On the variational noncommutative Poisson geometry

We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative associative algebras over the equivalence under cyclic permutations of the letters in the associative words. We state the basic properties of the variational Schouten bracket and derive an interesting criterion for (non)commutative differential operators to be Hamiltonian (and thus determine the (non)commutative Poisson structures). We place the noncommutative jet-bundle construction at hand in the context of the quantum string theory.Comment: Proc. Int. workshop SQS'11 `Supersymmetry and Quantum Symmetries' (July 18-23, 2011; JINR Dubna, Russia), 4 page

A convenient criterion under which Z_2-graded operators are Hamiltonian

We formulate a simple and convenient criterion under which skew-adjoint Z_2-graded total differential operators are Hamiltonian, provided that their images are closed under commutation in the Lie algebras of evolutionary vector fields on the infinite jet spaces for vector bundles over smooth manifolds.Comment: J.Phys.Conf.Ser.: Mathematical and Physical Aspects of Symmetry. Proc. 28th Int. colloq. on group-theoretical methods in Physics (July 26-30, 2010; Newcastle-upon-Tyne, UK), 6 pages (in press

Some aspects of electronic topological transition in 2D system on a square lattice. Excitonic ordered states

We study the ordered "excitonic" states which develop around the quantum critical point (QCP) associated with the electronic topological transition (ETT) in a 2D electron system on a square lattice. We consider the case of hopping beyond nearest neighbors when ETT has an unusual character. We show that the amplitude of the order parameter (OP) and of the gap in the electron spectrum increase with increasing the distance from the QCP, \delta_c - \delta, where \delta = 1-n and "n" is an electron concentration. Such a behavior is different from the ordinary case when OP and the gap decrease when going away from the point which is a motor for instability. The gap opens at "hot spots" and extends untill the saddle points (SP) whatever is the doping concentration. The spectrum gets a characteristic flat shape as a result of hybrydization effect in the vicinity of two different SP's. The shape of the spectrum and the angle dependence of the gap have a striking similarity with the features observed in the normal state of the underdoped high-T$_c$ cuprates. We discuss also details about the phase diagram and the behaviour of the density of states.Comment: 15 pages, 14 EPS figures included, EPJ style included, added references, changed conten

Biomixing by chemotaxis and efficiency of biological reactions: the critical reaction case

Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly influence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction. In continuation of our earlier work, we consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction. The model is motivated, in particular, by the studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We consider the case of the weakly coupled quadratic reaction term, which is the most natural from the biological point of view and was left open. The result is that similarly to higher power coupling, the chemotaxis plays a crucial role in ensuring efficiency of reaction. However, mathematically, the picture is quite different in the quadratic reaction case and is more subtle. The reaction is now complete even in the absence of chemotaxis, but the timescales are very different. Without chemotaxis, the reaction is very slow, especially for the weak reaction coupling coefficient. With chemotaxis, the timescale and efficiency of reaction are independent of the coupling parameter.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1101.244

Variational Lie algebroids and homological evolutionary vector fields

We define Lie algebroids over infinite jet spaces and establish their equivalent representation through homological evolutionary vector fields.Comment: Int. Workshop "Nonlinear Physics: Theory and Experiment VI" (Gallipoli, Italy; June-July 2010). Published v3 = v2 minus typos, to appear in: Theoret. and Mathem. Phys. (2011) Vol.167:3 (168:1), 18 page

Gold-plated Mode of CP-Violation in Decays of B_c Meson from QCD Sum Rules

The model-independent method based on the triangle ideology is implemented to extract the CKM-matrix angle gamma in the decays of doubly heavy long-lived meson B_c. We analyze a color structure of diagrams and conditions to reconstruct two reference-triangles by tagging the flavor and CP eigenstates of D^0 meson in the fixed exclusive channels. The characteristic branching ratios are evaluated in the framework of QCD sum rules.Comment: 11 pages, RevTeX4 file, 4 eps-figure

Polarized Electric Current in Semiclassical Transport with Spin-Orbit Interaction

Semiclassical solutions of two-dimensional Schrodinger equation with spin-orbit interaction and smooth potential are considered. In the leading order, spin polarization is in-plane and follows the evolution of the electron momentum for a given subband. Out-of-plane spin polarization appears as a quantum correction, for which an explicit expression is obtained. We demonstrate how spin-polarized currents can be achieved with the help of a barrier or quantum point contact open for transmission only in the lower subband.Comment: 6 pages, 2 figure

Various ordered states in a 2D interacting electron system close to an electronic topological transition

We consider a 2D electron system on a square lattice with hopping beyond nearest neighbors. The existence of the quantum critical point associated with an electronic topological transition in the noninteracting system results in density wave (DW) and high temperature d-wave superconducting (dSC) instabilities in the presence of an exchange interaction J. We analyse different DW ordering such as isotropic Spin DW (SDW), d-wave SDW, isotropic Charge DW (CDW) and d-wave CDW. The coexistence of dSC and SDW orders leads necessary to the existence of a third order which is a pi triplet superconducting (PTS) order. A new phase diagram with a mixed phase of SDW, dSC and PTS order is found. The theory is applied to high-Tc cuprates.Comment: 2 pages, 1 figure, submitted to LT22 (Physica B