Three Dimensionally Oriented Polyacetylene

Changes in the dimensions of oriented polyacetylene under isomerisation and iodine doping are presented. We show that the polymer chains are parallel to the fiber axis. In roll-oriented samples the relative change in dimensions in anisotropic in all three directions and this is atributed to an oredeing of the fibers with respect to the crystalline axes of the polymer. The volume depends libearly on iodine concentration in agreement with a model of inh omogeneous doping where it is assumed that for intermediate iodine concentrations the fibers consist of a fully doped surface layer surrounding the undoped interiour.     

Electron delocalization and dimerization in solid C59N doped C60 fullerene

Electron spin resonance and ab initio electronic structure calculations show an intricate relation between molecular rotation and chemical bonding in the dilute solid solution. The unpaired electron of C59N is delocalized over several C60 molecules above 700 K, while at lower temperatures it remains localized within short range. The data suggest that below 350 K rigid C59N-C60 heterodimers are formed in thermodynamic equilibrium with dissociated rotating molecules. The structural fluctuations between heterodimers and dissociated molecules are accompanied by simultaneous electron spin transfer between C60 and C59N molecules. The calculation confirms that in the C59N-C60 heterodimer the spin density resides mostly on the C60 moiety, while it is almost entirely on C59N in the dissociated case.     

Relaxation of fermionic excitations in a strongly attractive Fermi gas in an optical lattice

We theoretically study the relaxation of high energy single particle excitations into molecules in a system of attractive fermions in an optical lattice, both in the superfluid and the normal phase. In a system characterized by an interaction scale U and a tunneling rate t, we show that the relaxation rate scales as ～Ctexp[-αU(2)/t(2)ln(U/t)] in the large U/t limit. We obtain explicit expressions for the temperature and density dependent exponent α, both in the low temperature superfluid phase and the high temperature phase with pairing but no coherence between the molecules. We find that the relaxation rate decreases both with temperature and deviation of the fermion density from half filling. We show that quasiparticle and phase degrees of freedom are effectively decoupled within experimental time scales allowing for observation of ordered states even at high total energy of the system.     

Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.     

Polymeric sheets in Mg4C60

We present preliminary results on the preparation and structure of Mg₄C₆₀, a new fulleride polymer. A series of Mg_xC₆₀ compositions (0<x<6) were prepared by solid state reaction. While most samples were multiphase, a single phase material was obtained at the nominal composition Mg₄C₆₀. The X-ray diffraction pattern of Mg₄C₆₀ was successfully indexed and fitted to a rhombohedral structure based on two-dimensional polymeric sheets of C₆₀ ions. This result extends the family of fulleride polymers to the salts of multiply charged cations and thus opens a new direction in this field.     

On successive minima and the Absolute Siegel's Lemma

We prove a new bound on the product of the nth successive minimum of an automorphism of GL(N,kA) and the (N−n+1)th successive minimum of its dual, extending a classical inequality of K. Mahler for polar lattices to the geometry of numbers over the adèles. As a corollary we derive the Absolute Siegel's Lemma in as stated by D. Roy and J.L. Thunder.