Influence of pressure on the electric-field-induced phase transitions in liquid crystals

Within the framework of Landau-de-Gennes formulation, we analyse the effect of pressure on electric-field-induced phase transitions in a liquid crystal which shows spontaneously an isotropic-smectic A transition. Inferring from the experimental pressure dependences on the layer spacing in smectic A phase, as well as the nematic-smectic A metastable temperature T^*_AN, we incorporated the pressure dependence in the free energy through (the surface energy term) and the coupling between the quadrupolar nematic ordering Q_ij and the smectic order parameter ψ. From the S-T phase diagram, we found that the stability of field-induced nematic phase increases with pressure, whereas the discontinuity of the transition decreases. Also, the region where paranematic phase transits directly to smectic A phase increases with pressure.     

Variable-range hopping in 2D quasi-1D electronic systems

A semi-phenomenological theory of variable-range hopping (VRH) is developed for two-dimensional (2D) quasi-one-dimensional (quasi-1D) systems such as arrays of quantum wires in the Wigner crystal regime. The theory follows the phenomenology of Efros, Mott and Shklovskii allied with microscopic arguments. We first derive the Coulomb gap in the single-particle density of states, g(ε), where ε is the energy of the charge excitation. We then derive the main exponential dependence of the electron conductivity in the linear (L), i.e. σ(T) ∼exp [-(T_L/T)^γL], and current in the non-linear (NL), i.e. , response regimes ( is the applied electric field). Due to the strong anisotropy of the system and its peculiar dielectric properties we show that unusual, with respect to known results, Coulomb gaps open followed by unusual VRH laws, i.e. with respect to the disorder-dependence of T_L and and the values of γ_L and γ_NL.     

The Phase Transitions from Chiral Nematic Toward Smectic Liquid Crystals

A Chen-Lubensky energy is used to investigate phase transitions from chiral nematic to smectic C* and smectic A* liquid crystal phases. We consider a liquid crystalline material Ω confined between two parallel plates, where the dimensions of Ω are assumed to be large relative both to the width of a smectic layer and the material’s chiral pitch. We take boundary conditions so that the smectic phase melts at the plates’ surfaces and prove the existence of energy minimizers in an admissible set consisting of order parameters and molecular directors . Then under the physically observed assumption that the Frank elasticity constants become large near a phase transition, we establish estimates for the transition region separating phases. In particular we derive analytic estimates proving that chirality lowers the transition temperature regime above which minimizers are nematic and below which minimizers are in a smectic phase.Research supported by NSF grants DMS-0306516 and DMS-0456286.     

Study of W-boson polarisations and triple gauge boson couplings in the reaction e+e-→W+W- at LEP 2

A determination of the single W spin density matrix (SDM) elements in the reaction e⁺e^-→W⁺W^-→lνqq̄(l=e/μ) is reported at centre-of-mass energies between 189 and 209 GeV. The data sample used corresponds to an integrated luminosity of 520 pb^-1 taken by DELPHI between 1998 and 2000. The single W SDM elements, ρ_ττ’ ^W± (τ,τ’=± 1 or 0), are determined as a function of the W^- production angle with respect to the e^- beam direction and are obtained from measurements of the W decay products by the application of suitable projection operators, Λ_ττ’, which assume the V-A coupling of the W-boson to fermions. The measured SDM elements are used to obtain the fraction of longitudinally polarised Ws, with the result: at a mean energy of 198 GeV. The SDM elements are also used to determine the triple gauge couplings Δg₁ ^Z,Δκ_γ,λ_γ and g₄ ^Z, and . For the CP-violating couplings the results of single parameter fits are: The errors are a combination of statistical and systematic errors. All results are consistent with the Standard Model.     

Semiclassical analysis of edge state energies in the integer quantum Hall effect

Analysis of edge-state energies in the integer quantum Hall effect is carried out within the semiclassical approximation. When the system is wide so that each edge can be considered separately, this problem is equivalent to that of a one dimensional harmonic oscillator centered at x = x_c and an infinite wall at x = 0, and appears in numerous physical contexts. The eigenvalues E_n(x_c) for a given quantum number n are solutions of the equation S(E,x_c)=π[n+ γ(E,x_c)] where S is the WKB action and 0 < γ < 1 encodes all the information on the connection procedure at the turning points. A careful implication of the WKB connection formulae results in an excellent approximation to the exact energy eigenvalues. The dependence of γ[E_n(x_c),x_c] ≡γ_n(x_c) on x_c is analyzed between its two extreme values as x_c ↦-∞ far inside the sample and as x_c ↦∞ far outside the sample. The edge-state energiesE_n(x_c) obey an almost exact scaling law of the form and the scaling function f(y) is explicitly elucidated.     

Research on the Dynamic Problems of 3D Cross Coupling Quantum Harmonic Oscillator by Virtue of Intermediate Representation |<Emphasis Type="Italic">x</Emphasis>〉<Subscript><Emphasis Type="Italic">λ</Emphasis>,<Emphasis Type="Italic">ν</Emphasis></Subscript>

The intermediate representation (namely intermediate coordinate-momentum representation) |x〉 _λ,ν are introduced and employed to research the expression of the operator in intermediate representation |x〉 _λ,ν . The systematic Hamilton operator of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ,ν,τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator |x〉 _{λ,ν λ,ν} 〈x|, and the Radon transformation of Wigner function is just a margin distribution.     

Search for stop production in R-parity-violating supersymmetry at HERA

A search for stop production in R-parity-violating supersymmetry has been performed in e⁺p interactions with the ZEUS detector at HERA, using an integrated luminosity of 65 pb^-1. At HERA, the R-parity-violating coupling λ’ allows resonant squark production, . Since the lowest-mass squark state in most supersymmetry models is the light stop, , this search concentrated on production of , followed either by a direct R-parity-violating decay, or by the gauge decay to . No evidence for stop production was found and limits were set on λ’₁₃₁ as a function of the stop mass in the framework of the minimal supersymmetric standard model. The results have also been interpreted in terms of constraints on the parameters of the minimal supergravity model.     

Near-flat space limit of strings on AdS 4×ℂℙ3

The non-linear nature of string theory on non-trivial backgrounds, related to the AdS/CFT correspondence, force one to look for simplifications. Two such simplifications proved to be useful in studying string theory. These are the pp-wave limit, which describes point-like strings, and the so-called “near-flat space” limit which connects two different sectors of string theory—pp-wave and “giant magnons”. Recently another example of AdS/CFT duality emerged—AdS ₄/CFT ₃, which suggests duality between CS theory and superstring theory on . In this paper we study the “near-flat space” limit of strings on an background and discuss possible applications of the limiting theory. R.C. Rashkov is on leave from Department of Physics, Sofia University, Bulgaria.     

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.     

Precise predictions for Higgs production in association with a W-boson pair at ILC

Higgs-boson production in association with a W-boson pair at e ⁺ e ⁻ linear colliders is one of the important processes in probing the coupling between the Higgs boson and vector gauge bosons and discovering the signature of new physics. We describe the impact of the complete electroweak (EW) radiative corrections of to this process in the standard model (SM) at the International Linear Collider (ILC), and investigate the dependence of the lowest-order (LO) and EW next-to-leading order (NLO) corrected cross sections on the colliding energy and the Higgs-boson mass. The LO and NLO EW corrected distributions of the invariant mass of the W-boson pair and the transverse momenta of the final W-boson and Higgs boson are presented. Our numerical results show that the relative EW radiative correction (δ _ew) varies from −19.4% to 0.2% when m _H=120 GeV and grows from 300 GeV to 1.2 TeV.     

Unparticle searches through gamma–gamma scattering

We investigate the effects of unparticles on γγ→γγ scattering for the photon collider mode of the future multi-TeV e⁺e^- linear collider. We show the effects of unparticles on the differential, and total scattering cross sections for different polarization configurations. Considering 1-loop standard model background contributions from the charged fermions and W^± bosons to the cross section, we calculate the upper limits on the unparticle couplings λ₀ to the photons for various values of the scaling dimension d (1<d<2) at = 0.5–5 TeV.     

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PT\mathcal{PT} -symmetry

Non-Hermitian but -symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H _r , H _θ , and H _φ play essential roles and offer some “user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a -symmetrized H _φ , we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction V(θ)≠0 in the descendant Hamiltonian H _θ would manifest a change in the angular θ-dependent part of the general solution too. Whilst some -symmetrized H _φ Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the -symmetric ones (here the non-Hermitian -symmetric Hamiltonians) are nicknamed as pseudo- -symmetric.     

Alpha-gamma decay studies of 255No

The decay of ²⁵⁵No was investigated by means of α-γ spectroscopy. The isotope was produced in the reactions ²⁰⁸Pb(⁴⁸Ca, n)²⁵⁵No, , and $²³⁸U(²²Ne, 5n)²⁵⁵No$. Levels of the daughter nucleus ²⁵¹Fm were assigned by α-γ coincidence measurements and on the basis of systematics. Level energies were determined precisely using measured γ-rays. The results are compared with the known level schemes of the lighter isotones ²⁴⁷Cm and ²⁴⁹Cf as well as with data for ²⁵³No.     

New information on the T1/2 = 47 s isomer in the 136I nucleus

The ¹³⁶I nucleus, populated in the spontaneous fission of ²⁴⁸Cm, was studied by means of prompt γ-ray spectroscopy using the EUROGAM2 array. The observation in this work of the 42.6keV prompt-γ, M1 + E2 transition de-exciting the 7^- level in ¹³⁶I indicates that this level, interpreted as the configuration, does not correspond to the T = 47s, β-decaying isomer in ¹³⁶I. The isomer is placed 42.6keV below the 7^- level. It has spin 6^- and is interpreted as the configuration. This and other members of both multiplets can be reproduced properly only if one assumes that the πd_5/2 orbital in ¹³⁶I is located 400keV lower than in ¹³³Sb. Possible mechanisms causing this effect are discussed.     

Determination of the η and η<Superscript>′</Superscript> mixing angle from the pseudoscalar transition form factors

The possible range of the η– mixing angle is determined from the transition form factors F_ηγ(Q²) and with the help of up-to-date experimental data. For this purpose, the quark-flavor mixing scheme is adopted and the pseudoscalar transition form factors are calculated in the framework of light-cone pQCD, in which the transverse-momentum corrections and the contributions beyond the leading Fock state have been carefully taken into consideration. We construct a phenomenological expression to estimate the contributions to the form factors beyond the leading Fock state, based on their asymptotic behavior at Q²→0 and . By taking the quark-flavor mixing scheme, our results lead to , where the first error comes from the experimental uncertainty and the second error from the uncertainties of the parameters of the wavefunction. The possible intrinsic charm component in η and is discussed, and our present analysis also disfavors a large intrinsic charm component in η and , e.g. . PACS 13.40.Gp; 12.38.Bx; 14.40.Aq     

Analysis of Ωb? (bss) and Ωc0 (css) with QCD sum rules

We calculate the masses and the pole residues of the heavy baryons Ω _c ⁰(css) and Ω _b ⁻(bss) with the QCD sum rules. The numerical values  GeV (or  GeV) and  GeV (or  GeV) are in good agreement with the experimental data.     

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.     

Internal structure of fluctuating Cooper pairs

In order to obtain information about the internal structure of fluctuating Cooper pairs in the pseudogap state and below the transition temperature of high T_c superconductors, we solve the Bethe-Salpeter equation for the two-electron propagator in order to calculate a “pair structure function” that depends on the internal distance between the partners and on the center of mass momentum P of the pair. We use an attractive Hubbard model with a local potential for s-wave and a separable potential for d-wave symmetry. The amplitude of g_P for small ρ depends on temperature, chemical potential and interaction symmetry, but the ρ dependence itself is rather insensitive to the interaction strength. Asymptotically g_P decreases as an inverse power of ρ for weak coupling, but exponentially when a pseudogap develops for stronger interaction. Some possibilities of observing the pair structure experimentally are mentioned.     

The Invariant Eigen-Operator Method for?N?Harmonically Coupled Identical Oscillators

In this paper, we apply the method of “invariant eigen-operator” to study the Hamiltonian of arbitrary number of coupled identical oscillators and derive their invariant eigen-operator. The results show that, (1) for the system of arbitrary number of identical harmonic oscillators by coordinate coupling or momentum coupling, the invariant eigen operator of system always has the form of or ; (2) the energy level gap of the system has two kinds of possibilities: one is that gap only related to ω that the frequency of oscillators; another one is that gap not only related to ω that the frequency of oscillators, but also related to the number of the coupling oscillators.     

NLO contributions to <Emphasis Type="Italic">B</Emphasis>→<Emphasis Type="Italic">KK</Emphasis><Superscript>*</Superscript> decays in the pQCD approach

We calculate the important next-to-leading-order (NLO) contributions to the B→KK ^* decays from the vertex corrections, the quark loops, and the magnetic penguins in the perturbative QCD (pQCD) factorization approach. The pQCD predictions for the CP-averaged branching ratios are , , and Br(B ⁰→K ⁺ K ^*−+K ⁻ K ^*+)≈1.3×10⁻⁷, which agree well with both the experimental upper limits and the predictions based on the QCD factorization approach. Furthermore, the CP violating asymmetries of the considered decay modes are also evaluated. The NLO pQCD predictions for and decays are and .