁾ are determined. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 10, 668–673 (25 November 1996)