Lattice study of QCD at finite chiral density: topology and confinement

In this paper we study the properties of QCD at nonzero chiral density $$\rho _5$$ ρ 5 , which is introduced through chiral chemical potential $$\mu _5$$ μ 5 . The study is performed within lattice simulation of QCD with dynamical rooted staggered fermions. We first check that $$\rho _5$$ ρ 5 is generated at nonzero $$\mu _5$$ μ 5 and in the chiral limit observe $$\rho _5 \sim \varLambda _{QCD}^2 \mu _5$$ ρ 5 ∼ Λ QCD 2 μ 5 . We also test the possible connection between confinement and topological fluctuations. To this end, we measured the topological susceptibility $$\chi _{\mathrm{top}}$$ χ top and string tension $$\sigma $$ σ for various values of $$\mu _5$$ μ 5 . We observed that string tension grows with $$\mu _5$$ μ 5 . It seems that topological susceptibility also rises with $$\mu _5$$ μ 5 , but to state this more reliably the uncertainties should be reduced. We believe that our results indicate possible connection between topological fluctuations and the strength of confinement.

Spin Density Topology

Despite its role in spin density functional theory and it being the basic observable for describing and understanding magnetic phenomena, few studies have appeared on the electron spin density subtleties thus far. A systematic full topological analysis of this function is lacking, seemingly in contrast to the blossoming in the last 20 years of many studies on the topological features of other scalar fields of chemical interest. We aim to fill this gap by unveiling the kind of information hidden in the spin density distribution that only its topology can disclose. The significance of the spin density critical points, the 18 different ways in which they can be realized and the peculiar topological constraints on their number and kind, arising from the presence of positive and negative spin density regions, is addressed. The notion of molecular spin graphs, spin maxima (minima) joining paths, spin basins and of their valence is introduced. We show that two kinds of structures are associated with a spin–polarized molecule: the usual one, defined through the electron density gradient, and the magnetic structure, defined through the spin density gradient and composed in general by at least two independent spin graphs, related to spin density maxima and minima. Several descriptors, such as the spin polarization index, are introduced to characterize the properties of spin density critical points and basins. The study on the general features of the spin density topology is followed by the specific example of the water molecule in the 3B1 triplet state, using spin density distributions of increasing accuracy.

Porosity of 𝓢-approximately continuous functions

Considering the natural topology or 𝓢-density topology on the domain and on the range we obtain different families of continuous functions f : ℝ → ℝ. In this paper we compare these families in porosity terms. In particular, we obtain strengthening of some recent results by J. Hejduk, A. Loranty, R. Wiertelak.

A Detailed Classification of Three-Centre Two-Electron Bonds

We evaluate the three-centre two-electron (3c-2e) bonds using atoms in molecules (AIM) and natural bond orbital (NBO) theoretical analyses. They have been classified as ‘open (V)’ or ‘closed (Δ)’, depending on how the three centres were bonded. Herein, we show that they could be classified as V, L, Δ, Y, T and I (linear) arrangements depending on the way the three centres are bonded. These different structures are found in B2H6 (V), CH5+ (V), Me-C2H2+ (L), B3+ (Δ), C3H3+ (Δ), H3+ (Y), 2-norbornyl+ (T), SiH5+ (T), and Al2H7− (I). Our results suggest that CH3Li2+ does not contain a 3c-2e bond according to NBO analysis. Therefore, we propose that 3c-2e bonds are classified more accurately as V, L, Δ, Y, T, or I, based on the electron density topology.

Density, ψ-density and continuity

In this paper we consider classes of continuous functions with three kinds of topologies on the domain and/or range of the function: the natural topology, density topology and