Renormalons and analytic properties of the β function

The presence or absence of renormalon singularities in the Borel plane is shown to be determined by the analytic properties of the Gell-Mann-Low function β(g) and some other functions. A constructive criterion for the absence of singularities consists in the proper behavior of the β function and its Borel image at infinity, β(g) ∝ g^α and B(z) ∝ z^α with α ≤ 1. This criterion is probably fulfilled for the ?⁴ theory, quantum electrodynamics, and quantum chromodynamics, but is violated in the O(n)-symmetric sigma model with n → ∞.     

Investigation of low-lying levels of the <Stack><Subscript>4</Subscript><Superscript>8</Superscript></Stack>Be nucleus in the multiquantum approximation of the orthogonal scheme

In the multiquantum approximation of the orthogonal scheme, specific calculations for the energies and radii of the ₄ ⁸ Be nucleus are performed with allowance for all states characterized by the λ=[44] Young diagram, the quantum numbers K_min and K_min+2 of the O(3(A?1)) group, and the quantum numbers E=K+2N (N≤9) of the U(3(A?1)) group. The convergence of the results with respect to the extension of the basis is studied, and the structure of relevant wave functions is revealed. The results of these calculations are compared with the results obtained in the analogous approximation of the unitary scheme.     

Efficient Nonlocal <Emphasis Type="Italic">M</Emphasis>-Control and <Emphasis Type="Italic">N</Emphasis>-Target Controlled Unitary Gate Using Non-symmetric GHZ States

Efficient local implementation of a nonlocal M-control and N-target controlled unitary gate is considered. We first show that with the assistance of two non-symmetric qubit⁽¹⁾-qutrit^(N) Greenberger-Horne-Zeilinger (GHZ) states, a nonlocal 2-control and N-target controlled unitary gate can be constructed from 2 local two-qubit CNOT gates, 2N local two-qutrit conditional SWAP gates, N local qutrit-qubit controlled unitary gates, and 2N single-qutrit gates. At each target node, the two third levels of the two GHZ target qutrits are used to expose one and only one initial computational state to the local qutrit-qubit controlled unitary gate, instead of being used to hide certain states from the conditional dynamics. This scheme can be generalized straightforwardly to implement a higher-order nonlocal M-control and N-target controlled unitary gate by using M non-symmetric qubit⁽¹⁾-qutrit^(N) GHZ states as quantum channels. Neither the number of the additional levels of each GHZ target particle nor that of single-qutrit gates needs to increase with M. For certain realistic physical systems, the total gate time may be reduced compared with that required in previous schemes.     

Relativmessung integrierter Wirkungsquerschnitte für den Kernphotoeffekt: Die Reaktion O16(γ, n)O15

Li₂CO₃ and Na₂C₄H₈O₈ have been irradiated by 34 MeV bremsstrahlung. The yield of the induced O¹⁵ activity has been measured relative to the yield of the C¹²(γ, n)C¹¹ resp. Cu⁶³(γ, n)Cu⁶² reaction by detecting the annihilation quanta. Additional yield measurements with the bremsstrahlung beam attenuated by 18 mm of lead were made to determine the ratio of the integrated cross sections for the reactions O¹⁶(γ, n)O¹⁵ and C¹²(γ, n)C¹¹ resp. Cu⁶³(γ, n)Cu⁶². Using the cross section ofBarber et al. for C¹²(γ, n)C¹¹, the cross section integrated up to 33 MeV for O¹⁶(γ, n)O¹⁵ was obtained to 61±7 MeVmb.     

Untersuchungen über die Energieabhängigkeit von Kernreaktionen mit Neutronen im Energiebereich zwischen 12 und 19 MeV

Continuing earlier investigations we studied the energy dependence of the cross sections of the following nuclear reactions produced by neutrons in the energy range from 12 to 19 MeV: P³¹(n, 2n)P³², P³¹(n,α)Al²⁸, Cu⁶⁵(n, 2n)Cu⁶⁴, Cu⁶⁵(n, p)Ni⁶⁵, Zn⁶⁴(n, 2n)Zn⁶³, Zn⁶⁴(n, p)Cu⁶⁴, V⁵¹(n, p)Ti⁵¹, Br⁷⁹(n, α)As⁷⁶, O¹⁶(n, α)C¹³. The results were compared with cross sections calculated according to the statistical theory, considering the competition ofγ-ray emission and particle (predominantly neutron) emission from the excited residual nucleus.     

Intertwining Symmetry Algebras of Quantum Superintegrable Systems on Constant Curvature Spaces

A class of quantum superintegrable Hamiltonians defined on a hypersurface in a n+1 dimensional ambient space with signature (p,q) is considered and a set of intertwining operators connecting them are determined. It is shown that the intertwining operators can be chosen such that they generate the su(p,q) and so(2p,2q) Lie algebras and lead to the Hamiltonians through Casimir operators. The physical states corresponding to the discrete spectrum of bound states as well as the degeneration are characterized in terms of some particular unitary representations.     

Optimal Synthesis of the Joint Unitary Evolutions

Joint unitary operations play a central role in quantum communication and computation. We give a quantum circuit for implementing a type of unconstructed useful joint unitary evolutions in terms of controlled-NOT (CNOT) gates and single-qubit rotations. Our synthesis is optimal and possible in experiment. Two CNOT gates and seven R _x , R _y or R _z rotations are required for our synthesis, and the arbitrary parameter contained in the evolutions can be controlled by local Hamiltonian or external fields.     

Bidirectional Quantum Teleportation of a Class of <Emphasis Type="Italic">n</Emphasis>-Qubit States by Using (2<Emphasis Type="Italic">n</Emphasis> + <Emphasis Type="Bold">2</Emphasis>)-Qubit Entangled States as Quantum Channel

A new protocol of bidirectional quantum teleportation (BQT) is proposed in which the users can transmit a class of n-qubit state to each other simultaneously, by using (2n + 2)-qubit entangled states as quantum channel. The state of the art approaches can only transmit two-qubit states in each round. This scheme is based on control-not operation, single-qubit measurements and appropriate single-qubit unitary operations. It is shown that the protocol is secure in preparation phase.     

On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

Quantum Cryptography,Quantum Communication,and Quantum Computer in a Noisy Environment

First, we study several information theories based on quantum computing in a desirable noiseless situation. (1) We present quantum key distribution based on Deutsch’s algorithm using an entangled state. (2) We discuss the fact that the Bernstein-Vazirani algorithm can be used for quantum communication including an error correction. Finally, we discuss the main result. We study the Bernstein-Vazirani algorithm in a noisy environment. The original algorithm determines a noiseless function. Here we consider the case that the function has an environmental noise. We introduce a noise term into the function f(x). So we have another noisy function g(x). The relation between them is g(x) = f(x) ± O(??). Here O(??) ? 1 is the noise term. The goal is to determine the noisy function g(x) with a success probability. The algorithm overcomes classical counterpart by a factor of N in a noisy environment.     

Orbital fractional parentage coefficients for the harmonic oscillator shell model

The Hamiltonian ofn particles moving in a common harmonic oscillator potential has as its symmetry group the unitary groupU(3n) in 3n dimensions,n particle states of the harmonic oscillator shell model can be characterized as bases of irreducible representations (BIR) of the groupU(3n) and of certain subgroups of this group. Use is made of these subgroups for the factorization and calculation of 2, 3, and 4 particle fractional parentage coefficients (fpc) of the harmonic oscillator shell model. Recoupling coefficients for subgroup chains of the symmetric groupS (n) appear as factors in the fpc. These coefficients are analyzed and calculated explicitly. The 2, 3 and 4 particle fpc of the 1s 1p shell configuration are obtained as products of these recoupling coefficients with known reduced Wigner coefficients of the unitary groupU(3) in 3 dimensions. Possible applications are indicated.     

Quantum yield and rate constant of the singlet <Superscript>1</Superscript>Δ<Subscript><Emphasis Type="Italic">g</Emphasis></Subscript> oxygen luminescence in an aqueous medium in the presence of nanoscale inhomogeneities

The quantum yields and lifetimes of photosensitized luminescence of the ¹Δ _g state of singlet oxygen in an aquatic media with a controlled concentration of dielectric anisotropy centers (polyethylene glycol) have been measured using the methods of laser fluorometry. It is established that the quantum yield and the rate constant (k _r ) of the a ¹Δ _g → X ³Σ _g ^- luminescence of ¹O₂ increase as the polymer concentration increases. The effect is analyzed within a general approach involving a relationship between kr and dielectric properties of the medium and is explained by the increased density of photon states and the local field factor in the space around O₂(а ¹Δ _g ).     

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)}.     

Spectra and mean energies of prompt neutrons from <Superscript>238</Superscript>U fission induced by primary neutrons of energy in the region <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><20 MeV

The time-of-flight technique is used to measure the ratios R(E, E _n )=N(E, E _n )/N_Cf(E) of the normalized (to unity) spectra N(E, E _n ) of neutrons accompanying the neutron-induced fission of ²³⁸U at primary-neutron energies of E _n =6.0 and 7.0 MeV to the spectrum N_Cf(E) neutrons from the spontaneous fission of ²⁵²Cf. These experimental data and the results of their analysis are discussed together with data that were previously obtained for the neutron-induced fission of ²³⁸U at the primary energies of E _n =2.9, 5.0, 13.2, 14.7, 16.0, and 17.7 MeV.     

Thermodynamic study of compounds of the Nd-Ba-Cu-O system

Standard enthalpies of formation for solid solutions of composition Nd_{1 + x} Ba_{2 ? x} Cu₃O _y (x = 0–0.8, y = 6.65–7.24) from oxides were determined by solution calorimetry. The heat capacity of NdBa₂Cu₃O_6.87 phase was measured in the range 5–320 K by low-temperature adiabatic calorimetry. The absolute entropy S ^o(T), the difference of enthalpies H ^o(T)-H ^o(0 K), and the reduced Gibbs energy Φ^o(T) = S ^o(T)–[H ^o(T)–H ^o(0)]/T were calculated on the basis of smoothed dependence C _p (T) in the 0–320 K range. An assessment was made for the heat capacities and the absolute entropies of solid solutions Nd_1+x Ba_2?x Cu₃O _y . The obtained set of thermodynamic parameters can be used for the calculation of phase equilibria in the Nd-Ba-Cu-O system.     

Quantum groups as generalized gauge symmetries in WZNW models. Part II. The quantized model

This is the second part of a paper dealing with the “internal” (gauge) symmetry of the Wess–Zumino–Novikov–Witten (WZNW) model on a compact Lie group G. It contains a systematic exposition, for G = SU(n), of the canonical quantization based on the study of the classical model (performed in the first part) following the quantum group symmetric approach first advocated by L.D. Faddeev and collaborators. The internal symmetry of the quantized model is carried by the chiral WZNW zero modes satisfying quadratic exchange relations and an n-linear determinant condition. For generic values of the deformation parameter the Fock representation of the zero modes’ algebra gives rise to a model space of U _q (sl(n)). The relevant root of unity case is studied in detail for n = 2 when a “restricted” (finite dimensional) quotient quantum group is shown to appear in a natural way. The module structure of the zero modes’ Fock space provides a specific duality with the solutions of the Knizhnik–Zamolodchikov equation for the four point functions of primary fields suggesting the existence of an extended state space of logarithmic CFT type. Combining left and right zero modes (i.e., returning to the 2D model), the rational CFT structure shows up in a setting reminiscent to covariant quantization of gauge theories in which the restricted quantum group plays the role of a generalized gauge symmetry.     

A Bohmian approach to the perturbations of non-linear Klein–Gordon equation

In the framework of Bohmian quantum mechanics, the Klein–Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave ?(x) in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein–Gordon equation? We examine this approach for ?⁴(x) and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.     

Internal friction in alloys due to plasticity of the diffusion phase transformation

An analytic expression is obtained for the time dependence Q ^?1(t) of internal friction associated with plasticity of a phase transformation. Time dependences Q ^?1(t) of internal friction of the Pb-62Sn and Pb-1.9Sn alloys (wt.%) alloys were studied in the regime of continuous excitation of resonant flexural vibrations. The measurements of the Q ^?1(t) dependences for 1 h at room temperature and a fixed strain amplitude ε₀ ≈ 7 and 19 min) for the Pb-62Sn alloy. For the Pb-1.9Sn alloy under the same conditions, an exponential decrease followed by an internal friction peak (at t _m ≈ 7 min) is observed. It is shown numerically that the above singularities of internal friction are formed by processes of intermittent phase decomposition of Pb-Sn alloys in the cyclic stress field produced by an external load. Experimental data on Q ^?1(t) are used for reconstructing the kinetic curves describing the decomposition (conversion) ratio as a function of time and for calculating the corresponding values of parameters K and n of the Avrami kinetic equation for the Pb-62Sn alloy.     

Electric quadrupole moments of light nuclei and transition probabilities for them in the multiquantum approximation of the orthogonal scheme

A method for calculating electric quadrupole moments of light nuclei and probabilities of electric quadrupole transitions in them in the multiquantum approximation of the orthogonal scheme is proposed. Specific calculations of these quantities are performed for the ₄ ⁸ Be nucleus with allowance for all U(3(A ? 1)) states characterized by the λ = [44] Young diagram, the quantum numbers K _min and K _min + 2 of the O(3A ? 1)) group, and the number E = K + 2N (N = 0, 1, …, 9) of oscillator quanta. It is shown that an extension of the basis from the E = K _min to the E = K _min + 2 approximation leads to an increase of 15 to 45% in the electric quadrupole moments and to an increase in the transition probabilities B(E2) by a factor of 1.6 to 2.8. The inclusion of E = K + 2N (N = 0, 1, …), states involving multiquantum excitations (ρ excitations) increases additionally the results by 10 to 30%. The results of these calculations are compared with their counterparts obtained in the multiquantum approximation of the unitary scheme.     

On the structure of strips exhibiting the integral quantum Hall effect in an inhomogeneous 2D electron system

A formalism is developed to generalize the results obtained for “incompressible” strips exhibiting the integral quantum Hall effect in a spatially inhomogeneous 2D electron system to the cases of finite temperatures, significant electron density gradients, etc. Specifically, the concept of the “quality” of a given integer quantum Hall effect strip (channel) is introduced; the quality is proportional to the derivative dn(x)/dx in the central part of the channel [n(x) is the electron density distribution over the channel]. For a well-defined channel, this derivative tends to zero. If a noticeable gradient arises in the n(x) distribution, the channel does not exhibit the quantum Hall effect and ceases to exist. The conditions are determined under which a channel exhibiting the integral quantum Hall effect breaks down. The results of calculations are used to interpret the available experimental data.