Une étude cristallographique: Superspace description of a commensurate composite cocrystal of 4,4'-dinitrobiphenyl and biphenyl

We report the structure of a 3:1 cocrystal of 4,4'-dinitrobiphenyl and biphenyl. The cocrystal can be regarded as a commensurate column composite crystal and therefore is described in superspace. The...

Liouville theory and matrix models: a Wheeler DeWitt perspective

We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to c = 1 matter. Our motivation is to understand whether some form of averaging is essential for the boundary theory, if we wish to describe the bulk quantum gravity path integral of this two dimensional example. The analysis hence, is in a spirit similar to the recent studies of Jackiw-Teitelboim (JT)-gravity. Macroscopic loop operators define the asymptotic region on which the holographic boundary dual resides. Matrix quantum mechanics (MQM) and the associated double scaled fermionic field theory on the contrary, is providing an explicit “unitary in superspace” description of the complete dynamics of such two dimensional universes with matter, including the effects of topology change. If we try to associate a Hilbert space to a single boundary dual, it seems that it cannot contain all the information present in the non-perturbative bulk quantum gravity path integral and MQM.

Looking for alternatives to the superspace description of icosahedral quasicrystals

A multiple-cell approach is discussed as a possible alternative to the higher dimensional crystallography of icosahedral quasicrystals. It is based on the Socolar–Steinhardt tiling combined with the quasi-unit cell model. Quasi-unit cells fill the space without gaps and overlappings similar to those in periodic crystals. Similarly, the atoms can occupy general and special positions. The alloy stoichiometry and the packing density can be calculated through the relative tile frequencies, which in turn are determined as the components of the Perron–Frobenius eigenvector of the corresponding substitution matrix. The calculation of the diffraction pattern reduces to the Perron projection of a special matrix, the entries of which reflect the contribution of each type of quasi-unit cell to the coherent scattering.

Description and symmetry of aperiodic crystals

This chapter first introduces the mathematical concept of aperiodic and quasiperiodic functions, which will form the theoretical basis of the superspace description of the new recently discovered forms of matter. They are divided in three groups, namely modulated phases, composites, and quasicrystals. It is shown how the atomic structures and their symmetry can be characterized and described by the new concept. The classification of superspace groups is introduced along with some examples. For quasicrystals, the notion of approximants is also introduced for a better understanding of their structures. Finally, alternatives for the descriptions of the new materials are presented along with scaling symmetries. Magnetic systems and time-reversal symmetry are also introduced.

The Quantum Description of BF Model in Superspace

We consider the BRST symmetric four-dimensional BF theory, a topological theory, containing antisymmetric tensor fields in Landau gauge and extend the BRST symmetry by introducing a shift symmetry to it. Within this formulation, the antighost fields corresponding to shift symmetry coincide with antifields of standard field/antifield formulation. Furthermore, we provide a superspace description for the BF model possessing extended BRST and extended anti-BRST transformations.

Superspace description of trimethyltin hydroxide at T = 100 K

At low temperatures the metalorganic compound trimethyltin hydroxide, (CH

Crystal Chemistry and Symmetry based approaches to multiferroics.

The area of improper ferroelectrics and potentially multiferroics has recently received significant attention do the prediction that a combination of a–a–c+ tilting and layered ordering of the A site cations along [001]perov in perovskite ABX3 systems or in the even n Ruddlesden Popper (RP) phases (An+1BnX3n+1), leads to non-centrosymmetric structures which are predicted to have significant switchable polarisations. Two practical examples will be discussed: (i) Suitable doping of the RP phase SrLn2Fe2O7 can induce a polar tilted ground state where weak ferromagnetism and magnetocelecricity are induced by the appearance of the polar tilted state. The transition temperatures and phase sucession is dependant on the degree of doping. (ii) The oxide heterostructure [(YFeO3)5(LaFeO3)5]40,which is magnetically ordered and piezoelectric at room temperature, has been constructed from two weak ferromagnetic AFeO3 perovskites with different A cations using RHEED-monitored pulsed laser deposition.1 Here we elaborate a superspace description of cation ordering in tilted perovskites that allows the prediction of the symmetry of arbitrary cation ordered superlattices, along <100>perov, <110>perov and <111>perov and ordering of both A and B cations, of the various tilted perovskites, which also rationalizes the observed domain structures. This approach is expaned to include magnetic symmetry and the potential for finding other suitable structural distortions in non-perovskite systems will be discussed.