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

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

Parent field theory and unfolding in BRST first-quantized terms

For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space--time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.Comment: LaTeX, amsart++, 40 pages, references added, final version to appear in Commun. Math. Phy

Resonant Amplification of Electroweak Baryogenesis at Preheating

We explore viable scenarios for parametric resonant amplification of electroweak (EW) gauge fields and Chern-Simons number during preheating, leading to baryogenesis at the electroweak (EW) scale. In this class of scenarios time-dependent classical EW gauge fields, essentially spatially-homogeneous on the horizon scales, carry Chern-Simons number which can be amplified by parametric resonance up to magnitudes at which unsuppressed topological transitions in the Higgs sector become possible. Baryon number non-conservation associated with the gauge sector and the highly non-equilibrium nature of preheating allow for efficient baryogenesis. The requisite large CP violation can arise either from the time dependence of a slowly varying Higgs field (spontaneous baryogenesis), or from a resonant amplification of CP violation induced in the gauge sector through loops. We identify several CP violating operators in the Standard Model and its minimal extensions that can facilitate efficient baryogenesis at preheating, and show how to overcome would-be exponential suppression of baryogenesis associated with tunneling barriers.Comment: 51 pages, 8 figues; minor corrections; references adde

Influence of Sintering Conditions on Specific Electrical Conductivity in Aluminum-Graphene Composite

Dependence of specific electrical resistance on temperature (20 - 1600 ∘C) and processing method in an aluminum-graphene (up to 2wt.%) composite is investigated. It is established that spark plasma sintering (SPS) under pressure 40 MPа does not influence on electrical resistance, whereas SPS at low pressure (<10 MPa) reduces electrical resistance at a room temperature on 6 orders. Lower values of electrical resistance (up to 90 Ω *mm) received at sintering in hot pressing set at radiating heating. It is supposed that the reason of sharp decrease in electrical resistance at the lowered pressure is presence of current pulsations during SPS. They induces magnetic fields in graphene flake which lead to their moving and forming of particles to electroconductive chains or their capture in arched cells at applied pressure. Keywords: composite, aluminum, graphene, electrical resistance, temperature dependence