A chiral axial next nearest neighbour xy-model for antiferroelectric liquid crystals

We describe a chiral axial next nearest neighbour xy-model to account for the various subphases exhibited by antiferroelectric liquid crystals made of chiral rod-like molecules. The assumed form of the interlayer interactions is based on physical processes which are discussed. Using a discrete model, the predicted sequence of transitions is SmA-SmC-SmC-FI_H-FI_I-FI_L-SmC ^* A, where FI stands for a ferriphase, as seen in many compounds. The ferri and SmC phases are characterized by relatively large angles between the c-vectors of successive layers and occur only when the compounds have high optical purity. The calculated field induced structures exhibit a plateau of the apparent tilt angle at , where is the tilt angle of the molecules in the ferriphase. The conoscopic figures in the presence of a field and ellipsometric parameters in the absence of a field have also been generated, which agree extremely well with the experimental results. Recent anomalous X-ray scattering studies prove the xy-character of the configurations, though the commensurate structures that are found in the ferriphase require an extension of the model to include lock-in terms. Received 23 August 1999     

In-medium chiral perturbation theory

We report on how to tackle the problem of establishing a chiral effective field theory in nuclear matter with explicit pion fields and in the presence of external sources (Ann. Phys. 297, 27 (2002)). We have made use of the results of J.A. Oller (Phys. Rev. C 65, 025204 (2002)) where the generating functional for the in-medium chiral SU(2) x SU(2) Lagrangian has been derived. Within this approach we develop the so-called standard power counting rules for the calculation of in-medium pion properties if the residual nucleon energies are of the order of the pion mass. In addition, for the case of vanishing residual nucleon energies, a modified scheme (non-standard counting) is introduced. For both schemes the pertinent scales where the chiral expansions have to break down are established as well. We have performed a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.39.Fe Chiral Lagrangians - 11.30.Rd Chiral symmetries - 21.65. + f Nuclear matter     

Fermion zero modes on vortices in chiral superconductors

The energy levels of fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the class I superconducting state the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in an s-wave superconductor: E=(n+1/2)ω₀, with integral n. In class II the corresponding spectrum is E=nω₀ and thus contains a state with exactly zero energy. The effect of a single impurity on the spectrum of bound states is also considered. For class I the spectrum acquires the doubled period ΔE=2ω₀ and consists of two equidistant sets of levels, in accordance with A. I. Larkin and Yu. N. Ovchinnikov, Phys. Rev. B 57, 5457 (1998). For the class II states the spectrum is not influenced by a single impurity if the same approximation is applied. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 9, 601–606 (10 November 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

In silico design of chiral dimers to direct the synthesis of a chiral zeolite

ABSTRACT

We have applied in silico materials design in an effort to design chiral organic structure directing agents (OSDAs) for the synthesis of enantiomerically enriched STW zeolite. To do so, we have used both exhaustive virtual screening of a limited set of symmetrical imidazolium dimers and a multi-objective genetic algorithm to effectively search a larger virtual combinatorial chemistry space that is too vast for an exhaustive approach.     

Fluctuations of Goldstone modes and the chiral transition in QCD

We provide evidence for the influence of thermal fluctuations of Goldstone modes on the chiral condensate at finite temperature. We show that at fixed temperature, T<T_c, in the vicinity of the chiral transition temperature this leads to a characteristic dependence of the chiral condensate on the square root of the light quark mass (m_l), which is expected for 3-dimensional models with broken O(N) symmetry. As a consequence the chiral susceptibility shows a strong quark mass dependence for all temperatures below T<T_c and diverges like in the chiral limit.     

The effects of the lithium intercalation on the X-ray photoelectron spectra of NiPS3

Summary A detailed XPS study of the lithium-intercalated NiPS₃ specimens was performed at the 2p, 3p, 3s core levels of the nickel atoms and at the 2p core levels of the sulphur and phosphorous atoms for various lithium contents. Comparison of the Ni 2p, 3p and 3s XPS spectra corresponding to NiPS₃ and Li _x NiPS₃ systems shows some evident trends. In particular, a shift of the Ni main line towards lower binding energies, a decrease in the intensity of the Ni 3p, 2p satellite structures and a change in the full width at half maximum of the Ni 3s band with lithium content are observed. All these findings suggest a change in the 3d electron configuration for high lithium concentrations. As regards the cluster (P₂S₆)⁴⁻, with the addition of lithium, a P 2p main line shift towards higher binding energies is noted, while the S 2p peak shifts towards lower binding energies. These results are discussed in comparison with previous physical measurements concerning the nickel reduction process and the related electronic modifications. The authors of this paper have agreed to not receive the proofs for correction.     

The(q\bar q) - pion and its decay constant in a chiral potential modeland its decay constant in a chiral potential model

Pion mass and its decay constant have been studied in a chiral symmetric potential model of independent quarks. The non-perturbative multi-gluon interaction which is responsible for quark confinement in a hadron is phenomenologically represented here by an effective potentialU(r) = 1/2(1 +γ ⁰)(ar ² +V ₀). The residual interactions due to quark-pion coupling arising out of the chiral symmetry preservation and that due to quark-gluon coupling arising out of single-gluon exchange are treated as low order perturbations. The centre of mass correction is also taken into account appropriately. This leads to the mass in consistency with that of the PCAC-pion and the pion decay constant in reasonable agreement with experiment.     

An explicit construction of the quantum group in chiral WZW-models

It is shown how a chiral Wess-Zumino-Witten theory with globally defined vertex operators and a one-to-one correspondence between fields and states can be constructed. The Hilbert space of this theory is the direct sum of tensor products of representations of the chiral algebra and finite dimensional internal parameter spaces. On this enlarged space there exists a natural action of Drinfeld's quasi-quantum groupA _{g, t} which commutes with the action of the chiral algebra and plays the rôle of an internal symmetry algebra. TheR matrix describes the braiding of the chiral vertex operators and the coassociator gives rise to a modification of the duality property.For genericq the quasi-quantum group is isomorphic to the coassociative quantum groupU _q (g) and thus the duality property of the chiral theory can be restored. This construction has to be modified for the physically relevant case of integer level. The quantum group has to be replaced by the corresponding truncated quasiquantum group, which is not coassociative because of the truncation. This exhibits the truncated quantum group as the internal symmetry algebra of the chiral WZW model, which therefore has only a modified duality property. The case ofg=su(2) is worked out in detail.     

Kl3 form factors at order p of chiral perturbation theory

This paper describes the calculation of the semileptonic K_l3 decay form factors at order p⁶ of chiral perturbation theory, which is the next-to-leading order correction to the well-known p⁴ result achieved by Gasser and Leutwyler. At order p⁶ the chiral expansion contains one- and two-loop diagrams which are discussed in detail. The irreducible two-loop graphs of the sunset topology are calculated numerically. In addition, the chiral Lagrangian produces direct couplings with the W bosons. Due to these unknown couplings, one can always add linear terms in q² to the predictions of the form factor f _- (q ² ). For the form factor f ₊ (q ² ), this ambiguity involves even quadratic terms. Making use of the fact that the pion electromagnetic form factor involves the same q⁴ counterterm, the q⁴ ambiguity can be resolved. Apart from the possibility of adding an arbitrary linear term in q² our calculation shows that chiral perturbation theory converges very well in this application, as the corrections are small. Comparing the predictions of chiral perturbation theory with the recent CPLEAR data, it is seen that the experimental form factor f ₊ (q ² ) is well described by a linear fit, but that the slope is smaller by about 2 standard deviations than the prediction. The unavoidable q² counterterm of the corrections allows one to bring the predictions of chiral perturbation theory into perfect agreement with experiment. Received: 8 January 2002 / Revised version: 27 March 2002 / Published online: 20 September 2002 RID="*" ID="*" Now at Fraunhofer Gesellschaft, Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, D-53754 Sankt Augustin, Germany, e-mail: peter.post@scai.fraunhofer.de RID="**"     

The role of strange sea quarks in chiral extrapolations on the lattice

Since the strange quark has a light mass of order , fluctuations of sea pairs may play a special role in the low-energy dynamics of QCD by inducing significantly different patterns of chiral symmetry breaking in the chiral limits N _f = 2 (m _u = m _d = 0, m _s physical) and N _f = 3 (m _u = m _d = m _s = 0). This effect of vacuum fluctuations of pairs is related to the violation of the Zweig rule in the scalar sector, described through the two O(p ⁴) low-energy constants L ₄ and L ₆ of the three-flavour strong chiral lagrangian. In the case of significant vacuum fluctuations, three-flavour chiral expansions might exhibit numerical competition between leading- and next-to-leading-order terms according to the chiral counting, and chiral extrapolations should be handled with special care. We investigate the impact of the fluctuations of pairs on chiral extrapolations in the case of lattice simulations with three dynamical flavours in the isospin limit. Information on the size of the vacuum fluctuations can be obtained from the dependence of the masses and decay constants of pions and kaons on the light quark masses. Even in the case of large fluctuations, corrections due to the finite size of spatial dimensions can be kept under control for large enough boxes ( fm).Received: 20 October 2004, Revised: 28 December 2004, Published online: 9 February 2005Laboratoire de Physique Théorique: LPT is an Unité Mixte de Recherche du CNRS et de lUniversité Paris-Sud 11 (UMR 8627).     

Quantitative Brewster angle microscopy measurements of chiral symmetry breaking and chiral boundaries in fatty acid Langmuir monolayers

Brewster angle microscopy (BAM) measurements of the low temperature region of the phase diagram of eicosanoic acid monolayers at an acidic subphase are performed. The existence of a new chiral I phase intervening between the L₂ and L ₂ ' phase recently discovered by Durbin et al. [M.K. Durbin, A. Malik, A.G. Richter, R. Ghastkadvi, T. Gog, P. Dutta, J. Chem. Phys. 106, 8216 (1997)] using grazing incidence X-ray diffraction (GIXD) is confirmed. Chiral symmetry breaking within the monolayers creates characteristic boundaries separating domains of opposite handedness. These disclination lines are associated with a jump in the tilt azimuth of the director, while the underlying hexatic orientation is continuous across the boundary. The disclination lines are observed with the Brewster angle microscope and analyzed as a function of surface pressure. The jump in tilt azimuth is determined. Agreement with an extended Landau theory proposed by Durbin is achieved. Received: 26 January 1998 / Revised: 3 August 1998 / Accepted: 7 August 1998     

Characteristics of the temperature dependence of the EPR spectrum of a layered GaSe:Gd crystal

The temperature dependence of the axial constants b ₂ ⁰ characterizing the fine structure of the EPR spectra of Gd³⁺ in a layered GaSe crystal is investigated. The compound GaSe:Gd contains three types of centers, in which Gd³⁺ is associated with Li⁺ or Na⁺ ions situated in the interlayer space. The influence of these ions on the phonon spectrum of the crystal is studied. It is shown that the lithium atoms are too small to have any appreciable influence on low-frequency optical vibrations (the E″ mode), which govern the behavior of the temperature curve. Here b ₂ ⁰ (T) remains linear in the temperature range well below the Debye temperature Θ_D; this is a characteristic feature of layered structures. Sodium, on the other hand, completely suppresses the E″ mode, so that, for centers associated with it, the temperature dependence of b ₂ ⁰ (T) exhibits the same behavior as for ordinary (nonlayered) crystals, where linearity is observed only for T>Θ_D. Fiz. Tverd. Tela (St. Petersburg) 40, 63–65 (January 1998)     

Dependences of the refractive indices on the proton concentration in H:LiNbO3 waveguides

Proton-exchanged optical waveguides in lithium niobate crystals exhibit a rich variety of structures and phases. It is established that seven H_xLi_1−x NbO₃ crystalline phases with a lithium niobate structure may form under various conditions of proton exchange and post-exchange annealing. A method is proposed to determine the proton concentration in the various phases identified. Relationships are established between the structural parameters, the proton concentration, and the ordinary and extraordinary refractive indices of various H_xLi_1−x NbO₃ crystalline phases. The results can explain various optical phenomena observed in proton-exchanged waveguides and permit prediction of the characteristics of light-guide structures. Zh. Tekh. Fiz. 69, 47–57 (March 1999)     

Single-particle potential in a chiral approach to nuclear matter including short-range NN-terms

We extend a recent chiral approach to nuclear matter of Lutz et al.Phys. Lett. B 474, 7 (2000)) by calculating the underlying (complex-valued) single-particle potential U(p, k _f) + iW(p, k _f). The potential for a nucleon at the bottom of the Fermi sea, U(0, k _f0) = - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi surface. Also, the imaginary single-particle potential, W(0, k _f0) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear-matter equation of state can be obtained if the short-range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1π-exchange). We also consider the equation of state of pure neutron matter ˉE_n(k _n) and the asymmetry energy A(k _f) in that approach. The downward bending of these quantities above nuclear-matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics. Received: 19 December 2002 / Accepted: 11 February 2003 / Published online: 15 April 2003     

Discrimination in racemates of small chiral molecules

A comparison of similar chiral molecules provides information about the impact of molecular characteristics on selectivity. In this article, the intermolecular structure in racemic fluids is the basis for comparing the molecules: the radial distribution between atoms on identical molecules is compared with the corresponding distribution for atoms from a mirror-image pair. A difference in these distributions signals an enantiomeric imbalance in the local distribution of molecules. The structure in the racemic fluids is explored using Monte Carlo (MC) simulations and the integral equation theory of Chandler, Silbey and Ladanyi (CSL) [1982, Molec. Phys., 46, 1335].

Racemic fluids are examined for several categories of chiral molecules. First, symmetrically shaped molecules have been considered in order to isolate local excesses attributable to energetic contributions. Second, racemates of hard chiral molecules have been examined. Here, enantiomeric imbalances can only originate from asymmetry in the molecular shape. Finally, both the molecular shape and the interaction strengths have been varied in order to explore the competition between steric and energetic effects. Within each category, the number of chiral molecules is large and a selection mechanism is required to identify those molecules which are expected to show large local excesses. An appropriate selection criterion (chirality index) has been defined and evaluated for 400 000 chiral molecules. Based on the results of this assessment, 24 racemates have been chosen for detailed examination by MC simulations and integral equation theories.     

Configuration of a chiral smectic-C film with a circular inclusion

It was shown experimentally (P.V. Dolganov et al., Europhys. Lett. 76, 250 (2006)) and by numerical calculations (C. Bohley, R. Stannarius, Eur. Phys. J. E 23, 25 (2007)) that the c -director profile of a two-dimensional chiral smectic-C (SmC) film around a circular inclusion adopts dipolar rather than quadrupolar configuration observed in achiral SmC films. We give an analytical argument on how spontaneous bend inherent in chiral SmC liquid crystals influences the configuration of a SmC liquid crystal film around a circular inclusion imposing tangential anchoring. We find how the angle α between two surface defects seen from the center of the inclusion depends on the radius of the inclusion R and the strength of the spontaneous bend q . We show, however, that the contribution of the spontaneous bend to the free energy suffers from mathematical ambiguity; it depends on the mathematical treatment of the outer boundary even when it is at infinity. This might indicate that the shape as well as the treatment of the outer boundary of the film can significantly influence the equilibrium configuration of the c -director and the position of the surface defects.     

(Z N×) n−1 generalization of the chiral Potts model

We show that theR-matrix which intertwines twon-by-N ^n–1 state cyclicL-operators related with a generalization ofU _q(sl(n)) algebra can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction just as theR-matrix of the checkerboard chiral Potts model. The rapidity variables lie on the algebraic curve of the genusg=N ^{2(n–1)((n–1)N-n)+1} defined by 2n–3 independent moduli. This curve is a natural generalization of the curve which appeared in the chiral Potts model. Factorization properties of theL-operator and its connection to the SOS models are also discussed.     

Twisted-grain-boundary (TGB) phases: nanostructured liquid-crystal analogue of Abrikosov vortex lattices

Twisted-grain-boundary (TGB) phases shown by some liquid-crystalline materials have properties common to those of both smectic and cholesteric phases. Following analogy between liquid crystals and super conductors proposed by de Gennes [Solid State Commun., 10, 753 (1972)], Renn and Lubensky [Phys. Rev. A, 38, 2132 (1988)] theoretically predicted a chiral analog of the smectic A (SmA*) phase, which is now known as TGBA phase. The TGBA phase was experimentally observed for the first time by Goodby et al. [Nature, 337, 449 (1989)] in the chiral homologous series of ferroelectric liquid-crystal material R- and S-1-methylheptyl 4′-[(4′′-n-alkoxyphenyl)propionoyloxy]-biphenyl-4-carboxylates (nP₁M₇), with n?=?13,14,15. Since then, more than a hundred pure and mixed systems showing TGBA phase have been found. Later, Renn derived a mean-field phase diagram based on the chiral Chen-Lubensky model, and predicted two more TGB phases, namely TGBC and TGBC?. These two phases have also been experimentally observed in many systems, and in a few, the phase diagram is similar to that predicted by Renn. Unlike the TGBA phase, several theoretical models have been proposed for TGBC and TGBC? phases, and it remains to be ascertained whether all the types of proposed TGBC/TGBC? structures experimentally exist. A review of the theoretically predicted and experimentally observed TGB phases is given in the present article. Some recently observed novel optical textures of the TGB phases are also reported.     

Coexistence of color superconductivity and chiral symmetry breaking within the NJL model

The phase diagram for quark matter is investigated within a simple Nambu-Jona-Lasinio model without vector correlations. It is found that the phase structure in the temperature-density plane depends sensitively on the parametrization of the model. We present two schemes of parametrization of the model where, within the first one, a first-order phase transition from a phase with broken chiral symmetry to a color superconducting phase for temperatures below the triple point at T _t = 55 MeV occurs, whereas for the second one a second-order phase transition for temperatures below T _t = 7 MeV is found. In the latter case, there is also a coexistence phase of broken chiral symmetry with color superconductivity, which is a new finding within this class of models. Possible consequences for the phenomenology of the QCD phase transition at high baryon densities are discussed. Received: 3 January 2003 / Accepted: 21 February 2003 / Published online: 24 April 2003