Geometric quantities of lower doubly excited bound states of helium

Expectation values of single electron and interelectronic geometric quantities such as $\langle r\rangle$, $\langle r_{12}\rangle$, $\langle r_<\rangle$, $\langle r_>\rangle$, $\langle \cos\theta_{12}\rangle$ and $\langle \theta_{12}\rangle$ are calculated for doubly excited $2{\rm p}n{\rm p}\,{}^1P^{\,\rm e}\,(3\leq n\leq5),\, 2{\rm p}n{\rm p}\,{}^3\!P^{\,\rm e}\,(2\leq n\leq5)$ and $2{\rm p}n{\rm d}\,{}^{1,3}D^{\,\rm o}\,(3\leq n\leq5)$ states of helium using Hylleraas-$B$-spline basis set. The energy levels converge to at least 10 significant digits in our calculations. The extrapolated values of geometric quantities except for $\langle \theta_{12}\rangle$ reach 10 significant digits as well; $\langle \theta_{12}\rangle$ reaches at least 7 significant digits using a multipole expansion approach. Our results provide a precise reference for future research.     

Double Product Integrals and Enriquez Quantisation of Lie Bialgebras II: The Quantum Yang–Baxter Equation

For a Lie algebra with Lie bracket got by taking commutators in a nonunital associative algebra , let be the vector space of tensors over equipped with the Itô Hopf algebra structure derived from the associative multiplication in . It is shown that a necessary and sufficient condition that the double product integral satisfy the quantum Yang–Baxter equation over is that satisfy the same equation over the unital associative algebra got by adjoining a unit element to . In particular, the first-order coefficient r₁ of r[h] satisfies the classical Yang–Baxter equation. Using the fact that the multiplicative inverse of is where is the inverse of in we construct a quantisation of an arbitrary quasitriangular Lie bialgebra structure on in the unital associative subalgebra of consisting of formal power series whose zero order coefficient lies in the space of symmetric tensors. The deformation coproduct acts on by conjugating the undeformed coproduct by and the coboundary structure r of is given by where is the flip.Mathematical Subject Classification (2000). 53D55, 17B62     

Finite State and Finite Stop Quantum Languages

We propose the concept of finite stop quantum automata (ftqa) based on Hilbert space and compare it with the finite state quantum automata (fsqa) proposed by Moore and Crutchfield (Theoretical Computer Science 237(1–2), 2000, 275–306). The languages accepted by fsqa form a proper subset of the languages accepted by ftqa. In addition, the fsqa form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. We introduce complex-valued acceptance degrees and two types of finite stop quantum automata based on them: the invariant ftqa (icftq) and the variant ftqa (vcftq). The languages accepted by icftq form a proper subset of the languages accepted by vcftq. In addition, the icftq form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. In this way, we establish two proper inclusion relations (fsqa) ⊂ (ftqa) and (icftq) ⊂ (vcftq), where the symbol means languages, and two infinite language hierarchies (fsqa) ⊂ (fsqa), (icftq) (icftq).     

Electroweak and CP violation physics at a Linear Collider Z-factory

A future linear collider such as TESLA may be able to run on the Z⁰ resonance with very high luminosity and polarised electron and positron beams. The possibilities of measuring electroweak quantities with high precision are investigated. Huge improvements with respect to the present precision can be expected, especially for the asymmetries A_LR and where beam polarisation can be exploited. The very large sample of events also allows studies of various CP-violating b decays. The precision achievable on the CKM unitarity triangle angles is comparable to experiments at b factories and future hadron colliders.     

Bicross-Product Structure of Affine Quantum Groups

We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.     

Quantum Groups and Double Quiver Algebras

For a finite dimensional semisimple Lie algebra and a root q of unity in a field k, we associate to these data a double quiver . It is shown that a restricted version of the quantized enveloping algebras is a quotient of the double quiver algebra .*The author is partially supported by the National Science Foundation of China (Grant. 10271014) and Natural Science Foundation of Beijing City (grant. 1042001)     

Thermal Entanglement for Interacting Spin-1/2 Systems and its Quantum Criticality

In this work, we investigate the thermal entanglement for interacting spin systems , by varying the parameters of temperature T, direction and magnetic field B. PACS numbers: 03.67.Mn, 03.65.Ud, 05.30.Cd, 73.43.Nq     

Updated estimate of the muon magnetic momentusing revised results from <Emphasis Type="Italic">e</Emphasis><Superscript> + </Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>-</Superscript>annihilation

A new evaluation of the hadronic vacuum polarization contribution to the muon magnetic moment is presented. We take into account the reanalysis of the low-energy e ⁺ e ^-annihilation cross section into hadrons by the CMD-2 Collaboration. The agreement between e ⁺ e ^-and spectral functions in the channel is found to be much improved. Nevertheless, significant discrepancies remain in the center-of-mass energy range between 0.85 and , so that we refrain from averaging the two data sets. The values found for the lowest-order hadronic vacuum polarization contributions are where the errors have been separated according to their sources: experimental, missing radiative corrections in e ⁺ e ^-data, and isospin breaking. The corresponding Standard Model predictions for the muon magnetic anomaly read where the errors account for the hadronic, light-by-light (LBL) scattering and electroweak contributions. The deviations from the measurement at BNL are found to be (1.9 ) and (0.7 ) for the e ⁺ e ^-- and -based estimates, respectively, where the second error is from the LBL contribution and the third one from the BNL measurement.Received: 7 September 2003, Published online: 30 October 2003     

Alpha-gamma decay studies of 255Rf, 251No and 247Fm

The decay of the isotopes ²⁵⁵Rf, ²⁵¹No and ²⁴⁷Fm produced in the reactions , and was investigated by means of α-γ spectroscopy. Previously observed γ transitions in coincidence with α decays of ²⁵⁵Rf were confirmed, their energies and line intensities were measured more precisely, and their multipolarities were determined as E1. In ²⁵¹No a new isomeric state at E ^* > 1700keV with a half-life of ≈ 2μs was identified. The decay of ²⁴⁷Fm was measured more precisely. A partial level scheme of the daughter nucleus ²⁴³Cf could be established.     

Time dependent gravitational potential in the universe and some consequences

In this paper, assuming a linear change of the gravitational potential V in the universe, i.e. , some consequences are obtained. 1. The Hubble red shift is explained by the potential difference between the considered galaxy long time ago and the observer at this epoch. 2. The anomalous acceleration a _P from the spacecraft Pioneer 10 and 11 [1] is explained. 3. The deformations of the trajectories of planets are studied. It is shown that the planetary orbits are not axially symmetric and the angle from the perihelion to the aphelion is , while the angle from the aphelion to the perihelion is , where is the orbital period. There is no perihelion precession caused by the time dependent gravitational potential V. The quotient of two consecutive orbital periods ₁ and ₂ is equal to This formula is tested for the pulsars B1885+09 and B1534+12, and the results are good.This revised version was published online in April 2005. The publishing date was inserted.     

Light quark masses in quantum chromodynamics and chiral symmetry breaking

We derive model independent lower bounds for the sums of effective quark masses \(\bar m_u + \bar m_d \) and \(\bar m_u + \bar m_s \) . The bounds follow from the combination of the spectral representation properties of the hadronic axial currents two-point functions and their behavior in the deep euclidean region (known from a perturbative QCD calculation to two loops and the leading non-perturbative contribution). The bounds incorporate PCAC in the Nambu-Goldstone version. If we define the invariant masses \(\hat m\) by $$\bar m_i = \hat m_i \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^{{{\gamma _1 } \mathord{\left/ {\vphantom {{\gamma _1 } {\beta _1 }}} \right. \kern-\nulldelimiterspace} {\beta _1 }}} $$ and <F ²> is the vacuum expectation value of $$F^2 = \Sigma _a F_{(a)}^{\mu v} F_{\mu v(a)} $$ , we find, e.g., $$\hat m_u + \hat m_d \geqq \sqrt {\frac{{2\pi }}{3} \cdot \frac{{8f_\pi m_\pi ^2 }}{{3\left\langle {\alpha _s F^2 } \right\rangle ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }}} $$ ; with the value <α _u F ²?0.04GeV⁴, recently suggested by various analysis, this gives $$\hat m_u + \hat m_d \geqq 35MeV$$ . The corresponding bounds on \(\bar m_u + \bar m_s \) are obtained replacingm _π ² f _π bym _K ² f _K . The PCAC relation can be inverted, and we get upper bounds on the spontaneous masses, \(\hat \mu \) : $$\hat \mu \leqq 170MeV$$ where \(\hat \mu \) is defined by $$\left\langle {\bar \psi \psi } \right\rangle \left( {Q^2 } \right) = \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^d \hat \mu ^3 ,d = {{12} \mathord{\left/ {\vphantom {{12} {\left( {33 - 2n_f } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {33 - 2n_f } \right)}}$$ .     

A Class of Generalized Gamma Functions

We study a family of holomorphic functions defined by infinite products of the form (a, r real, ar > 0) which generalize Eulers definition since . We obtain analogues of classical formulas (e.g. Gauss multiplication and complement formulas) for these functions _a,r(s)     

Trigonometric Dynamical <Emphasis Type="Italic">r</Emphasis>-Matrices Over Poisson Lie Base

Let be a finite dimensional complex Lie algebra and a Lie subalgebra equipped with the structure of a factorizable quasitriangular Lie bialgebra. Consider the Lie group Exp with the Semenov-Tjan-Shansky Poisson bracket as a Poisson Lie manifold for the double Lie bialgebra . Let be an open domain parameterizing a neighborhood of the identity in Exp by the exponential map. We present dynamical r-matrices with values in over the Poisson Lie base manifold .*This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center Group Theoretic Methods in the study of Algebraic Varieties of the Israel Science foundation, and by the RFBR grant no. 03-01-00593.     

Quantum Computational Semantics on Fock Space

In the Fock space semantics, meanings of sentences are identified with density operators of the (unsymmetrized) Fock space based on the Hilbert space ℂ². Generally, the meaning of a sentence is smeared over different sectors of . The standard quantum computational semantics is a limit case of the Fock space semantics, where the meaning of any sentence α only “lives” in one sector of , which is determined by the logical complexity of α. We prove that the global Fock space semantics and the standard quantum computational semantics characterize the same logic. PACS: 03.67.Lx.     

Jet production in charged current deep inelastic <Emphasis Type="Italic">e</Emphasis><Superscript> + </Superscript><Emphasis Type="Italic">p</Emphasis> scatteringat HERA

The production rates and substructure of jets have been studied in charged current deep inelastic e ⁺ p scattering for Q ² > 200 GeV² with the ZEUS detector at HERA using an integrated luminosity of 110.5 pb^-1. Inclusive jet cross sections are presented for jets with transverse energies GeV and pseudorapidities in the range . Dijet cross sections are presented for events with a jet having GeV and a second jet having GeV. Measurements of the mean subjet multiplicity, , of the inclusive jet sample are presented. Predictions based on parton-shower Monte Carlo models and next-to-leading-order QCD calculations are compared to the measurements. The value of , determined from at for jets with GeV, is . The mean subjet multiplicity as a function of Q ² is found to be consistent with that measured in NC DIS.Received: 5 June 2003, Published online: 10 October 2003     

Lifetime vibrational interference during the NO 1s-1π* resonant excitation studied by the NO+(A 1Π → X 1Σ+) fluorescence

Dispersed fluorescence from fragments formed after the de-excitation of the 1s^-1π^* resonances of N^*O and NO^* has been measured in the spectral range of 118–142 nm. This range is dominated by lines of atomic nitrogen and oxygen fragments and by the bands in the NO⁺ ion which result from the participator Auger decay of the 1s^-1π^* resonances. Ab-initio calculations of the transition probabilities between vibrational levels during the reaction NO N^*O ⇒ NO were used to explain the observed intensity dependence for the fluorescence bands on the exciting-photon energy across the resonances and on both v^′ and v^′′ vibrational quantum numbers. The multiplet structure of the 1s^-1π^* resonance and lifetime vibrational interference explain the observed exciting-photon energy dependence of the fluorescence intensity. A strong spin-orbit coupling between singlet and triplet states of NO⁺ is proposed to reduce additional cascade population of the state via radiative transitions from the and states and to explain remaining differences between measured and calculated integral fluorescence intensities.