Regensburg 2013 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 18: Statistical Physics Far from Thermal Equilibrium
DY 18.5: Vortrag
Mittwoch, 13. März 2013, 10:30–10:45, H48
Random perfect lattices and the sphere packing problem — •Alexei Andreanov1,2 and Antonello Scardicchio1,3 — 1The Abdus Salam ICTP, Trieste, Italy — 2Max-Planck-Institut fur Physik complexer Systeme, Dresden, Germany — 3INFN, Sezione di Trieste, Trieste, Italy
We study random sets of perfect lattices in dimensions up to d=19. Perfect lattices are relevant for solution of lattice sphere packing problem. In fact the best lattice packing is a perfect lattice and perfect and eutactic lattices are local maxima of the packing fraction. We use a stochastic generating algorithm for perfect lattices and define a random ensemble with an effective temperature (reminiscent of a Monte Carlo simulation) to study typical properties of perfect lattices and show how as the temperature is decreased the best known packers are easily recovered. We find that the typical perfect lattices are denser than known families and propose two hypotheses for typical packing density between which we cannot distinguish: φ∼ 2−(0.84± 0.06) d (improvement of the Minkowksi bound), and a competitor φ∼ d−a d with a very small coefficient a=0.06±0.04. We also find properties of the random walk which are suggestive of a glassy system already for moderately small dimensions.