Λc+\Lambda_\mathrm{c}^+ production in Pb-Pb collisions at sNN=5.02\sqrt{s_{\rm NN}} = 5.02 TeV

A measurement of the production of prompt $\Lambda_{\rm c}^{+}$ baryons in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV with the ALICE detector at the LHC is reported. The $\Lambda_{\rm c}^{+}$ and $\overline{\Lambda}_{\rm c}^{-}$ were reconstructed at midrapidity ($|y| < 0.5$) via the hadronic decay channel $\Lambda_{\rm c}^{+}\rightarrow {\rm p} {\rm K}_{\rm S}^{0}$ (and charge conjugate) in the transverse momentum and centrality intervals $6 < p_{\rm T} <12$ GeV/$c$ and 0-80%. The $\Lambda_{\rm c}^{+}$/D$^0$ ratio, which is sensitive to the charm quark hadronisation mechanisms in the medium, is measured and found to be larger than the ratio measured in minimum-bias pp collisions at $\sqrt{s} = 7$ TeV and in p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV. In particular, the values in p-Pb and Pb-Pb collisions differ by about two standard deviations of the combined statistical and systematic uncertainties in the common $p_{\rm T}$ interval covered by the measurements in the two collision system. The $\Lambda_{\rm c}^{+}$/D$^0$ ratio is also compared with model calculations including different implementations of charm quark hadronisation. The measured ratio is reproduced by models implementing a pure coalescence scenario, while adding a fragmentation contribution leads to an underestimation. The $\Lambda_{\rm c}^{+}$ nuclear modification factor, $R_{\rm AA}$, is also presented. The measured values of the $R_{\rm AA}$ of $\Lambda_{\rm c}^{+}$, D$_{\rm s}$ and non-strange D mesons are compatible within the combined statistical and systematic uncertainties. They show, however, a hint of a hierarchy $(R_{\rm AA}^{{\rm D}^{0}}<R_{\rm AA}^{{\rm D}_{\rm s}}<R_{\rm AA}^{\Lambda_{\rm c}^{+}})$, conceivable with a contribution of recombination mechanisms to charm hadron formation in the medium.Comment: 19 pages, 3 captioned figures, 1 table, authors from page 14, published, figures at http://alice-publications.web.cern.ch/node/469

Enhanced Kondo Effect in an Electron System Dynamically Coupled with Local Optical Phonon

We discuss Kondo behavior of a conduction electron system coupled with local optical phonon by analyzing the Anderson-Holstein model with the use of a numerical renormalization group (NRG) method. There appear three typical regions due to the balance between Coulomb interaction $U_{\rm ee}$ and phonon-mediated attraction $U_{\rm ph}$. For $U_{\rm ee}>U_{\rm ph}$, we observe the standard Kondo effect concerning spin degree of freedom. Since the Coulomb interaction is effectively reduced as $U_{\rm ee}-U_{\rm ph}$, the Kondo temperature $T_{\rm K}$ is increased when $U_{\rm ph}$ is increased. On the other hand, for $U_{\rm ee}<U_{\rm ph}$, there occurs the Kondo effect concerning charge degree of freedom, since vacant and double occupied states play roles of pseudo-spins. Note that in this case, $T_{\rm K}$ is decreased with the increase of $U_{\rm ph}$. Namely, $T_{\rm K}$ should be maximized for $U_{\rm ee} \approx U_{\rm ph}$. Then, we analyze in detail the Kondo behavior at $U_{\rm ee}=U_{\rm ph}$, which is found to be explained by the polaron Anderson model with reduced hybridization of polaron and residual repulsive interaction among polarons. By comparing the NRG results of the polaron Anderson model with those of the original Anderson-Holstein model, we clarify the Kondo behavior in the competing region of $U_{\rm ee} \approx U_{\rm ph}$.Comment: 8 pages, 8 figure

Fundamental Plane of Black Hole Activity in Quiescent Regime

A correlation among the radio luminosity ($L_{\rm R}$), X-ray luminosity ($L_{\rm X}$), and black hole mass ($M_{\rm BH}$) in active galactic nuclei (AGNs) and black hole binaries is known to exist and is called the "Fundamental Plane" of black hole activity. Yuan & Cui (2005) predicts that the radio/X-ray correlation index, $\xi_{\rm X}$, changes from $\xi_{\rm X}\approx 0.6$ to $\xi_{\rm X}\approx 1.2-1.3$ when $L_{\rm X}/L_{\rm Edd}$ decreases below a critical value $\sim 10^{-6}$. While many works favor such a change, there are also several works claiming the opposite. In this paper, we gather from literature a largest quiescent AGN (defined as $L_{\rm X}/L_{\rm Edd} < 10^{-6}$) sample to date, consisting of $75$ sources. We find that these quiescent AGNs follow a $\xi_{\rm X}\approx 1.23$ radio/X-ray relationship, in excellent agreement with the Yuan \& Cui prediction. The reason for the discrepancy between the present result and some previous works is that their samples contain not only quiescent sources but also "normal" ones (i.e., $L_{\rm X}/L_{\rm Edd} > 10^{-6}$). In this case, the quiescent sources will mix up with those normal ones in $L_{\rm R}$ and $L_{\rm X}$. The value of $\xi_{\rm X}$ will then be between $0.6$ and $\sim1.3$, with the exact value being determined by the sample composition, i.e., the fraction of the quiescent and normal sources. Based on this result, we propose that a more physical way to study the Fundamental Plane is to replace $L_{\rm R}$ and $L_{\rm X}$ with $L_{\rm R}/L_{\rm Edd}$ and $L_{\rm X}/L_{\rm Edd}$, respectively.Comment: 11 pages, 7 figures, accepted for publication in The Astrophysical Journa

Duality and Serre functor in homotopy categories

For a (right and left) coherent ring $A$, we show that there exists a duality between homotopy categories {\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A^{{\rm op}}) and {\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A). If $A=\Lambda$ is an artin algebra of finite global dimension, this duality restricts to a duality between their subcategories of acyclic complexes, {\mathbb{K}}^{{\rm{b}}}_{\rm ac}({\rm mod}{\mbox{-}}\Lambda^{\rm op}) and {\mathbb{K}}^{{\rm{b}}}_{\rm ac}({\rm mod}{\mbox{-}}\Lambda). As a result, it will be shown that, in this case, {\mathbb{K}}_{\rm ac}^{{\rm{b}}}({\rm mod}{\mbox{-}}\Lambda) admits a Serre functor and hence has Auslander-Reiten triangles.Comment: arXiv admin note: text overlap with arXiv:1605.0474

Kernel solutions of the Kostant operator on eight-dimensional quotient spaces

After introducing the generators and irreducible representations of the ${\rm su}(5)$ and ${\rm so}(6)$ Lie algebras in terms of the Schwinger's scillators, the general kernel solutions of the Kostant operators on eight-dimensional quotient spaces ${\rm su}(5)/{\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(6)/{\rm so}(4)\times {\rm so}(2)$ are derived in terms of the diagonal subalgebras ${\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(4)\times {\rm so}(2)$, respectively.Comment: 13 pages. Typos correcte