Effective field theory for quasicrystals and phasons dynamics

We build an effective field theory (EFT) for quasicrystals -- aperiodic incommensurate lattice structures -- at finite temperature, entirely based on symmetry arguments and a well-define action principle. By means of Schwinger-Keldysh techniques, we derive the full dissipative dynamics of the system and we recover the experimentally observed diffusion-to-propagation crossover of the phason mode. From a symmetry point of view, the diffusive nature of the phason at long wavelengths is due to the fact that the internal translations, or phason shifts, are symmetries of the system with no associated Noether currents. The latter feature is compatible with the EFT description only because of the presence of dissipation (finite temperature) and the lack of periodic order. Finally, we comment on the similarities with certain homogeneous holographic models and we formally derive the universal relation between the pinning frequency of the phonons and the damping and diffusion constant of the phason.

On Symmetry Properties of The Corrugated Graphene System

The properties of the ballistic electron transport through a corrugated graphene system are analysed from the symmetry point of view. The corrugated system is modelled by a curved surface (an arc of a circle) connected from both sides to flat sheets. The spin–orbit couplings, induced by the curvature, give rise to equivalence between the transmission (reflection) probabilities of the transmitted (reflected) electrons with the opposite spin polarisation, incoming from opposite system sides. We find two integrals of motion that explain the chiral electron transport in the considered system.

On the real combinations of cubes and octahedra

All the real combinations of cubes and octahedra (77657 in total) are enumerated and characterized by facet symbols and symmetry point groups. The most symmetrical polyhedra (with automorphism group orders not less than 6, 163 in total) are shown. It is assumed that they represent the most probable forms of natural diamond crystals. The results are discussed with respect to the Curie dissymmetry principle.

Refuge and Age Structures Impact on the Bifurcation Analysis of an Ecological Model

In this paper, the conditions of the incidence of the local bifurcation, such as a saddle-node pitchfork bifurcation and transcritical of an ecological system (consistingprey shelter (refuge) and age stages for both populations) considered to study. Lotka-Volterra type of functional response was suggested. Subsequently, the inquiry and analysis are remarked that the transcritical bifurcation transpires close to the equilibrium(symmetry) point , in addition to the incidence of asaddle-node bifurcation at symmetry points and . It should be mentioned that there is no likelihood of the incidence of the pitchfork bifurcation at every single point. In conclusion,s to illustrate the incidence of the local bifurcation of this system, some simulations were used. The aim of this study is to examine the effect of each parameter on the stability of equilibrium points.

Linear Response in Topological Materials

The discovery of topological insulators and semimetals has opened up a new perspective to understand materials. Owing to the special band structure and enlarged Berry curvature, the linear responses are strongly enhanced in topological materials. The interplay of topological band structure and symmetries plays a crucial role for designing new materials with strong and exotic new electromagnetic responses and provides promising mechanisms and new materials for the next generation of technological applications. We review the fundamental concept of linear responses in topological materials from the symmetry point of view and discuss their potential applications.