Orientational order and polarizability of molecules in a nematic liquid crystal

The influence of the orientational order of molecules in a nematic liquid crystal on the mean value $\bar \gamma$ and anisotropy Δγ of the molecular polarizability has been studied in the framework of the molecular statistical approach with allowance for the perturbation of the electronic structure of molecules due to the change in the conformation of their aromatic core and intermolecular interactions. Experimental dependences of $\bar \gamma$ and Δγ on the molecular orientational order parameter S have been derived, and their specific features for the known objects have been explained. The possibility of separating the contributions of opposite signs to the dependence Δγ(S) due to the change in the conformation of molecules and intermolecular interactions has been shown using nematic MBBA as an example.     

Renormalized perturbation theory flow equations for the Anderson impurity model

We apply the renormalized perturbation theory (RPT) to the symmetric Anderson impurity model. Within the RPT framework exact results for physical observables such as the spin and charge susceptibility can be obtained in terms of the renormalized values \(\tilde \mu = (\tilde \Delta ,\tilde U)\) of the hybridization Δ and Coulomb interaction U of the model. The main difficulty in the RPT approach usually lies in the calculation of the renormalized values themselves. In the present work we show how this can be accomplished by deriving differential flow equations describing the evolution of \(\tilde \mu = (\tilde \Delta )\) with Δ. By exploiting the fact that \(\tilde \mu = (\tilde \Delta )\) can be determined analytically in the limit Δ → ∞ we solve the flow equations numerically to obtain estimates for the renormalized parameters in the range 0 <U/πΔ< 3.5.     

Change in the polarizability of MBBA molecules upon the nematic-isotropic liquid transition and physical consequences

The Lorentz tensor components L _j and the polarizability tensor components γ _j of 4-methoxyben-zylidene-4′-butylaniline (MBBA) liquid crystal molecules in nematic and isotropic phases have been determined experimentally. The quadratic dependences of the mean value $\bar \gamma $ (S) and anisotropy Δγ(S) of the polarizability in the nematic phase on the orientational order parameter S of molecules have been established. Within the phenomenological approach, the dependences $\bar \gamma $ (S) and Δγ(S) have been derived, and their features for MBBA and other known objects have been interpreted. The relation of the dependences $\bar \gamma $ (S) and Δγ(S) to the features of the nematic-isotropic liquid phase transition has been found.     

Angles, Scales and Parametric Renormalization

We discuss the structure of renormalized Feynman rules. Regarding them as maps from the Hopf algebra of Feynman graphs to ${\mathbb{C}}$ originating from the evaluation of graphs by Feynman rules, they are elements of a group ${G=\mathrm{Spec}_{\mathrm{Feyn}}(H)}$ . We study the kinematics of scale and angle-dependence to decompose G into subgroups ${G_{\mathrm{\makebox{1-s}}}}$ and ${G_{\mathrm{fin}}}$ . Using parametric representations of Feynman integrals, renormalizability and the renormalization group underlying the scale dependence of Feynman amplitudes are derived and proven in the context of algebraic geometry.     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

Three-loop relation of quark\overline {MS} and pole masses

We calculate, exactly, the next-to-leading correction to the relation between the \(\overline {MS} \) quark mass, \(\bar m\) , and the scheme-independent pole mass,M, and obtain $$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$ as an accurate approximation forN _F?1 light quarks of massesM _i <M. Combining this new result with known three-loop results for \(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the \(\overline {MS} \) mass, \(\bar m\) (μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom \(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections.     

Renormalization Theory of a Two Dimensional Bose Gas: Quantum Critical Point and Quasi-Condensed State

We present a renormalization group construction of a weakly interacting Bose gas at zero temperature in the two-dimensional continuum, both in the quantum critical regime and in the presence of a condensate fraction. The construction is performed within a rigorous renormalization group scheme, borrowed from the methods of constructive field theory, which allows us to derive explicit bounds on all the orders of renormalized perturbation theory. Our scheme allows us to construct the theory of the quantum critical point completely, both in the ultraviolet and in the infrared regimes, thus extending previous heuristic approaches to this phase. For the condensate phase, we solve completely the ultraviolet problem and we investigate in detail the infrared region, up to length scales of the order \((\lambda ^3\rho _0)^{-1/2}\) (here \(\lambda \) is the interaction strength and \(\rho _0\) the condensate density), which is the largest length scale at which the problem is perturbative in nature. We exhibit violations to the formal Ward Identities, due to the momentum cutoff used to regularize the theory, which suggest that previous proposals about the existence of a non-perturbative non-trivial fixed point for the infrared flow should be reconsidered.     

Smectic order parameters via liquid crystal NMR spectroscopy: Application to a partial bilayer smectic A phase

Solute molecules were dissolved in the liquid crystal 4-cyano-4??-n-octyloxybiphenyl (8OCB), known to form a partial bilayer smectic-A phase. Through measurement of solutes?? and solvent??s orientational order parameters via nuclear magnetic resonance spectroscopy, and their analysis via a statistical thermodynamic density functional theory, values of the solvent??s positional order parameters and solutes?? positional-orientational distribution functions were obtained. Near to the transition to the nematic phase, the main positional order parameter of the smectic liquid crystal turned out to be comprised in the interval 0.4?C0.6, though the quality of the fittings assuming the phase as nematic all across the temperature range investigated was only slightly worse. This may be ascribed to the looseness of the partial bilayer smectic structure. Solutes were found to preferentially lie in those regions where liquid crystal molecule terminal chains are located.      

Influence of nematic and smectic orders on polarizability of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals

Experimental values of the polarizability tensor γ components of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals in the nematic and smectic A phases have been obtained. Quadratic dependences of the longitudinal, γ _l , and transverse, γ _t , components, the mean value $\bar \gamma $ , and anisotropy Δγ in both phases have been established as functions of the orientational order parameter S of molecules in a maximally wide range of S. The nematic-smectic A phase transition with a continuous variation of S manifests itself as kinks in the linear dependences of $\bar \gamma $ , Δγ, and γ _l on S ² and does not influence the dependence γ _t (S ²). The observed dependences have been derived in the framework of the theory of the nematic-smectic A phase transition. The factors responsible for different influences of the orientational and positional orderings of molecules on the polarizability parameters have been determined.     

Asymptocic Freedom of Gluons in Hamiltonian Dynamics

We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang–Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang–Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian \({\beta}\) -function coincides with the one obtained in an earlier calculation using a different generator.     

Renormalization of the electron spectrum by confined and interface phonons in a spherical nanoheterosystem (β-HgS/CdS)

The mechanisms of the electron spectrum renormalization by confined (L) and interface (I) phonons in a spherical quantum dot (QD) embedded in a semiconducting sphere are studied for the specific case of the β-HgS/CdS nanosystem. It is shown that, in view of the absence of interaction between an electron in spherically symmetric states and interface phonons forming only one bound state in a small-size QD, the shift Δ of this single level is formed only by confined phonons. As the size of the QD increases, the contribution of L and I phonons to Δ changes accordingly (L phonons slightly dominate), and the shift varies from Δ _CdS ^3D to Δ _HgS ^3D .     

Correlation of the molecular structure of discotic nematic liquid crystals with their orientational order and specific features of the nematic-isotropic phase transition

The orientational order parameter S of molecules in high-temperature discotic nematic liquid-crystal phases of triphenylene derivatives is investigated as a function of the length of side flexible molecular chains at different temperatures. It is established that the orientational order parameters S in the range of the transition from the nematic phase to the isotropic liquid phase (the N _D -I transition) are smaller than those predicted from the molecular-statistical theory and computer simulation. It is shown that the N _D -I transition is close to both the isolated Landau point and the tricritical point (regardless of the chemical structure of the molecules and the anisotropy of dispersion intermolecular interactions). Consistent explanations are offered for a number of experimental findings, such as the anomalously small changes in the enthalpy and entropy upon the N _D -I transition (as compared to those revealed upon the N-I transition in calamitic nematic liquid crystals), the anomalously strong response of the isotropic phase of discotic nematic liquid crystals to external fields (thermodynamically conjugate to the order parameter S) and the long relaxation times of this response, and the formation of cybotactic discotic molecular clusters in the isotropic phase in the vicinity of the N _D -I transition.     

On the threshold behaviour of heavy top production

If the top is heavy, as now seems likely, the \(t\bar t\) threshold behaviour is given by perturbative QCD. The QCD threshold interaction can be formulated in terms of a potential, attractive or repulsive depending on whether the \(t\bar t\) is in a colour singlet or octet state. This gives a suppression factor for octet production. Singlet production is enhanced, both above threshold and, by resonance formation, below it. Whilee ⁺ e ^? annihilation only proceeds in the singlet \(t\bar t\) channel, hadronhadron collisions contain a non-trivial mixture of the two. In this paper we review the relevant threshold factor formulae, and present phenomenological consequences for hadron colliders, current and future.     

Self energy of heavy quarks in confined QCD

We calculate the self energy of a heavy quark in order α _s of QCD confined to a spherical cavity. Only the radius-(and position-) dependent terms which cannot be renormalized away are taken into account. Besides the leadingO(M ⁰) contribution which acts as a confining potential we determine theO (1/M ²) corrections which contain orbital terms and contributions to theLS potential. This calculation completes the determination of the Breit-Fermi Hamiltonian for a confinedQ \(\bar Q\) system whose interaction parts have been discussed previously. We give some preliminary estimates of the resultant spin dependent level splittings in charmonium.     

{^6_{\Lambda} \rm{H}} Modeled as {^4_{\Lambda} \rm{H}} + n + n

A three-body calculation for the \({^4_{\Lambda} \rm{He}}\) and \({^6_{\Lambda}{\rm H}}\) hypernuclei has been undertaken. The respective cores are \({^4_{\Lambda}{\rm H}}\) . The interactions in the \({^6_{\Lambda}{\rm He}}\) system, modeled as \({^4_{\Lambda} {\rm H+p+n}}\) , are reasonably well known. For example, the p n interaction is well determined by the p n scattering data, the \({^4_{\Lambda}{\rm H}}\) –p interaction can be fitted to the \({^5_{\Lambda}{\rm He}}\) binding energy. The \({^4_{\Lambda}{\rm He}}\) –n interaction can be fitted to α–n scattering data. For the ⁴He–n system the s-wave can be modeled alternatively as a repulsive potential or as an attractive potential with a forbidden bound state. We explore these alternatives in ⁶He, because the interaction comes into play in modeling \({^6_{\Lambda}{\rm He}}\) as well as in our \({^4_{\Lambda}{\rm H}}\) + n + n model of \({^6_{\Lambda}{\rm H}}\) , where the valence neutrons are Pauli blocked from the s-shell of the core nucleus.     

Unitary scalar-vector mixing in the <Emphasis Type="Italic">ξ</Emphasis> gauge

The effect of the unitary mixing of scalar and vector fields is considered in the ξ gauge. For this effect to emerge, it is necessary that the vector current not be conserved; in the ξ gauge, there arise additional complications because of the presence of an unphysical scalar field. Solutions to the Dyson-Schwinger equations are obtained, and the renormalization of complete propagators is investigated. The use of the Ward identity, which relates a few different Green's functions, is a key point in performing this renormalization. It is shown that the dependence on the gauge parameter ξ disappears in the renormalized matrix element.     

Frequenzabhängige magnetische Suszeptibilitäten und renormierte Spinwellenenergien von GdCl3

GdCl₃ is a ferromagnet with two equivalent sub-lattices in which the dipolar interaction is comparable with the exchange interaction. In the Callen decoupling approximation the time and temperature dependent Green’s functions are derived and the transversal complex susceptibilitiesχ _xx(ω,h ₀) andχ _yx(ω,h ₀) are calculated. The energies of the acoustical and the optical spinwave modes following from the Green’s functions are renormalized by the magnetization and the spin correlation. The spinwave spectrum, showing an unusual angular dependence, is calculated analytically in the whole Brillouin zone and numerically in the long wavelength region.     

Anomalous diffusion and fluctuation effects in highly disordered media

The model of impurity transport in highly disordered fractal media is generalized with account taken of the superdiffusional behavior at large distances and fluctuative behavior at small distances. It is found that the impurity source power is renormalized due to the spatial fluctuations of medium characteristics. The renormalization coefficient K decreases dramatically with changing the source dimension R for R values smaller than the correlation length in the medium. In the same domain of R values, the coefficient K, together with the effective power, undergoes increasing statistical scatter.