The estimates of periodic potentials in terms of effective masses

LetG _n=(A _n ⁻ , A _n ⁺ ),n≧1, denote the gaps,M _n ^± be the effective masses and Σn=[A _n−1 ⁺ ,A _n ^- ],A ₀ ⁺ =0, be the spectral bands of the Hill operatorT=−d ²/dx ²+V(x) inL ² (R), whereV is a 1-periodic real potential fromL ²(0,1). Let the length gapL _n=|G_n|, h_n be the height of the corresponding slit on the quasimomentum domain and Δ_n=π²(2n−1)−∣Σ_n∣>0 be the band reduction. Let ,n≧1, denote the gap length for the operator . Introduce the sequencesL={L_n}, h={h_n}, l={l_n}, Δ={Δ_n},M ^±={M _n ^± } and the norms ,m≧0. The following results are obtained: i) The estimates of‖V‖, ‖L‖, ‖h‖ ₁, ‖l‖₁, ‖δ‖ in terms of ‖M^±‖₂, ii) identities for the Dirichlet integral of quasimomentum and integral of potentials and so on, iii) the generation of i), ii) for more general potentials. The research described in this publication was made possible in part by grant from the Russian Fund of Fundamental Research and INTAS.     

Convergence Radii for Eigenvalues of Tri-Diagonal Matrices

Consider a family of infinite tri-diagonal matrices of the form L + zB, where the matrix L is diagonal with entries L _kk  = k ², and the matrix B is off-diagonal, with nonzero entries B _k,k+1 = B _k+1,k  = k ^α , 0 ≤ α < 2. The spectrum of L + zB is discrete. For small |z| the nth eigenvalue E _n (z), E _n (0) = n ², is a well-defined analytic function. Let R _n be the convergence radius of its Taylor’s series about z = 0. It is proved that

Strong decay Δ<Superscript>++</Superscript>→<Emphasis Type="Italic">p</Emphasis><Emphasis Type="Italic">π</Emphasis> with light-cone QCD sum rules

We calculate the strong coupling constant g _{ΔN π} and study the strong decay Δ⁺⁺→p π with light-cone QCD sum rules. The numerical value of the strong coupling constant g _{ΔN π} is consistent with the experimental data. The small discrepancy may be due to the failure to take into account perturbative corrections.     

New physics hints in B decays and collider outlook

There are currently two hints for new physics involving CP violation in b → s transitions: ΔS ≡ S _f − S _J ^ϕK ≠ 0, and difference in direct CP asymmetry ΔA _Kπ ≡ A _K+π ⁰ − A _K+π ⁻ ≠ 0. We explore the two scenarios with a large and unique new CP phase in b ↔ s transitions. Motivated by ΔS ≠ 0, we update on the right-handed strange-beauty squark sb _1R at TeV scale. Motivated by ΔA _Kπ ≠ 0, we explore sequential fourth generation t′ and b′ quarks. Both scenarios can survive constraints such as SM level b → sγ, sll and B _s mixing, and predict sizable CP violation in B _s mixing. The fourth generation picture predicts sizable K _L → π ⁰ vv. Direct search for sb _R, b′ and t′ at hadronic colliders, such as Tevatron Run II and LHC, can complement further CP violation studies at these machines, as well as at the future Super B factory.     

Confrontation of nucleus deformation and multipole mixture parameters in (2+0 n ?2+01) transitions with rotational band structure for K π = 0 2+ and 0 3+

The difference of the energies of levels Δ _n = E _lev(2⁺0 _n ) − E _lev(0⁺0 _n ) at n = 1, 2, and 3 and the multipole-mixture parameter δ for (2⁺0₂−2⁺0₁) and (2⁺0₃−2⁺0₁) transitions are contrasted against the structure of the K ^π = 0₂⁺ and 0₃⁺ rotational bands that was calculated on the basis of the quasiparticle-phonon model. The values of (Δ₂ − Δ₁), (Δ₃ − Δ₁), and (Δ₂ − Δ₃) are found to correlate with the sign of the parameter δ and with the calculated structure of the K ^π = 0₂⁺ and 0₃⁺ bands. Original Russian Text ? A.M. Demidov, L.I. Govor, V.A. Kurkin, I.V. Mikhailov, 2009, published in Yadernaya Fizika, 2009, Vol. 72, No. 2, pp. 236–240.     

Synchronization of high-frequency vibrations of slipping phase centers in a tin whisker under microwave radiation

Current-voltage characteristics of a system with a variable number of slipping phase centers resulting from phase separation in a tin whisker under external microwave field with a frequency Ω/2π≅35–45 GHz have been studied experimentally. Emergence and disappearance of steps with zero slope in a whisker’s current-voltage characteristic at U _m/n =(m/n)U _Ω, where m and n are integers and U _Ω is determined by Josephson’s formula _ℏΩ=2eU _Ω, have been investigated. Microwave field generated by slipping phase centers is nonharmonic, and the system of slipping phase centers permits synchronization of internal oscillations at a microwave frequency by an external field with a frequency which is the n-th harmonic of internal oscillations. The estimated microwave power generated by a whisker is 10⁻⁸ W. Stimulation of superconductivity in a current-carrying whisker has been detected. Zh. éksp. Teor. Fiz. 113, 1364–1375 (April 1998)     

Enhanced direct <Emphasis Type="Italic">CP</Emphasis> violation and branching ratios in bottom hadron decays

In the framework of factorization we study direct CP violation in the decays of bottom hadrons containing a strange quark or a charm quark, H _b →f ρ ⁰(ω)→f π ⁺ π ⁻ (H _b is the bottom hadron and f is the product hadron) including the effect of ρ–ω mixing. We find that the CP violating asymmetry can be enhanced greatly via the ρ–ω mixing mechanism when the invariant mass of the π ⁺ π ⁻ pair is in the vicinity of the ω resonance. For the processes associated with b→d transitions, e.g. , , B _c ⁻→D ⁻ π ⁺ π ⁻, B _c ⁻→D ^*− π ⁺ π ⁻, Ξ _b ⁰→Λ π ⁺ π ⁻, and Ω _b ⁻→Ξ ⁻ π ⁺ π ⁻, the maximum CP violating asymmetries can reach about −84%, while for the processes associated with b→s transitions, e.g. , , B _c ⁻→D _s ⁻ π ⁺ π ⁻, B _c ⁻→D _s ^*− π ⁺ π ⁻, Ξ _b ⁻→Ξ ⁻ π ⁺ π ⁻, and Ω _b ⁻→Ω ⁻ π ⁺ π ⁻, the CP violating asymmetries can be enhanced to about 95%. Furthermore, taking ρ–ω mixing into account we calculate the b-hadron decay branching ratios. We also discuss the possibility to observe the predicted CP violating asymmetries at the LHC.     

The model-independent analysis indications for spectroscopy of scalar mesons. Proof for the K0* (900)

In a model-independent approach the data on ππ → ππ, K $ \bar K $ \bar K , ηη, ηη′ in the I ^G J ^PC = 0⁺0⁺⁺ channel and on the Kπ scattering in the $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) channel are analyzed jointly for studying the status and QCD nature of the f ₀- and the K*₀-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q $ \bar q $ \bar q ). In the Kπ-scattering data analysis, the proof for the K*₀(900) is given.     

Observation of Δ+→ pπ0 decay in heavy-ion collisions

Proton-π⁰ coincidences have been measured at the beam energy of 180A MeV in the reaction Ar+Ca studied by TAPS at SIS/GSI. In the proton-π⁰ invariant mass spectrum we observe a significant excess of strength above the background obtained by event mixing. We attribute this signal to the strength distribution N _Δ of the Δ baryonic resonance. No correlation is observed in the case of deuteron-π⁰ coincidences. Assuming isotropic emission of π⁰ and Δ⁺ from a midrapidity thermal source and isospin symmetry, we determined the global N _Δ/N _πratio of 0.79 ±0.30(stat) ±0.2(syst). This value indicates that most pions produced at subthreshold energy in heavy-ion reaction are mediated by the Δ-resonance. Received: 7 April 2000 / Accepted: 29 August 2000     

Study of the reaction γp → pπ0η

The reaction γp → pπ⁰η has been studied with the CBELSA detector at the tagged photon beam of the Bonn electron stretcher facility. The reaction shows contributions from Δ⁺(1232)η , N(1535)⁺π⁰ and pa ₀(980) as intermediate states. A partial-wave analysis suggests that the reaction proceeds via formation of six Δ -resonances, Δ(1600)P ₃₃ , Δ(1920)P ₃₃ , Δ(1700)D ₃₃ , Δ(1940)D ₃₃ , Δ(1905)F ₃₅ , Δ(2360)D ₃₃ , and two nucleon resonances N(1880)P ₁₁ and N(2200)P ₁₃ , for which pole positions and decay branching ratios are given.     

Power corrections in e+e?→π+π?,K+K? and B→Kπ,ππ

CLEO-c measurements of the timelike form factors F _π , F _K at ?s=3.671\sqrt{s}=3.671 GeV provide a direct probe of power corrections (PC’s) at energies near m _B . PC’s in F _π,K and B→Kπ,ππ are separated into perturbative and soft parts. In F _π,K the latter are ≥O(10) larger. A PC fit to the B→Kπ,ππ data also yields a ≥O(10) soft-to-perturbative hierarchy for the QCD penguin PC’s. Hence, both can be attributed to dominance of the soft-overlap between energetic (approximately) back-to-back collinear partons, and consistency of the B→Kπ,ππ fit with the Standard Model appears to be naturally realized. The CP asymmetries S_{Ks p⁰}S_{K_{s} \pi^{0}}, C_{Ks p⁰}C_{K_{s} \pi^{0}} are well determined, providing a clean test for new physics.     

Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization

For a quasi-Fuchsian group Γ with ordinary set Ω, and Δ _n the Laplacian on n-differentials on Γ\Ω, we define a notion of a Bers dual basis for ker Δ _n . We prove that det , is, up to an anomaly computed by Takhtajan and the second author in (Commun. Math Phys 239(1-2):183–240, 2003), the modulus squared of a holomorphic function F(n), where F(n) is a quasi-Fuchsian analogue of the Selberg zeta function Z(n). This generalizes the D’Hoker–Phong formula det , and is a quasi-Fuchsian counterpart of the result for Schottky groups proved by Takhtajan and the first author in Analysis 16, 1291–1323, 2006.      

The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow

We propose a mathematical derivation of Brinkman’s force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Ω⊂ℝ³ for the velocity field u of an incompressible fluid with kinematic viscosity ν and density 1. Brinkman’s force consists of a source term 6π ν j where j is the current density of the particles, and of a friction term 6π ν ρ u where ρ is the number density of particles. These additional terms in the motion equation for the fluid are obtained from the Stokes or steady Navier-Stokes equations set in Ω minus the disjoint union of N balls of radius ε=1/N in the large N limit with no-slip boundary condition. The number density ρ and current density j are obtained from the limiting phase space empirical measure , where x _k is the center of the k-th ball and v _k its instantaneous velocity. This can be seen as a generalization of Allaire’s result in [Arch. Ration. Mech. Anal. 113:209–259, [1991]] who considered the case of periodically distributed x _k s with v _k =0, and our proof is based on slightly simpler though similar homogenization arguments. Similar equations are used for describing the fluid phase in various models for sprays.     

Kinetic energy of π− p-atoms in liquid and gaseous hydrogen

We have measured the Doppler broadening of neutron time-of-flight spectra from the reaction π⁻ p → π⁰ + n in atomic states. From the data, we infer that the kinetic energy distribution of π⁻ p-atoms in liquid and gaseous hydrogen contains discrete ‘high-energy’ components with energies as high as 200 eV attributed to Coulomb de-excitation. In liquid hydrogen, evidence for Coulomb de-excitation transitions with Δn = 2 has been found. This revised version was published online in August 2006 with corrections to the Cover Date.     

Evidence for narrow Δ0(1232) states in the 12 C(e,e'pπ−}11 C Reaction

The reaction ¹²C(e,e'Δ⁰)¹¹C →¹²C(e,e'pπ⁻)¹¹C was investigated at the Mainz Microtron MAMI in a triple coincidence measurement using the three spectrometer setup of the A1 Collaboration. The good missing mass resolution of σ_m= 0.27 MeV/c² allowed to select the events belonging to the ground state of ¹¹C. Cutting on these events the excitation energy spectra of ¹²C_Δ0 show evidence for two peaks of about 4 MeV width (FWHM) at 282 MeV and 296 MeV with a significance of about 4.5 standard deviations. The peaks are interpreted in a simple weak coupling model as bound Δ⁰ states in ¹²C_Δ0. Received: 23 December 1998     

Four-Vertex Theorems, Sturm Theory and Lagrangian Singularities

We prove that the vertices of a curve γ⊂R ⁿ are critical points of the radius of the osculating hypersphere. Using Sturm theory, we give a new proof of the (2k+2)-vertex theorem for convex curves in the Euclidean space R ^2k . We obtain a very practical formula to calculate the vertices of a curve in R ⁿ . We apply our formula and Sturm theory to calculate the number of vertices of the generalized ellipses in R ^2k . Moreover, we explain the relations between vertices of curves in Euclidean n-space, singularities of caustics and Sturm theory (for the fundamental systems of solutions of disconjugate homogeneous linear differential operators L:C ^∞(S ¹)→C ^∞(S ¹)).     

πNN Dynamics in pp → pp,pp →πd and πd →πd Processes Below 1 GeV

pp and πd scattering and pp →πd reaction processes at incident proton laboratory energies T _L ≤ 1 GeV are studied in the framework of πNN dynamics. For this purpose three-body calculations are performed with the πN interaction in the P ₁₁, P ₃₃, S ₁₁ and S ₃₁ states and NN forces in the ³ S ₁ -³ D ₁, ¹ S ₀, and ³ P ₂ states. In addition, the backward-going pion contribution at the πNΔ vertex, the πN-ρN coupling, the heavy-meson exchanges in the NN → NN driving term, and the effect of the off-shell structure in the πN-ρN P ₃₃ interaction are taken into account. Received March 28, 1994; revised July 29, 1994; accepted for publication August 31, 1994     

Luminescence of oxotetrahydrobenzo[c]phenanthridine in polar and nonpolar solvents: Inversion of the energy levels of the Sππ* and Tnπ* states

The spectral-luminescent properties and electronic-level structure of a derivative of oxotetrahydrobenzo[c]phenanthridine—3,3-dimethyl-1,2,3,4-tetrahydrobenzo[c]phenanthridine-1-one (DTP)—in polar and nonpolar solutions are studied by the luminescence and picosecond spectroscopy techniques at 293 and 77 K. It is shown that DTP exhibits ππp* fluorescence only in polar proton-containing methanol, ethanol, and n-propanol and that this fluorescence is associated with a chromophore + alcohol complex. Solutions of DTP in n-propanol and the nonpolar mixture methylcyclohexane + toluene (6:1) at 77 K display ππp* phosphorescence with a quantum yield Φ_Ph=0.1, a lifetime τ_Ph=1.9 s, and a frequency of the 0-0 transition equal to 21550 cm⁻¹. The fact that DTP fluorescence is absent in aprotic solvents and exists in alcohols is explained by the inversion of the energy levels of the S _ππ* and T _n π* states, as a result of which the energy level of the fluorescing S _ππ* state in alcohol becomes the lowest. The picosecond spectra and kinetics of the inducedS _n (ππ*) ← S ₁(π π*) and T _k (ππ*) ← T ₁(ππ*) absorption made it possible to estimate the lifetime of the S ₁(ππ*) state of DTP in n-propanol at 293 K (20±10 ps) and the position of the triplet-triplet absorption peak (495 nm). __________ Translated from Optika i Spektroskopiya, Vol. 94, No. 6, 2003, pp. 993–998. Original Russian Text Copyright ? 2003 by Bondarev, Knyukshto, Tikhomirov, Pyrko.     

Numerical study of the directed polymer in a 1 + 3 dimensional random medium

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length L, the high temperature phase is characterized by a diffusive behavior for the end-point displacement R² ∼L and by free-energy fluctuations of order ΔF(L) ∼O(1). The low-temperature phase is characterized by an anomalous wandering exponent R²/L ∼L^ω and by free-energy fluctuations of order ΔF(L) ∼L^ω where ω∼0.18. In this paper, we first study the scaling behavior of various properties to localize the critical temperature T_c. Our results concerning R²/L and ΔF(L) point towards 0.76 < T_c ≤T₂=0.79, so our conclusion is that T_c is equal or very close to the upper bound T₂ derived by Derrida and coworkers (T₂ corresponds to the temperature above which the ratio remains finite as L ↦ ∞). We then present histograms for the free-energy, energy and entropy over disorder samples. For T ≫T_c, the free-energy distribution is found to be Gaussian. For T ≪T_c, the free-energy distribution coincides with the ground state energy distribution, in agreement with the zero-temperature fixed point picture. Moreover the entropy fluctuations are of order ΔS ∼L^1/2 and follow a Gaussian distribution, in agreement with the droplet predictions, where the free-energy term ΔF ∼L^ω is a near cancellation of energy and entropy contributions of order L^1/2.