Renormalization Group and Asymptotic Spin-Charge Separation for Chiral Luttinger Liquids

The phenomenon of Spin-Charge separation in non-Fermi liquids is well understood only in certain solvable d=1 fermionic systems. In this paper we furnish the first example of asymptotic Spin-Charge separation in a d=1 nonsolvable model. This goal is achieved using Renormalization Group approach combined with Ward-Identities and Schwinger-Dyson equations, corrected by the presence of a bandwidth cut-offs. Such methods, contrary to bosonization, could be in principle applied also to lattice or higher dimensional systems.     

Performance study of the KrCl discharge laser with liquid chlorine donors

The effects of liquid chlorine donors (BCl₃ and CCl₄) on the output energy and the efficiency of a KrCl laser (222 nm) are investigated. Maximum laser energies of 230 mJ (3.3 J/l) in pulses of 16 ns duration were obtained from a 0.035% BCl₃/10.1% Kr/89.8% Ne mixture at a total pressure of 2600 Torr, and at a specific power loading of about 24 MW/cm³, a power conversion efficiency of 0.86% was obtained. These figures are reduced by a factor of two when He is used as buffer gas. Much weaker laser emissions were obtained when CCl₄ was used as a chlorine donor.     

Almost contact metric manifolds whose Reeb vector field is a harmonic section

We investigate almost contact metric manifolds whose Reeb vector field is a harmonic unit vector field, equivalently a harmonic section. We first consider an arbitrary Riemannian manifold and characterize the harmonicity of a unit vector field ??, when ??? is symmetric, in terms of Ricci curvature. Then, we show that for the class of locally conformal almost cosymplectic manifolds whose Reeb vector field ?? is geodesic, ?? is a harmonic section if and only if it is an eigenvector of the Ricci operator. Moreover, we build a large class of locally conformal almost cosymplectic manifolds whose Reeb vector field is a harmonic section. Finally, we exhibit several classes of almost contact metric manifolds where the associated almost contact metric structures ?? are harmonic sections, in the sense of Vergara-Diaz and Wood?[25], and in some cases they are also harmonic maps.     

Geodesic Ricci solitons on unit tangent sphere bundles

In the paper, (Abbassi and Kowalski, Ann Glob Anal Geom, 38: 11–20, 2010) the authors study Einstein Riemannian $g$ natural metrics on unit tangent sphere bundles. In this study, we equip the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,g)$ with an arbitrary Riemannian $g$ natural metric $\tilde{G}$ and we show that if the geodesic flow $\tilde{\xi }$ is the potential vector field of a Ricci soliton $(\tilde{G},\tilde{\xi },\lambda )$ on $T_1M,$ then $(T_1M,\tilde{G})$ is Einstein. Moreover, we show that the Reeb vector field of a contact metric manifold is an infinitesimal harmonic transformation if and only if it is Killing. Thus, we consider a natural contact metric structure $(\tilde{G}, \tilde{\eta }, \tilde{\varphi }, \tilde{\xi })$ over $T_1 M$ and we show that the geodesic flow $\tilde{\xi }$ is an infinitesimal harmonic transformation if and only if the structure $(\tilde{G}, \tilde{\eta }, \tilde{\varphi },\tilde{\xi })$ is Sasaki $\eta $ -Einstein. Consequently, we get that $(\tilde{G},\tilde{\xi }, \lambda )$ is a Ricci soliton if and only if the structure $(\tilde{G}, \tilde{\eta }, \tilde{\varphi }, \tilde{\xi })$ is Sasaki-Einstein with $\lambda = 2(n-1) >0.$ This last result gives new examples of Sasaki–Einstein structures.     

Levi Harmonic Maps of Contact Riemannian Manifolds

We study Levi harmonic maps, i.e., C ^∞ solutions f:M→M′ to \(\tau_{\mathcal{H}} (f) \equiv \operatorname{trace}_{g} ( \varPi_{\mathcal{H}}\beta_{f} ) = 0\) , where (M,η,g) is an (almost) contact (semi) Riemannian manifold, M′ is a (semi) Riemannian manifold, β _f is the second fundamental form of f, and \(\varPi_{\mathcal{H}} \beta_{f}\) is the restriction of β _f to the Levi distribution \({\mathcal{H}} = \operatorname{Ker}(\eta)\) . Many examples are exhibited, e.g., the Hopf vector field on the unit sphere S ²ⁿ⁺¹, immersions of Brieskorn spheres, and the geodesic flow of the tangent sphere bundle over a Riemannian manifold of constant curvature 1 are Levi harmonic maps. A CR map f of contact (semi) Riemannian manifolds (with spacelike Reeb fields) is pseudoharmonic if and only if f is Levi harmonic. We give a variational interpretation of Levi harmonicity. Any Levi harmonic morphism is shown to be a Levi harmonic map.     

Nonsymmetric 2‐(v,k,λ) designs,with (r,λ) = 1, admitting a solvable flag‐transitive automorphism group of affine type

Nonsymmetric $2‐\left(v,k,\lambda \right)$ designs, with $\left(r,\lambda \right)=1$, admitting a solvable flag‐transitive automorphism group of affine type not contained in $A\mathrm{\Gamma }{L}_1\left(v\right)$ are classified.     

The three corrugated surfaces of 1,4-divinyltetramethylene diradical intermediates and their connections to 1,2-divinylcyclobutane, 4-vinylcyclohexene, 1,5-cyclooctadiene, and two butadienes

The three potential energy surfaces of the trans-trans, cis-trans, and cis-cis divinyltetramethylene diradicals have been located with DFT calculations at the BPW91/6-311+G levels. The three surfaces account well for the experimental results reported for the thermolysis of optically active trans-1,2-divinylcyclobutane and optically active and deuterated 4-vinylcyclohexene. The surfaces account also for the outcome of the dimerization of butadiene and the thermolysis of cis,cis-1,5-cyclooctadiene. The three diradical intermediates are connected to the cyclization and dissociation products through conformations that are explored fully here.     

A dihydrogen bond between a bridging hydride and the NH proton of a coordinated dimethylamine: solid state, solution and theoretical characterization

The addition of one equivalent of dimethylamine (DMA) to the 44 valence-electron triangular cluster anion [Re₃(μ₃-H)(μ-H)₃(CO)₉]⁻ (1) affords the novel unsaturated derivative [Re₃(μ-H)₄(CO)₉(DMA)]⁻ (2, 46 valence electrons) which contains a dimethylamine molecule terminally coordinated to a cluster vertex. Theoretical calculations (DFT) reveal that in the more stable conformation the dimethylamine NH proton is directed towards the hydride bridging the opposite cluster edge in syn position, the close proximity of the ligands bound to the cluster surface allowing the formation of an unconventional N-H ? (μ-H)Re₂ hydrogen bond. The presence of this conformation in the solid state has been proven by an X-ray structural analysis of crystalline [PPh₄]2. Spectroscopic evidences (IR and NMR) indicate that the dihydrogen bond is maintained also in solution and, by the evaluation of the proton spin-lattice relaxation rates at variable temperature, a good estimate of the H ? H distance in solution has been determined.