The Hausdorff chirality measure and a proposed Hausdorff structure measure

The Hausdorff chirality measure quantifies the chirality of a geometric representation of an object by measuring the degree of coincidence of the object with its mirror image. It can also allow comparison between a chiral dopant and host molecules which may illuminate mechanisms for chirality transfer. It has been applied to real molecules very infrequently in comparison to application of chiral indices as it is complex and time consuming to calculate. In this paper we introduce and verify a simulated annealing algorithm for the Hausdorff chirality measure that has proven rapid, robust and relatively simple to apply. We verify the method, finding good agreement between its results and those of Mislow and co-workers. We introduce a Hausdorff structure measure that does not permit overlap and allows a structure to be built one molecule at a time. We present results for a simple model and real biphenyl molecules and discuss promising building blocks of crystal and incommensurate structures formed in relation to experimental results.     

Exact solution for a degenerate Anderson impurity in the limit embedded into a correlated host

We consider the one-dimensional t - J model, which consists of electrons with spin S on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J = t. Without spoiling the integrability we introduce an Anderson-like impurity of spin S (degenerate Anderson model in the limit), which interacts with the correlated conduction states of the host. The lattice model is defined by the scattering matrices via the Quantum Inverse Scattering Method. We discuss the general form of the interaction Hamiltonian between the impurity and the itinerant electrons on the lattice and explicitly construct it in the continuum limit. The discrete Bethe ansatz equations diagonalizing the host with impurity are derived, and the thermodynamic Bethe ansatz equations are obtained using the string hypothesis for arbitrary band filling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter related to the Kondo exchange coupling. The impurity can localize up to one itinerant electron and has in general mixed valent properties. Groundstate properties of the impurity, such as the energy, valence, magnetic susceptibility and the specific heat coefficient, are discussed. In the integer valent limit the model reduces to a Coqblin-Schrieffer impurity. Received: 31 December 1997 / Accepted: 17 March 1998     

Cationic Substitution Sites in Mn2+-doped ZnS Nanoparticles

Mn²⁺-doped ZnS nanoparticles of average size 2.5±0.3 nm have been studied and characterized in the dopant concentration range 0.1–0.3% using XRD, EPR, XPS and photoluminescence methods. The experimental results obtained from these studies indicate that the doping of Mn²⁺ occurs primarily at the T _d sites at low dopant concentration, causing the⁴T₁(G) → ⁶A₁(S) transition to take place in the host lattice; the observed decrease in the intensity of photoluminescence at high dopant concentration is due to the setting in of the strong Mn²⁺–Mn²⁺ interaction arising from cluster formation at the highly distorted sites near the particle surface.An erratum to this article can be found at     

Structural and electronic properties of Na/Cu(111) at different coverages by first principles

Nanostructures are presently enjoying an increasing interest in the field of materials science. In particular, importance is given to ordered monolayers prepared by deposition of atoms on a crystalline surface. The growth of these superlattices can be controlled so as to obtain an ordered structure by means of the lateral interaction of adatoms lying on the metal surface. The objective of our study is to investigate the structural and electronic properties using DFT total-energy calculations; we employ a jellium-like model to describe the substrate but we also take into account the presence of discrete surface states that are known to affect the lateral interaction. Our treatment of the substrate is based on the model proposed by E.V. Chulkov et al. [Surf. Sci. 437, 330 (1999)]; in this model one constructs a mono-dimensional potential so as to reproduce some important electronic properties of the metal surface, such as i) the energy gap in the projected bulk band-structure and ii) the energy position of surface states. We put into practice Chulkov potential implementing into an existing plane-waves code (ABINIT, URL http://www.abinit.org) an ionic potential, so as to obtain a self-consistent Kohn-Sham effective potential which corresponds to the Chulkov one. Using this effective potential in a fully three-dimensional code we are able to study the adsorption process and the interaction between adsorbates. We illustrate some details of our implementation of the Chulkov model and we present our results about the simple system of Na adatoms on a Cu(111) surface for different coverages. In particular, we compare electronic properties and adsorption energies with those obtained within a standard jellium model substrate and with those obtained for Na adsorption on a realistic Cu(111) surface.     

Phase transitions in nanocomposites of hydrogen-bonded dimeric liquid crystals with mesogenic and non-mesogenic components

Microtextural polarization, phase transitions, and electro-optical effects are studied in a series of nanocomposites, grown by mixing alkyloxybenzoic acids (nOBAs), displaying hydrogen-bonded dimeric liquid crystal (LC) state, with non-mesogens (single-walled carbon nanotubes (SWCNTs), perfluorooctanoic acid) or mesogens (bent-core LC compound D14F3). Each of the studied nanocomposites, in which the nOBA serves as a matrix, forms complexes with bent-shaped dimeric, caused by the interaction between the dopant structural units and the dimer rings. This feature, coordinated with the surface anchoring, bulk and electrical effects, leads to drastic reduction of the LC system symmetry. As a result, transitions from achiral (characteristic for the pristine nOBA) to chiral states (including ferroelectric smectic C with C₂ symmetry and ferroelectric smectic C_G with the lowest C₁ triclinic one) take place. The functionalization of the SWCNTs causes drastic increase of the ferroelectricity.     

Landau-Fermi liquid analysis of the 2D t-t' Hubbard model

We calculate the Landau interaction function f (k,k') for the two-dimensional t-t' Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface. Received 18 March 2002 Published online 9 July 2002     

Association energies in Re3+-doped alkaline-earth fluorides studied by computational methods

Association energies of nearest-neighbour and next-nearest-neighbour associates between substitutional, trivalent rare-earth ions and interstitial fluoride ions CaF₂, SrF₂ and BaF₂ are obtained by lattice simulation calculations. The dopant ion-fluoride ion interaction is described (i) with a set of potentials obtained with electron gas methods, and (ii) with a set of potentials derived semi-empirically from the host lattice cation-anion interaction potentials. The calculations successfully simulate the experimentally observed variations of the dopant-interstitial binding energies with the radius of the dopant ion, and with the lattice parameter of the host. The better quantitative agreement is obtained with the semi-empirical potentials. The variations are explained by an evaluation of the displacements of the ions constituting the associates.     

Stoichiometry,Association Constant,and Solvation Model of Chiral Hydroxyfuranones in the Presence of Pirkle's Alcohols

ABSTRACT

(S)-(+)-Dihydro-3-hydroxy-4,4-dimethyl-2(3H)-furanone, (R)-(-)-dihydro-3-hydroxy-4,4-dimethyl-2(3H)-furanone, (S)-(-)-dihydro-4-hydroxy-2(3H)-furanone, and (S)-(-)-5-hydroxymethyl-2(5H)-furanone in the presence of pure enantiomers of 2,2,2-trifluoro-1-(9-anthryl)ethanol were studied by ¹H NMR in deuterated chloroform solutions. Experimental Job's plots suggest that the resulting solvates are formed with one molecule of solute and one of the chiral solvating agent. From the magnitude of the association constant determined for (S)-(+)-dihydro-3-hydroxy-4,4-dimethyl-2(3H)-furanone in the presence of (R)-(-)-2,2,2-trifluoro-1-(9-anthryl)ethanol (1.26 ± 0.09 M^?1), it is inferred that the solvate is weak and cannot be isolated at 298 K. The correlation between the magnitude of induced chemical shifts, NOESY maps, and the known configuration of solutes and chiral solvating agents suggests that intermolecular hydroxyl-hydroxyl interaction is the primary interaction. Accordingly, the secondary interaction might occur between benzylic-hydrogen of the chiral solvating agent and the carbonyl- or furan ring-oxygen atoms of the solute.     

Topological gauge theories and group cohomology

We show that three dimensional Chern-Simons gauge theories with a compact gauge groupG (not necessarily connected or simply connected) can be classified by the integer cohomology groupH ⁴(BG,Z). In a similar way, possible Wess-Zumino interactions of such a groupG are classified byH ³(G,Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map fromH ⁴(BG,Z) toH ³(G,Z). We generalize this correspondence to topological spin theories, which are defined on three manifolds with spin structure, and are related to what might be calledZ ₂ graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.     

Hadronic decays of N and Δ resonances in a chiral quark model

π and η decay modes of light baryon resonances are investigated within a chiral quark model whose hyperfine interaction is based on Goldstone-boson exchange. For the decay mechanism a modified version of the ³ P ₀ model is employed. Our primary aim is to provide a further test of the recently proposed Goldstone-boson exchange constituent quark model. We compare the predictions for π and η decay widths with experiment and also with results from a traditional one-gluon exchange constituent quark model. The differences between nonrelativistic and semirelativistic versions of the constituent quark models are outlined. We also discuss the sensitivity of the results on the parameterization of the meson wave function entering the ³ P ₀ model. Received: 11 May 2001 / Accepted: 17 September 2001     

Monopoles and holography

Several lattice collaborations performing simulations with 2+1 light dynamical quarks have experienced difficulties in fitting their data with standard N _f = 3 chiral expansions at next-to-leading order, yielding low values of the quark condensate and/ or the decay constant in the N _f = 3 chiral limit. A reordering of these expansions seems required to analyse these data in a consistent way. We discuss such a reordering, known as Resummed Chiral Perturbation Theory, in the case of pseudoscalar masses and decay constants, pion and kaon electromagnetic form factors and K _ℓ3 form factors. We show that it provides a good fit of the recent results of two lattice collaborations (PACS-CS and RBC/UKQCD). We describe the emerging picture for the pattern of chiral symmetry breaking, marked by a strong dependence of the observables on the strange quark mass and thus a significant difference between chiral symmetry breaking in the N _f = 2 and N _f =3 chiral limits. We discuss the consequences for the ratio of decay constants F _K /F _π and the K ℓ3 form factor at vanishing momentum transfer.

     

Structure and reactions of pentaquark baryons

We review the current status of the exotic pentaquark baryons. After a brief look at experiments of both positive and negative results, we discuss theoretical methods to study the structure and reactions for the pentaquarks. First we introduce the quark model and the chiral soliton model, where we discuss the relation of mass spectrum and parity with some emphasis on the role of chiral symmetry. It is always useful to picture the structure of the pentaquarks in terms of quarks. As for other methods, we discuss a model-independent method, and briefly mention the results from the lattice and QCD sum rule. Decay properties are then studied in some detail, which is one of the important properties of ⊝⁺. We investigate the relation between the decay width and the quark structure having certain spin-parity quantum numbers. Through these analyses, we consider as plausible quantum numbers of ⊝⁺,J ^P = 3/2⁻. In the last part of this note, we discuss production reactions of ⊝⁺ which provide links between the theoretical models and experimental information. We discuss photoproductions and hadron-induced reactions which are useful to explore the nature of ⊝⁺     

Noether-Symmetry Analysis using Alternative Lagrangian Representations

We have sought to work with an approach to Noether symmetry analysis which uses the properties of infinitesimal point transformations in the space-time (q, t) variable to establish the association between symmetries and conservation laws of a dynamical system. In this approach symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of two uncoupled Harmonic oscillators and two such oscillators coupled by an interaction. Both these systems can have alternative Lagrangian representations. We have studied in detail how the association between symmetries and conservation laws changes as one alters the analytic or Lagrangian representation. This analysis is carried out with a view to explicitly demonstrate that the correlation between symmetry transformation and corresponding invariant quantity depends crucially on the choice of the analytic representation. PACS 45.20.Jj, 45.20.df, 45.20.dh     

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.     

Subbarrier conversion in 125Te45+

We discuss the process of resonant subbarrier internal conversion of γ rays, where the converted electron is transferred to one of the atomic orbitals. For the first time we study how this process is affected by residual interactions: the splitting of the atomic terms in the total angular momentum of the atom, configuration mixing, and the magnetic interaction between the electrons of the atom. The calculations are done by the relativistic multiconfiguration Dirac-Fock method with allowance for the Breit interaction for the M1 transition with an energy of 35 492 eV in multiply charged ions of ¹²⁵Te. We show that allowing for the residual interaction is obligatory if we want to calculate the conversion rate in the vicinity of a resonance correctly. Zh. éksp. Teor. Fiz. 116, 1565–1574 (November 1999)     

Aspects of the phase diagram in (P)NJL-like models

We discuss three applications of NJL- and PNJL-like models to assess aspects of the QCD phase diagram: First, we study the effect of mesonic correlations on the pressure below and above the finite temperature phase transition within a non-local PNJL model beyond the mean-field approximation. Second, we reconstruct the phase boundary of an NJL model from a Taylor expansion of the chiral susceptibility about μ=0 and compare the result with the exact phase boundary. Finally, we demonstrate the realization of the “non-standard scenario” for the critical surface in a three-flavor PNJL model with a μ-dependent determinant interaction.     

Unification,KK-thresholds and the top Yukawa coupling in F-theory GUTs

In a class of F-theory SU(5) GUTs the low energy chiral mass spectrum is obtained from rank one fermion mass textures with a hierarchical structure organized by U(1) symmetries embedded in the exceptional E ₈ group. In these theories chiral fields reside on matter ‘curves’ and the tree-level masses are computed from integrals of overlapping wave functions of the particles at the triple intersection points. This calculation requires knowledge of the exact form of the wave functions. In this work we propose a way to obtain a reliable estimate of the various quantities which determine the strength of the Yukawa couplings. We use previous analysis of KK-threshold effects to determine the (ratios of) heavy mass scales of the theory which are involved in the normalization of the wave functions. We consider similar effects from the chiral spectrum of these models and discuss possible constraints on the emerging matter content. In this approach, we find that the Yukawa couplings can be determined solely from the U(1) charges of the states in the ‘intersection’ and the torsion which is a topological invariant quantity. We apply the results to a viable SU(5) model with minimal spectrum which satisfies all the constraints imposed by our analysis. We use renormalization group analysis to estimate the top and bottom masses and find that they are in agreement with the experimental values.     

-wave nonadiabatic superconductivity

The inclusion of nonadiabatic corrections to the electron-phonon interaction leads to a strong momentum dependence in the generalized Eliashberg equations beyond Migdal's limit. For a s-wave symmetry of the order parameter, this induced momentum dependence leads to an enhancement of when small momentum transfer is dominant. Here we study how the d-wave symmetry affects the above behavior. We find that the nonadiabatic corrections depend only weakly on the symmetry of the order parameter provided that only small momentum scatterings are allowed for the electron-phonon interaction. In this situation, We show that also for a d-wave symmetry of the order parameter, the nonadiabatic corrections enhance . We also discuss the possible interplay and crossover between s- and d-wave depending on the material's parameters. Received 12 May 2000     

Tuning magnetism of MnO by doping with 2p elements

We show that the antiferromagnetic coupling between Mn atoms in MnO can be tuned to a ferromagnetic one by doping it with a small concentration of 2p elements like boron, carbon and nitrogen. Our ab initio density functional calculations in the Hubbard U framework show that the coupling between Mn atoms turns ferromagnetic for 3 at% B doping. B is found to be the most effective one in stabilizing ferromagnetism. We discuss the role of 2p states of the dopant atoms to explain the trend of ferromagnetism in MnO.     

Cobalt-doped TiO2: a computational analysis of dopant placement and charge transfer direction on thin film anatase

ABSTRACT

Titanium dioxide (TiO₂) nanocrystals are promising materials for photo-electrochemical water splitting. This study focuses on how surface dopant placement can affect the electronic properties. TiO₂ anatase thin films are doped two ways: a cobalt ion replacing a surface titanium ion (surface ingrained) and a cobalt ion chemisorbed to two surface oxygen ions and two NH₃ ligands. Specifically, when studying the binding pattern, the cobalt ion dopant changes from an electron acceptor for the surface ingrained model to an electron donor for the chemisorbed model. The optical absorption peaks of the surface ingrained model are attributed to p→d transitions and are much stronger when compared to the d→d transitions for the chemisorbed model. It is the conclusion of this computational study that one can alter the cobalt dopant on the anatase thin film to focus a positive or negative charge at the surface by changing the surface dopant location.