From BRST to light-cone description of higher spin gauge fields

In this short note we show, at the level of action principles, how the light-cone action of higher spin gauge fields can easily be obtained from the BRST formulation through the elimination of quartets. We analyze how the algebra of cohomology classes is affected by such a reduction. By applying the reduction to the Poincare generators, we give an alternative way of analyzing the physical spectrum of the Fronsdal type actions, with or without trace condition.Comment: 13 pages Latex file, Proceedings of the Workshop "Quantum Field Theory and Hamiltonian Systems'', Caciulata, Romania, 16 - 21 Oct, 2004; more references added, acknowledgments correcte

Solvable model for spatiotemporal chaos

We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a nontrivial spatial behavior. We also introduce and calculate a generalized spatiotemporal correlation function

Pinning control of spatiotemporal chaos

Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a coupled map lattice as an example. The optimal arrangement of the control sites is shown to depend on the symmetry properties of the system, while their minimal density depends on the strength of noise in the system. The method is shown to work in any region of parameter space and requires a significantly smaller number of controllers compared to the method proposed earlier by Hu and Qu [Phys. Rev. Lett. 72, 68 (1994)]. A nonlinear generalization of the method for a 1D lattice is also presented

Limitations of Algebraic Approaches to Graph Isomorphism Testing

We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and only if if the graphs are isomorphic, and then to (try to) decide satisfiability of the system using, for example, the Gr\"obner basis algorithm. In some cases this can be done in polynomial time, in particular, if the equations admit a bounded degree refutation in an algebraic proof systems such as Nullstellensatz or polynomial calculus. We prove linear lower bounds on the polynomial calculus degree over all fields of characteristic different from 2 and also linear lower bounds for the degree of Positivstellensatz calculus derivations. We compare this approach to recently studied linear and semidefinite programming approaches to isomorphism testing, which are known to be related to the combinatorial Weisfeiler-Lehman algorithm. We exactly characterise the power of the Weisfeiler-Lehman algorithm in terms of an algebraic proof system that lies between degree-k Nullstellensatz and degree-k polynomial calculus

Quantum treatment of neutrino in background matter

Motivated by the need of elaboration of the quantum theory of the spin light of neutrino in matter ($SL\nu$), we have studied in more detail the exact solutions of the Dirac equation for neutrinos moving in the background matter. These exact neutrino wavefunctions form a basis for a rather powerful method of investigation of different neutrino processes in matter, which is similar to the Furry representation of quantum electrodynamics in external fields. Within this method we also derive the corresponding Dirac equation for an electron moving in matter and consider the electromagnetic radiation ("spin light of electron in matter", $SLe$) that can be emitted by the electron in this case.Comment: 10 pages, in: Proceedings of QFEXT'05 (The Seventh Workshop on Quantum Field Theory under the Influence of External Conditions, IEEC, CSIC and University of Barcelona, Barcelona, Catalonia, Spain, 5-9 September 2005.), ed. by Emilio Elizalde and Sergei Odintsov; published in Journal of Physics

Cumulene Molecular Wire Conductance from First Principles

We present first principles calculations of current-voltage characteristics (IVC) and conductance of Au(111):S2-cumulene-S2:Au(111) molecular wire junctions with realistic contacts. The transport properties are calculated using full self-consistent ab initio NEGF-DFT methods under external bias. The conductance of the cumulene wires shows oscillatory behavior depending on the number of carbon atoms (double bonds). Among all conjugated oligomers, we find that cumulene wires with odd number of carbon atoms yield the highest conductance with metallic-like ballistic transport behavior. The reason is the high density of states in broad LUMO levels spanning the Fermi level of the electrodes. The transmission spectrum and the conductance depend only weakly on applied bias, and the IVC is nearly linear over a bias region from +1 to -1 V. Cumulene wires are therefore potential candidates for metallic connections in nanoelectronic applications.Comment: Accepted in Phys. Rev. B; 5 pages and 6 figure