Line Groups in Physics

Thermodynamic properties of nanotubes: zone-folding approach

“…The symmetry of SWCNTs was analyzed in many publications, using the graphene layer folding approach [24][25][26]. The symmetry of the graphene layer is described by hexagonal layer group 80 (P6/mmm) being a 2D subgroup of graphite symmetry space group 194 (P6 3 /mmc).…”

Symmetry of quasi one-dimensional systems: line groups and applications

“…Th e monomer symmetry is one of axial point groups (groups of transformations that leave z-axis invariant). Th ese are C n (successive rotations C n by 2π/n around z-axis, n=1,2,…), S 2n , C nh , C nv , D n (which combine C n with rotation by π/n followed by horizontal mirror refl ection, horizontal and vertical mirror plane and rotation U by π around x-axis, respectively) and D nd and [2]) to make L W@W' fi nite: equi-energetic positions are continual along Z, and E(Φ,Z) is constant along Z. Walls are super slippery as their mutual translation costs no energy.…”

“…Th us, only symmetry and properties of the atom determine all properties of the nanotube. Th is is fruitfully and efficiently used in research [2,4].…”

“…line groups for physical applications did not start until 1977 at the Faculty of Physics, University of Belgrade, by Božović, Vujičić and Herbut [1], and their coworkers (presently NanoLab, www.nanolab.rs); a synthesis of the existing results was given in 2010 [2]. Simultaneously, the modifi ed group projector technique (MGPT), enabling full symmetry calculations, and computer code POLSym, suited for symmetry assisted research of quasi one-dimensional systems, were developed [2].…”

“…Simultaneously, the modifi ed group projector technique (MGPT), enabling full symmetry calculations, and computer code POLSym, suited for symmetry assisted research of quasi one-dimensional systems, were developed [2].…”