Percival Lagrangian approach to Aubry-Mather theory

We present some streamlined proofs of some of the basic results in Aubry-Mather theory (existence of quasi-periodic minimizers, multiplicity results when there are gaps among minimizers) based on the study of hull functions. We present results in arbitrary number of dimensions We also compare the proofs and results with those obtained in other formalisms

Low dimensional cohomology of general conformal algebras gcNgc_N

We compute the low dimensional cohomologies $\tilde H^q(gc_N,C)$, H^q(gc_N,\C) of the infinite rank general Lie conformal algebras $gc_N$ with trivial coefficients for $q\le3, N=1$ or $q\le2, N\ge2$. We also prove that the cohomology of $gc_N$ with coefficients in its natural module is trivial, i.e., H^*(gc_N,\C[\ptl]^N)=0; thus partially solve an open problem of Bakalov-Kac-Voronov in [{\it Comm. Math. Phys.,} {\bf200} (1999), 561-598].Comment: 18 page

Magnetic properties of a spin-3 Chromium condensate

We study the ground state properties of a spin-3 Cr condensate subject to an external magnetic field by numerically solving the Gross-Piteavskii equations. We show that the widely adopted single-mode approximation is invalid under a finite magnetic field. In particular, a phase separation like behavior may be induced by the magnetic field. We also point out the possible origin of the phase separation phenomenon.Comment: 6 pages, 5 figure

The conformation of conducting polymer chains: Hubbard polymers

The conformational and electronic properties of conducting flexible random and self-avoiding walk polymer chains are under investigation. A Hamiltonian for conjugated flexible polymers is introduced and its physical consequences are presented. One important result is that the electronic degrees of freedom greatly affect the conformational statistics of the walks and vice versa. The electronic degrees of freedom extend the size of the chain. The end-to-end distance behaves as $R\propto L^{\nu}$ with $\nu=(d+1)/(d+2)$, where $d$ is the spatial dimension.Comment: 11 pages of Latex + uuencoded postscript figur