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%.     

On the linearized relativistic Boltzmann equation

The linearized relativistic Boltzmann equation inL ²(r,p) is investigated. The detailed analysis of the collision operatorL is carried out for a wide class of scattering cross sections.L is proved to have a form of the multiplication operatorv(p) plus the compact inL ²(p) perturbationK. The collisional frequencyv(p) is analysed to discriminate between relativistic soft and hard interactions. Finally, the existence and uniqueness of the solution to the linearized relativistic Boltzmann equation is proved.     

Higher orders in residual two-electron interaction

Precise methods of calculations of many-electron atoms are under intensive development. In such calculations, higher orders of the perturbation theory in regard to residual interaction of electrons should be taken into account. In this study, a model of an atom with two electrons in its core and two valence electrons is considered. In terms of this model, expansion with respect to residual interaction is analyzed for two initial approximations based on the potentials V ⁽²⁾ and V ⁽⁴⁾. It turns out that the higher order corrections are nearly the same in both cases. At the same time, the potential V ⁽²⁾ has a number of advantages.     

Reichenbach's common cause principle and quantum field theory

Reichenbach's principles of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory, and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebrasA(V₁) andA(V₂) pertaining to spacelike separated spacetime regions V₁ and V₂ can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the vacuum state between events inA(V₁) andA(V₂) have a genuinely probabilistic common cause, then the local algebrasA(V₁) andA(V₂) must be statistically independent in the sense of C^*-independence.     

Electric quadrupole interactions in Ru-Sc alloys

In TDPAC studies of the electric quadrupole interaction in Ru_xSc_1–x alloys two different electric fieldgradients (EFG) have been observed at the site of⁹⁹Ru: V_zz(I)=12.6·10¹⁷ V/cm² and V_zz(II)=18.9·10₁₇ V/cm². The corresponding relative fractions f(I) and f(II), respectively, vary with the Ru concentration x. For low concentrations x<0.01 most nuclei (f(I)0.8) experience the smaller EFG V_zz(I). At x=0.01, however, the fraction f(I) goes abruptly to zero and V_zz(II) becomes dominant. In view of these results the previous interpretation of V_zz(II) as the EFG of dilute Ru on substitutional Sc sites can no longer be maintained. The Ru-Sc configurations producing these EFG's have not yet been identified. In the intermetallic compound Ru₂Sc the interaction is completely different, in RuSc₃, however, similar values have been observed.     

Neutron scattering by anharmonic crystals and the effect of sublattice displacements

A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV ⁽³⁾ (k _1j1; —k _1j1;o _j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV ⁽³⁾ (k _1j1;k _2j2;k _3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients.     

On the connectivity index for lattices of nonintegral dimensionality

We define the connectivity indexc for an infinite graph by the requirement that to disconnect a subset of at leastV points from the rest of the graph requires the deletion of a minimum ofS(V) bonds whereS(V) ∼V ^(c−1)/c for largeV. For ad-dimensional hypercubical lattice withd integral,c=d. We construct explicit examples of lattices with nonintegral connectivity indexc, 1<c<∞. It is argued that the connectivity index is an important parameter determining the critical behaviour of Hamiltonians on these lattices.     

Energy levels of vanadium ions in CdTe

In CdTe doped with vanadium the photoluminescence due to the ³ T ₂(F) ³ A ₂(F) transition of V³⁺(d ²) is detected. Its decay time is determined as (630±20) s, a result comparable to the analogous emissions in various host lattices. Further emissions around 5000 cm^–1 and 9000 cm^–1 are caused by charge-transfer transitions or bound-exciton decay. Excitation and sensitization spectra yield information on the positions of the energy levels within the gap, which are discussed using two different models. At T=4.2 K, the distance of the V²⁺/V³⁺ donor level is 7300 cm^–1 and 5700 cm^–1 referred to the valence and the conduction band edges, respectively. The absence of V²⁺(d ³) centres is tentatively ascribed to the existence of deeply bound excitons.     

Some perturbation calculations for 1s2p, 1s 22p,and 1s 22s

The Dalgarno interchange theorem is used, together with the U function approach, to evaluate the first order perturbation corrections to <r ₁ ^-1+r ₂ ^-1> and <r ₁ + r ₂> for the two-electron states 1s2p ¹ P and 1s2p ³ P. The results for <r ₁ + r ₂> are extended by using a screening approximation, and are compared with the results of accurate variational calculations. The first order perturbation correction to spin-weighted expectation values of type <ΣV(r_j )s_zj > is given for the three-electron states 1s ²2p ² P and 1s ²2s ² S. The case V(r_j ) = r _j ^-1 is treated in detail.     

Current-voltage characteristics of YBa2Cu3O7−x single crystals and Kosterlitz-Thouless transition

The nonlinear I-V characteristic (V(I)) of YBa₂Cu₃O_7−x single crystal was investigated near the transition from the resistive to the superconducting state in the absence of a magnetic field. A modulation Fourier analysis at temperature T* (the maximum of the amplitudes of the higher (n>1) harmonics of the response voltage) was used to determine an analytic dependence V(I) which accurately describes the experimental results (direct measurements and harmonics) in the range of currents I<30 mA (j<310 A/cm²). It is shown that at T* the power approximation of the I-V characteristic V∼I ³ is only found in the low current density limit (j≪j ₀=140 A/cm²). The results are interpreted in terms of the Kosterlitz-Thouless (KT) transition model. It is established that T* corresponds to the temperature of the KT transition T _KT, which means that T _KT can be determined directly. The deviation of V(I) from a power dependence is caused by the nonlogarithmic variation of the vortex interaction energy as a function of the distance between them. Fiz. Tverd. Tela (St. Petersburg) 40, 202–204 (February 1998)     

Current-voltage characteristics for a Peierls-conducting point contact

Current-voltage (J-V) and differential-conductivity-voltage ( dJ/dV-V) characteristics are analytically calculated at zero temperature for a point contact consisting of: two Peierls conductors P ( = 1, 2) separated by an insulator (I). Here P is a conductor with charge density wave (CDW). The J-V and dJ/dV-V characteristics depend on the CDW phases ( = 1, 2) in the mean field approximation. To calculate them analytically we assumed, = ≡Δ where ( = 1, 2) are the energy gaps of P ( = 1, 2). The current J has a discontinuous jump at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The differential conductivity dJ/dV has a singularity at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The relation J(V,ϕ ₁,ϕ ₂) = - J(- V,ϕ ₁ + π,ϕ ₂ + π) is obtained. Received 4 July 2001 and Received in final form 13 September 2001     

Time Quasi-Periodic Unbounded Perturbations¶of Schrödinger Operators and KAM Methods

We eliminate by KAM methods the time dependence in a class of linear differential equations in ℓ² subject to an unbounded, quasi-periodic forcing. This entails the pure-point nature of the Floquet spectrum of the operator H ₀+εP(ωt) for ε small. Here H ₀ is the one-dimensional Schr?dinger operator p ²+V, V(x)∼|x|^α, α <2 for |x|→∞, the time quasi-periodic perturbation P may grow as |x|^β, β <(α−2)/2, and the frequency vector ω is non resonant. The proof extends to infinite dimensional spaces the result valid for quasiperiodically forced linear differential equations and is based on Kuksin's estimate of solutions of homological equations with non-constant coefficients. Received: 3 October 2000 / Accepted: 20 December 2000     

悬浮颗粒散射脉冲信号群的统计分形特性

将PCI-9812高速数据采集卡与激光尘埃粒子计数光电传感器结合,对空气中悬浮颗粒群产生的散射脉冲信号数随幅度的统计分布p(l)进行高分辨率的测定.实验数据表明,在大样本条件下,脉冲信号集合整体及不同脉宽信号子集的p(l)函数在幅度定义域(V0,VM)内均以很高的精度满足对数正态分布形式,即该随机脉冲信号群具有统计分形(自相似)特征.进一步理论研究表明,p(l)函数具有非线性缩放不变性;且当统计参数满足(lnl-lnl)2lnl时,该函数与幂函数l-(1-ε)表现出几何相似性,其中ε1.     

典型随机信号特征参数统计分布的分形特性

建立了一种能够描述随机信号结构基本特征的双参数脉冲信号统计模型.基于此模型,脉冲信号群幅度计数分布q(l_V),宽度计数分布p(l_τ)及给定宽度信号子集的幅度计数分布ε_lτ(l_V),给定幅度信号子集的宽度计数分布δ_lV(l_τ)均能很稳定的服从以序列自然数为自变量的对数正态分布.且计数分布的统计特征量μ_lnV,μ_lnτ,σ_lnV,σ_lnτ与信号的特征参数l_V,l_τ之间存在内在联系,这种联系的形式即随机信号分形特性的表现,表明随机信号特征参数的统计分布之间具有非整数维分形特征. 关键词： 分形 随机信号 双参数 统计     

A Note on the Koszul Complex in Deformation Quantization

The aim of this short note is to present a proof of the existence of an A _∞-quasi-isomorphism between the A _∞-S(V ^*)-ù(V){\wedge(V)} -bimodule K, introduced in Calaque et al. (Bimodules and branes in deformation quantization, 2009), and the Koszul complex K(V) of S(V ^*), viewed as an A _∞-S(V ^*)-ù(V){\wedge(V)} -bimodule, for V a finite-dimensional (complex or real) vector space.     

Exact Solutions of the Two-Dimensional Schrödinger Equation with Certain Central Potentials

By applying an ansatz to the eigenfunction, an exact closed-form solution of theSchrödinger equation in two dimension is obtained with the potentials V(r) =ar ² + br ⁴ + cr ⁶,V(r) = ar + br² + cr ^–1,and V(r) = ar ² + br ^–2+ cr ^–4 + dr ^–6,respectively. The restrictions on the parameters of the given potential andthe angular momentum m are obtained.     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).     

The Büttiker-Landauer model generalized

Büttiker and Landauer studied scattering off an oscillating rectangular barrier in order to shed light on the time aspects of tunneling. The expression for the traversal time resulting from this study is controversial. In addition, doubts have recently been expressed on technical aspects of their work. In an attempt to clarify these issues, we investigate a generalization of their model to arbitrary oscillating barriers,V(x, t)=V ₀(x)+V ₁(x)cos t. In the process, we confirm that Büttiker and Landauer's work is technically sound. However, we show, by several examples, that no direct general relation exists between the characteristic frequency of an oscillating barrier and the duration of the tunneling process. For a wide range of realistic parameters this characteristic frequency does not even exist.This paper is dedicated to E. G. D. Cohen.     

The electron spin resonance spectrum of the trichloromethyl radical in solution

The equation of state PV = - a/V + RT(1 - y)^-4 is shown to be considerably better at high densities than van der Waals' equation PV = - a/V + RT(1 - 4y)^-1 and to be equal in accuracy to two other slightly more complicated equations for PV.     

Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals

We consider a generic classical many particle system described by an autonomous Hamiltonian H(x ¹,…,x ^N+2) which, in addition, has a conserved quantity V(x ¹,…,x ^N+2)=v, so that the Poisson bracket {H,V} vanishes. We derive in detail the microcanonical expressions for entropy and temperature. We show that both of these quantities depend on multidimensional integrals over sub-manifolds given by the intersection of the constant energy hyper-surfaces with those defined by V(x ¹,…,x ^N+2)=v. We show that temperature and higher order derivatives of entropy are microcanonical observable that, under the hypothesis of ergodicity, can be calculated as time averages of suitable functions. We derive the explicit expression of the function that gives the temperature.