Space group symmetry applied to SCF calculations with periodic boundary conditions and Gaussian orbitals

Space group symmetry is exploited and implemented in density functional calculations of extended systems with periodic boundary conditions. Our scheme for reducing the number of two-electron integrals employs the entire set of operations of the space group, including glide plains and screw axes. Speedups observed for the Fock matrix formation in simple 3D systems range from 2X to 9X for the near field Coulomb part and from 3X to 8X for the Hartree–Fock-type exchange, the slowest steps of the procedure, thus leading to a substantial reduction of the computational time. The relatively small speedup factors in special cases are attributed to the highly symmetric positions atoms occupy in crystals, including the ones tested here, as well as to the choice of the smallest possible unit cells. For quasi-1D systems with most atoms staying invariant only under identity, the speedup factors often exceed one order of magnitude reaching almost 70X (near-field Coulomb) and 57X (HFx) for the largest tested (16,7) single-walled nanotube with 278 symmetry operations

A quantum group version of quantum gauge theories in two dimensions

For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi i/r,\ r\ge 3)$ we present an alternative approach to quantum gauge theories in two dimensions. We exhibit the similarities to Witten's combinatorial approach which is based on ideas of Migdal. The main ingredient is the Turaev-Viro combinatorial construction of topological invariants of closed, compact 3-manifolds and its extension to arbitrary compact 3-manifolds as given by the authors in collaboration with W. Mueller.Comment: 6 pages (plain TeX

Observation of time quasicrystal and its transition to superfluid time crystal

We report experimental realization of a quantum time quasicrystal, and its transformation to a quantum time crystal. We study Bose-Einstein condensation of magnons, associated with coherent spin precession, created in a flexible trap in superfluid $^3$He-B. Under a periodic drive with an oscillating magnetic field, the coherent spin precession is stabilized at a frequency smaller than that of the drive, demonstrating spontaneous breaking of discrete time translation symmetry. The induced precession frequency is incommensurate with the drive, and hence the obtained state is a time quasicrystal. When the drive is turned off, the self-sustained coherent precession lives a macroscopically-long time, now representing a time crystal with broken symmetry with respect to continuous time translations. Additionally, the magnon condensate manifests spin superfluidity, justifying calling the obtained state a time supersolid or a time super-crystal