Standard model cross-over on the lattice

With the physical Higgs mass the standard model symmetry restoration phase transition is a smooth cross-over. We study the thermodynamics of the cross-over using numerical lattice Monte Carlo simulations of an effective SU(2)×U(1) gauge+Higgs theory, significantly improving on previously published results. We measure the Higgs field expectation value, thermodynamic quantities like pressure, energy density, speed of sound and heat capacity, and screening masses associated with the Higgs and Z fields. While the cross-over is smooth, it is very well defined with a width of only ∼5  GeV. We measure the cross-over temperature from the maximum of the susceptibility of the Higgs condensate, with the result Tc=159.5±1.5  GeV. Outside of the narrow cross-over region the perturbative results agree well with nonperturbative ones.

Monte Carlo determination of the phase diagram of the double-exchange model

We study the phase diagram of the double exchange model, with antiferromagnetic interactions, in a cubic lattice both at zero and finite temperature. There is a rich variety of magnetic phases, combined with regions where phase separation takes place. We identify phases, intrinsic to the cubic lattice, which are stable for realistic values of the interactions and dopings. Some of these phases break chiral symmetry, leading to unusual features.

Restoration of symmetry by radiative corrections

It is shown using an explicit model that radiative corrections can restore the symmetry of a system which may appear to be broken at the classical level. This is the reverse of the phenomenon demonstrated by Coleman and Weinberg. Our model is different from theirs, but the techniques are the same. The calculations are done up to the two-loop level and it is shown that the two-loop contribution is much smaller than the one-loop contribution, indicating good convergence of the loop expansion.

Comparison of the NMR enantiodifferentiation of a chiral ruthenium(II) complex of C2 symmetry using the TRISPHAT anion and a lanthanide shift reagent

The tris[tetrachlorobenzenediolato]phosphate(v) anion (TRISPHAT) is known to be an efficient NMR chiral shift agent for various chiral cationic species. Here we compare the efficiency of TRISPHAT and of a chiral lanthanide shift reagent for the determination of the enantiomeric purity of the chiral building block [Ru(phen)[2]PY[2]][2][+] which possesses C[2] symmetry. We also discuss our results in terms of the geometry of interaction between the Ru(II) complex and the TRISPHAT anion.

Symmetry-breaking in chiral polymerisation

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to `poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable. The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomers and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steady-state solutions described above.

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the ``fully frustrated'' Bose-Hubbard model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time-reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose-Hubbard model

Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of a ``synthetic'' orbital magnetic field, we study the ``fully frustrated'' Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group method, we show that these kinetically frustrated boson models admit three phases at integer filling: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable ``chiral Mott insulator'' (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, study a Jastrow variational wave function which captures its correlations, present results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we consider generalizations to a staggered flux Bose-Hubbard model and a two-dimensional (2D) version of the CMI in weakly coupled ladders.

eta photoproduction on the proton in a chiral constituent quark approach via a one-gluon-exchange model

A formalism based on a chiral quark model (chi QM) approach complemented with a one-gluon-exchange model, to take into account the breakdown of the SU(6)circle times O(3) symmetry, is presented. The configuration mixing of wave functions for nucleon and resonances are derived. With few adjustable parameters, differential cross-section and polarized-beam asymmetry for the gamma p -> eta p process are calculated and successfully compared with the data in the center-of-mass energy range from threshold to 2 GeV. The known resonances S-11(1535), S-11(1650), P-13(1720), D-13(1520), and F-15(1680), as well as two new S-11 and D-15 resonances, are found to be dominant in the reaction mechanism. Moreover, connections among the scattering amplitudes of the chi QM approach and the helicity amplitudes, as well as decay widths of resonances, are established. Possible contributions from the so-called missing resonances are investigated and found to be negligible.

Helical single-lamellar crystals thermotropically formed in a synthetic nonracemic chiral main-chain polyester

Phase structures and transformation mechanisms of nonracemic chiral biological and synthetic polymers are fundamentally important topics in understanding their macroscopic responses in different environments. It has been known for many years that helical structures and morphologies can exist in low-ordered chiral liquid crystalline (LC) phases. However, when the chiral liquid crystals form highly ordered smectic liquid crystal phases, the helical morphology is suppressed due to the crystallization process. A double-twisted morphology has been observed in many liquid crystalline biopolymers such as dinoflaggellate chromosomes (in Prorocentrum micans) in an in vivo arrangement. Helical crystals grown from solution have been reported in the case of Bombyx mori silk fibroin crystals having the beta modification. This study describes a synthetic nonracemic chiral main-chain LC polyester that is able to thermotropically form helical single lamellar crystals. Flat single lamellar crystals can also be observed under the same crystallization condition. Moreover, flat and helical lamellae can coexist in one single lamellar crystal, within which one form can smoothly transform to the other. Both of these crystals possess the same structure, although translational symmetry is broken in the helical crystals. The polymer chain folding direction in both flat and helical lamellar crystals is determined to be identical, and it is always along the long axis of the lamellae. This finding provides an opportunity to study the chirality effect on phase structure, morphology, and transformation in condensed states of chiral materials. [S0163-1829(99)01042-5].

Optical and Thermal Properties of Diethyl-(2R, 3R) (1)-tartrate Based Chiral Polyurethanes with Main Chain Amido Chromophores

The toluene diisocyanate based optically active chiral polyurethanes were synthesized according to the symmetry conditions. The noncentrosymmetric (both charge asymmetry and spatial asymmetry) environment were attained by the incorporation of the chiral units (diethyl-(2R,3R)(þ)-tartrate) and donor-acceptor building blocks in the main chain which induce a helical conformation in the macromolecular chain. A series of optically active polyurethanes containing chiral linkages in the polymer back bone have been synthesized by using DBTDL catalyst by incorporating the amido diols which were obtained by the aminolysis of e-caprolactone by using the diamines, diaminoethane, diaminobutane, and diaminohexane respectively. The effect of incorporation of the chiral molecule diethyl-(2R,3R)(þ)-tartrate on the properties of polyurethanes was studied by changing the chromophores and also by varying the chiral-chromophore composition. Various properties of polyurethanes were investigated by UV, Fluorescence, TG/DTA, XRD, polarimetric techniques, Kurtz-Perry powder techniques, etc.

Isosorbide based chiral polyurethanes: optical and thermal studies

A new class of chiral polyurethanes containing amido linkages in the polymer backbone have been synthesized by reacting toluene diisocyanate with isosorbide (IS) chiral moiety and the chromophores [N,N0-ethane- 1,2-diyl bis(6-hydroxy hexanamide), N,N0-butane-1,4-diyl bis(6-hydroxy hexanamide) and N,N0-hexane-1,6-diyl bis (6-hydroxy hexanamide)]. The corresponding chromophores were obtained by the aminolysis of e-caprolactone by using the diamines, diaminoethane, diaminobutane and diaminohexane, respectively. All the polymers were synthesized according to the symmetry conditions so as to obtain the non-centrosymmetric environment. A series of polyurethanes were synthesized by varying the chiral– chromophore composition. The polyurethanes developed were characterized by optical and thermal methods.

The chemistry of intrinsically chiral surfaces

Intrinsically chiral metal and mineral surfaces show enantioselective behaviour without modifiers. Examples are artificial high-Miller-index surfaces of metal single crystals with cubic bulk lattice symmetry, which have no mirror planes and are therefore chiral, or surfaces of naturally occurring crystallites of some common minerals, such as alpha-quartz or calcite. Recent findings with regards to the surface geometry, reactivity and thermal stability of intrinsically chiral surfaces are discussed. A number of enantioselective effects have been reported in connection with the adsorption of small chiral molecules (e.g. alanine, cysteine) on intrinsically chiral surfaces under well-defined conditions. From a combination of experimental surface science techniques and theoretical ab initio model calculations it emerges that these effects are due to a combination of attractive and repulsive adsorbate-substrate and inter-adsorbate interactions.

Spontaneous local symmetry breaking: a conformational study of glycine on Cu{311}

Understanding the interplay between intrinsic molecular chirality and chirality of the bonding footprint is crucial in exploiting enantioselectivity at surfaces. As such, achiral glycine and chiral alanine are the most obvious candidates if one is to study this interplay on different surfaces. Here, we have investigated the adsorption of glycine on Cu{311} using reflection-absorption infrared spectroscopy, low-energy electron diffraction, temperature-programmed desorption and first-principles density-functional theory. This combination of techniques has allowed us to accurately identify the molecular conformations present under different conditions, and discuss the overlayer structure in the context of the possible bonding footprints. We have observed coverage-dependent local symmetry breaking, with three-point bonded glycinate moieties forming an achiral arrangement at low coverages, and chirality developing with the presence of two-point bonded moieties at high coverages. Comparison with previous work on the self-assembly of simple amino acids on Cu{311} and the structurally-similar Cu{110} surface has allowed us to rationalise the different conditions necessary for the formation of ordered chiral overlayers.

Extending distannoxane double ladders using rigid spacers: a double ladder with eight chiral tin atoms-and a twist!

The new bulky silicon-containing ditin precursor p-(RCl₂SnCH₂SiMe₂)₂C₆H₄ (R = CH₂SiMe₃ (4)) has been synthesized and further reacted to form a unique double ladder {[p-(R(Cl)SnCH₂SiMe₂)₂C₆H₄]O}₄ (6). The two layers within 6 are twisted with respect to one another, resulting in a helical motif and a total absence of molecular symmetry so that there are eight chiral tin atoms within the system. The structure is compared to the double ladder {[m-(R(Cl)SnCH₂CH₂)₂C₆H₄]O}₄ (11), which was prepared from the less sterically demanding ditin precursor m-(RCl₂SnCH₂CH₂)₂C₆H₄ (10). The two layers within 11 are parallel, and the molecule contains only two kinds of tin atom.

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and gamma(5) chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.