Chirality violating condensates in QCD and their connection with zero mode solutions of quark Dirac equations

It is demonstrated, that chirality violating condensates in massless QCD arise entirely from zero mode solutions of Dirac equations in arbitrary gluon fields. The model is suggested, where the zero mode solutions are the ones for quarks, moving in the instanton field. Basing on this model were calculated the quark condensate magnetic susceptibilities of dimensions $3(\chi)$ and 5 ($\kappa$ and $\xi$). The good considence of the values $\chi,\kappa$ and $\xi$, obtained in this approach with ones, found from the hadronic spectrum ia a serious argument in favour, that instantons are the only source of chirality violating condensates in QCD. The temperature dependence of the quark condensate is discussed. It is shown that the phase transition, corresponding to the $T$-dependence of the quark condensate $\alpha(T)$ as an order parameter, is of the type of crossover.Comment: The talk presented of Gribov-80 Workshop, May 28-30, 2010, Trieste, 8 pages, minor change

Spontaneous violation of chiral symmetry in QCD vacuum is the origin of baryon masses and determines baryon magnetic moments and their other static properties

A short review is presented of the spontaneous violation of chiral symmetry in QCD vacuum. It is demonstrated, that this phenomenon is the origin of baryon masses in QCD. The value of nucleon mass is calculated as well as the masses of hyperons and some baryonic resonances and expressed mainly through the values of quark condensates -- $, ~q=u,d,s$ -- the vacuum expectation values (v.e.v.) of quark field. The concept of vacuum expectation values induced by external fields is introduced. It is demonstrated that such v.e.v. induced by static electromagnetic field results in quark condensate magnetic susceptibility, which plays the main role in determination of baryon magnetic moments. The magnetic moments of proton, neutron and hyperons are calculated. The results of calculation of baryon octet $\beta$-decay constants are also presented.Comment: 13 pades, 5 figures. Dedicated to 85-birthday of acad. S.T.Belyaev. To be published in Phys.At.Nucl. Few references are correcte

Necessary and sufficient condition on global optimality without convexity and second order differentiability

The main goal of this paper is to give a necessary and sufficient condition of global optimality for unconstrained optimization problems, when the objective function is not necessarily convex. We use Gâteaux differentiability of the objective function and its bidual (the latter is known from convex analysis)

Metal-insulator transition in hydrogenated graphene as manifestation of quasiparticle spectrum rearrangement of anomalous type

We demonstrate that the spectrum rearrangement can be considered as a precursor of the metal-insulator transition observed in graphene dosed with hydrogen atoms. The Anderson-type transition is attributed to the coincidence between the Fermi level and the mobility edge, which appearance is induced by the spectrum rearrangement. Available experimental data are thoroughly compared to the theoretical results for the Lifshitz impurity model

The structure functions of longitudinal virtual photon at low virtualities

The structure functions of longitudinal virtual photon at low virtualities are calculated in the framework of chiral pertubation theory(ChPT) in the zero and first order of ChPT. It is assumed that the virtuality of target longitudinal photon is much less than the virtuality of the hard projectile photon and both are less than the characteristic ChPT scale.Comment: 16 pages, 8 figure

Experimental demonstration of Aharonov-Casher interference in a Josephson junction circuit

A neutral quantum particle with magnetic moment encircling a static electric charge acquires a quantum mechanical phase (Aharonov-Casher effect). In superconducting electronics the neutral particle becomes a fluxon that moves around superconducting islands connected by Josephson junctions. The full understanding of this effect in systems of many junctions is crucial for the design of novel quantum circuits. Here we present measurements and quantitative analysis of fluxon interference patterns in a six Josephson junction chain. In this multi-junction circuit the fluxon can encircle any combination of charges on five superconducting islands, resulting in a complex pattern. We compare the experimental results with predictions of a simplified model that treats fluxons as independent excitations and with the results of the full diagonalization of the quantum problem. Our results demonstrate the accuracy of the fluxon interference description and the quantum coherence of these arrays