Structure,ionic conduction,and phase transformations in lithium titanate Li<Subscript>4</Subscript>Ti<Subscript>5</Subscript>O<Subscript>12</Subscript>

The spinel structure of lithium titanate Li₄Ti₅O₁₂ is refined by the Rietveld full-profile analysis with the use of x-ray and neutron powder diffraction data. The distribution and coordinates of atoms are determined. The Li₄Ti₅O₁₂ compound is studied at high temperatures by differential scanning calorimetry and Raman spectroscopy. The electrical conductivity is measured in the high-temperature range. It is shown that the Li₄Ti₅O₁₂ compound with a spinel structure undergoes two successive order-disorder phase transitions due to different distributions of lithium atoms and cation vacancies (□, V) in a defect structure of the NaCl type: (Li)_8a[Li_0.33Ti_1.67]_16dO₄ → [Li□]_16c[Li_1.33Ti_1.67]_16dO₄ → [Li_1.33□_0.67]_16c[Ti_1.67□_0.33]_16dO₄. The low-temperature diffusion of lithium predominantly occurs either through the mechanism ... → Li(8a) → V(16c) → V(8a) → ... in the spinel phase or through the mechanism ... → Li(16c) → V(8a) → V(16c) → ... in an intermediate phase. In the high-temperature phase, the lithium cations also migrate over 48f vacancies: ... Li(16c) → V(8a, 48f) → V(16c) → ....     

Analytic properties of the effective dielectric constant of a two-dimensional Rayleigh model

Analytic properties of the dimensionless static effective dielectric constant f(p, h) of a two-dimensional Rayleigh model (p is the concentration and h is the ratio of the dielectric constants of components) are considered as a function of the complex variable h. It is shown that the only singularities of the function f(p, h) are first-order poles for real h = h _n < 0 (n = 1, 2, ...) with the condensation point h = ?1, which form an infinite discrete (countable) set. The positions of the first ten poles of the function f(p, h) and the residues at these points are calculated and represented graphically versus the concentration. Based on the results obtained, a pole-type approximate formula is proposed that describes the behavior of the function f(p, h) over a wide range of p and complex h.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Energy scan of cross sections for <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>–</Superscript> annihilation into quarkonia and light hadrons in the Belle experiment

The cross sections of the reactions e⁺e^– → ?(nS)π⁺π^? (n = 1, 2,3) and e⁺e^– → h _b (nP)π⁺π^? (n = 1, 2) are measured as a function of the cms collision energy from their thresholds up to 11.02 GeV using the data of the Belle experiment operating at the KEKB e⁺e^– collider. The peaks of the ?(10 860) and ?(11020) resonances are observed in the cross sections with an insignificant contribution of the continuum. The decay ?(11020) → h _b (nP)π⁺π^? is found to fully proceed through intermediate isovector states Z _b (10610) and Z _b (10650).     

Mehrfache Dispersionsrelationen für kurzreichweitige Potentiale,die sich nicht durch eine Überlagerung von Yukawa-Potentialen darstellen lassen

A triple dispersion relation is derived for the functionf(s, t, u) which becomes the scattering amplitudef(s, t) foru=4s?t. Besides the usual conditions which are needed for deriving a dispersion relation ins, the potential must decrease faster than exponentially at infinity. For this class of potentialsf(s, t, u) has essential singularities fort→∞ andu→∞. It is shown thatf(s, t, u) is bounded in the physical sheets of two independent Riemannian surfaces which are constructed by conformal mappings of thet- and theu-plane. In the new variables the conditions for the existence of dispersion relations are fulfilled.     

Behavior of the excitation cross sections of the perturbed series of the xenon atom

Behavior of the excitation cross sections of the perturbed 6s[3/2]_n°?np[1/2]₀ spectral series of the xenon atom is experimentally studied. By using the methods of extended electron beam and optical spectroscopy, the cross sections are measured and the optical excitation functions are recorded for the transitions of this series with n=6–13. A deviation of the dependence Q=f(n) from a power-law function is revealed, as well as changes in the form of optical excitation functions and in the nature of the branching caused by perturbation of the 7p[1/2]₀ level by levels of the 5p ⁵(² P _1/2°)6p configuration.     

Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

Fluctuations for the Ginzburg-Landau $${\nabla \phi}$$ Interface Model on a Bounded Domain

We study the massless field on \({D_n = D \cap \tfrac{1}{n} \mathbf{Z}^2}\), where \({D \subseteq \mathbf{R}^2}\) is a bounded domain with smooth boundary, with Hamiltonian \({\mathcal {H}(h) = \sum_{x \sim y} \mathcal {V}(h(x) - h(y))}\). The interaction \({\mathcal {V}}\) is assumed to be symmetric and uniformly convex. This is a general model for a (2 + 1)-dimensional effective interface where h represents the height. We take our boundary conditions to be a continuous perturbation of a macroscopic tilt: h(x) = n x · u + f(x) for \({x \in \partial D_n,\,u \in \mathbf{R}^2}\), and f : R ² → R continuous. We prove that the fluctuations of linear functionals of h(x) about the tilt converge in the limit to a Gaussian free field on D, the standard Gaussian with respect to the weighted Dirichlet inner product \({(f,g)_\nabla^\beta = \int_D \sum_i \beta_i \partial_i f_i \partial_i g_i}\) for some explicit β = β(u). In a subsequent article, we will employ the tools developed here to resolve a conjecture of Sheffield that the zero contour lines of h are asymptotically described by SLE(4), a conformally invariant random curve.     

Limit of Fluctuations of Solutions of Wigner Equation

We consider fluctuations of the solution W _ε (t, x, k) of the Wigner equation which describes energy evolution of a solution of the Schrödinger equation with a random white noise in time potential. The expectation of W _ε (t, x, k) converges as ε → 0 to \({\bar{W}(t,x,k)}\) which satisfies the radiative transport equation. We prove that when the initial data is singular in the x variable, that is, W _ε (0, x, k) = δ(x)f(k) and \({f\in {\mathcal{S}}(\mathbb{R}^d)}\), then the laws of the rescaled fluctuation \({Z_\varepsilon(t):=\varepsilon^{-1/2}[W_\varepsilon(t,x,k)-\bar{W}(t,x,k)]}\) converge, as ε → 0+, to the solution of the same radiative transport equation but with a random initial data. This complements the result of [6], where the limit of the covariance function has been considered.     

ABC effect and resonance d*(2380)

A new state in the two-baryon system with mass 2380 MeV and width 80 MeV has been detected in the experiments at the Juelich Cooler Synchrotron (COSY). The new particle denoted now d*(2380) has quantum numbers I(J ^p ) = 0(3⁺). The total cross sections for the d and ⁴He fusion reactions show similar to each other resonance-like energy dependence. The resonance-like structure is sensed in the double-pionic fusion channels and polarized np scattering.     

Symmetric elastic and spin-flip low-energy collisions of the hydrogen-isotope mesic atoms in the adiabatic hyperspherical approach

The reduced adiabatic hyperspherical (RAHS) basis suggested previously is used to calculate elastic and spin-flip cross sections in the processes (aμ)_F+a → (aμ)_F′+a, a=(p, d, t), for collision energies 10^?3≤?≤10² eV. The rapid convergence of the method is demonstrated: to achieve an accuracy of ?1% in the calculated cross sections, it is sufficient to use N≤10 of the basis RAHS functions. The comparison of the obtained results with the previous ones is presented.     

Symmetry energy of the nucleus in the relativistic Thomas–Fermi approach with density-dependent parameters

We introduce an inhomogeneous term, f(t,x), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f(t,x) which depend nontrivially on both t and x, we find that there is just one symmetry. If f is a function of only x, there are three symmetries with the algebra s l(2,R). When f is a function of only t, there are five symmetries with the algebra s l(2,R) ⊕ _s 2A ₁. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.     

Observation of high efficiency of Raman scattering in the process of the three-photon ionization of samarium atom

Very high efficiency of Raman scattering on samarium atoms in the process of three-photon ionization has been detected. An intense maximum attributed to the one-photon transition 4f ⁶5d6s ⁹ H ₂ → 4f ⁵5d6s ^{2 7} D ₃° between two excited states is observed in the dependence of the yield of Sm⁺ ions on the laser-radiation frequency. The 4f ⁶5d6s ⁹ H ₂ state is populated owing to the spontaneous Raman scattering 4f ⁶6s ^{2 7} F ₃ + ω ? ν → 4f ⁶5d6s ⁹ H ₂.     

Excitation of the Yb II transitions terminating on the low-lying odd levels

Excitation of the transitions from the even levels of a singly charged ytterbium ion that terminate on the low-lying odd levels 4f ¹³(² F°)6s ^{2 2} F°, 4f ¹⁴(¹ S)6p ² P°, and 4f ¹³(² F°_7/2)5d6p(³ D)³[3/2]° is experimentally studied by measuring 51 excitation cross sections at an electron energy of 50 eV, and 16 optical excitation functions are determined within the electron energy range 0–200 eV. The largest magnitudes of the measured cross sections exceed 3 × 10^?17 cm².     

Resolvent Expansion and Time Decay of the Wave Functions for Two-Dimensional Magnetic Schrödinger Operators

We consider two-dimensional Schrödinger operators H(B, V) given by Eq. (1.1) below. We prove that, under certain regularity and decay assumptions on B and V, the character of the expansion for the resolvent (H(B, V) ? λ)^?1 as λ → 0 is determined by the flux of the magnetic field B through \({\mathbb{R}^2}\) . Subsequently, we derive the leading term of the asymptotic expansion of the unitary group e ^{?i t H(B, V)} as t → ∞ and show how the magnetic field improves its decay in t with respect to the decay of the unitary group e ^{?i t H(0, V)}.     

Signal velocity in oscillator arrays

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. After describing necessary and sufficient conditions for asymptotic stability, we derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocitiesc₊ > 0 and c_? < 0 such that low frequency disturbances travel through the flock as f₊(x ? c₊t) in the direction of increasing agent numbers and f_?(x ? c_?t) in the other.     

Kinetic Theory and Lax Equations for Shock Clustering and Burgers Turbulence

We study shock statistics in the scalar conservation law ? _t u+? _x f(u)=0, x∈?, t>0, with a convex flux f and spatially random initial data. We show that the Markov property (in x) is preserved for a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps). The kinetics of shock clustering is then described completely by an evolution equation for the generator of the Markov process u(x,t), x∈?. We present four distinct derivations for this evolution equation, and show that it takes the form of a Lax pair. The Lax equation admits a spectral parameter as in Manakov (Funct. Anal. Appl. 10:328–329, 1976), and has remarkable exact solutions for Burgers equation (f(u)=u ²/2). This suggests the kinetic equations of shock clustering are completely integrable.     

VUV-luminescence and excitation spectra of the heavy trivalent rare-earth ions in fluoride matrices

VUV 4f ⁿ → 4f^n?15d transitions of Gd³⁺, Er³⁺, Tm³⁺, and Lu³⁺ in fluoride matrices have been analyzed with high-resolution luminescence and excitation spectroscopy. In trifluorides, strong electron-phonon coupling has been found. In the other matrices, the luminescence spectra clearly yield zero-phonon lines and phonon replica, indicating intermediate coupling. The energies of the zero-phonon lines observed are compared with theoretical predictions. Near the threshold of f → d excitations, some of the excitation spectra yield sharp structures which cannot be explained with phonon replica but will be discussed in terms of the energy levels of the 4f^n?15d configuration.     

37 Years with the light scalar mesons. The learned lessons

Attention is paid to the production mechanisms of light scalars that reveal their nature. We reveal the chiral shielding of the σ(600) meson. We show that the kaon loop mechanism of the ? radiative decays, ratified by experiment, is four-quark transition and points to the four-quark nature of light scalars. We show also that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor qq? mesons that are produced via two-quark transitions γγ → qq?. We study the mechanism of production of the light scalar mesons in the D _s ⁺ → π⁺π^? e ⁺ν decays: D _s ⁺ → ss?e ⁺ν → [σ(600) + f ₀(980)]e ⁺ν → π⁺π^? e ⁺ν, and compare it with the mechanism of production of the light pseudoscalar mesons in the D _s ⁺ → (η/η′)e ⁺ν decays: D _s ⁺ → ss?e ⁺ν → (η/η′)e ⁺ν. As a result we find support to four-quark nature of light scalars. In the end, we outline the future research program.     

Asymptotics of Self-similar Solutions to Coagulation Equations with Product Kernel

We consider mass-conserving self-similar solutions for Smoluchowski’s coagulation equation with kernel K(ξ,η)=(ξη) ^λ with λ∈(0,1/2). It is known that such self-similar solutions g(x) satisfy that x ^?1+2λ g(x) is bounded above and below as x→0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x)=h _λ x ^?1+2λ g(x) in the limit λ→0. It turns out that \(h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)\) as x→0. As x becomes larger h develops peaks of height 1/λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x→∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE.