Publications (102) View all
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Article: The Coulomb problem on a 3-sphere and Heun polynomials
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ABSTRACT: The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables. After quantization we get the explicit form of the spectrum and present an algebraic equation for the eigenvalues of the Runge-Lentz vector. We also present the wave functions expressed via Heun polynomials.02/2013; -
Article: Isospin particle systems on quaternionic projective spaces
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ABSTRACT: We construct the isospin particle system on $n$-dimensional quaternionic projective spaces in the presence of BPST-instanton by the reduction from the free particle on $(2n+1)$-dimensional complex projective space. Then we add to this system a "quaternionic oscillator potential" and show, that this oscillator-like system is superintegrable. We show, that besides the analogs of quadratic constants of motion of the spherical (Higgs) and $\mathbb{C}P^n $- oscillators, it possesses the third-order constants of motion, which are functionally independent from the quadratic ones.12/2012; -
Article: Correlation functions in one-dimensional spin lattices with Ising and Heisenberg bonds
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ABSTRACT: A general technique of exact calculation of any correlation functions for the special class of one-dimensional spin models containing small clusters of quantum spins assembled to a chain by alternating with the single Ising spins is proposed. The technique is a natural generalization of that in the models solved by a classical transfer matrices. The general expressions for corresponding matrix operators which are the key components of the technique are obtained. Despite the spatial inhomogeneity, such class of spin chains is proven to have only one correlation length for all types of correlation functions. The technique is illustrated on two examples: symmetric diamond chain and asymmetric sawtooth chain.11/2012; -
Article: Comparative cyto-genotoxicity assessment of functionalized and pristine multiwalled carbon nanotubes on human lung epithelial cells.
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ABSTRACT: Chemical functionalization extends CNT applications conferring them new functions, but could modify their toxicity. We compared cytotoxicity and genotoxic/oxidative effects of -OH functionalized and pristine MWCNTs to evaluated the influence of the functionalization exposing A549 cells to 1-40μg/ml of both MWCNTs for 2, 4 and 24h. Cytotoxicity was evaluated by MTT and LDH tests and apoptosis induction, direct/oxidative DNA damage by Fpg-modified comet assay. After 24h we found viability reduction significant at 20 and 40μg/ml for both the MWCNTs with a detectable viability reduction already at lower concentrations for MWCNTs. A significant LDH release was found only for MWCNTs. Significant apoptosis induction was found from 10μg/ml of MWCNT-OH. A concentration-dependent increase of direct DNA damage, significant at 40μg/ml of MWCNTs and beginning from 5μg/ml of MWCNT-OH was detected at all exposure times. Oxidative DNA damage was not observed for both CNTs. The results indicate a different cytotoxic mechanism, by membrane damage for MWCNTs and apoptosis for MWCNT-OH, that could be explained by a different cellular uptake. Moreover, we found an earlier genotoxic effect for MWCNT-OH. The findings suggest that further studies on functionalized CNTs are necessary before using them in several applications particularly in biomedical field.Toxicology in Vitro 05/2012; 26(6):831-40. · 2.78 Impact Factor -
Article: Action-angle variables for the particle near extreme Kerr throat
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ABSTRACT: We construct the action-angle variables for the spherical part of conformal mechanics describing the motion of a particle near extreme Kerr throat. We indicate the existence of the critical point $|p_\varphi|=mc R_{\rm Sch}$ (with $m$ being the mass of the particle, $c$ denoting the speed of light, $R_{\rm Sch}=2\gamma M /c^2$ being the Schwarzschild radius of a black hole with mass $M$, and $\gamma$ denoting the gravitational constant), where these variables are expressed in terms of elementary functions. Away from this point the action-angle variables are defined by elliptic integrals. The proposed formulation allows one to easily reconstruct the whole dynamics of the particle both in initial coordinates, as well as in the so-called conformal basis, where the Hamiltonian takes the form of conventional non-relativistic conformal mechanics. The related issues, such as semiclassical quantization and supersymmetrization are also discussed.12/2011;
