Charge-transfer in time-dependent density-functional theory via spin-symmetry-breaking

Long-range charge-transfer excitations pose a major challenge for time-dependent density functional approximations. We show that spin-symmetry-breaking offers a simple solution for molecules composed of open-shell fragments, yielding accurate excitations at large separations when the acceptor effectively contains one active electron. Unrestricted exact-exchange and self-interaction-corrected functionals are performed on one-dimensional models and the real LiH molecule within the pseudopotential approximation to demonstrate our results.Comment: 5 pages, 4 figure

Cohomology of Lie superalgebras and of their generalizations

The cohomology groups of Lie superalgebras and, more generally, of color Lie algebras, are introduced and investigated. The main emphasis is on the case where the module of coefficients is non-trivial. Two general propositions are proved, which help to calculate the cohomology groups. Several examples are included to show the peculiarities of the super case. For L = sl(1|2), the cohomology groups H^1(L,V) and H^2(L,V), with V a finite-dimensional simple graded L-module, are determined, and the result is used to show that H^2(L,U(L)) (with U(L) the enveloping algebra of L) is trivial. This implies that the superalgebra U(L) does not admit of any non-trivial formal deformations (in the sense of Gerstenhaber). Garland's theory of universal central extensions of Lie algebras is generalized to the case of color Lie algebras.Comment: 50 pages, Latex, no figures. In the revised version the proof of Lemma 5.1 is greatly simplified, some references are added, and a pertinent result on sl(m|1) is announced. To appear in the Journal of Mathematical Physic

Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes

We investigate the generic 3D topological field theory within AKSZ-BV framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue that the perturbative partition function gives rise to secondary characteristic classes. We investigate a toy model which is an odd analogue of Chern-Simons theory, and we give some explicit computation of two point functions and show that its perturbation theory is identical to the Chern-Simons theory. We give concrete example of the homomorphism taking Lie algebra cocycles to Q-characteristic classes, and we reinterpreted the Rozansky-Witten model in this light.Comment: 52 page

Electroweak superpartner production at 13.6 TeV with Resummino

Due to the greater experimental precision expected from the currently ongoing LHC Run 3, equally accurate theoretical predictions are essential. We update the documentation of the Resummino package, a program dedicated to precision cross section calculations for the production of a pair of sleptons, electroweakinos, and leptons in the presence of extra gauge bosons, and for the production of an associated electroweakino-squark or electroweakino-gluino pair. We detail different additions that have been released since the initial version of the program a decade ago, and then use the code to investigate the impact of threshold resummation corrections at the next-to-next-to-leading-logarithmic accuracy. As an illustration of the code we consider the production of pairs of electroweakinos and sleptons at the LHC for centre-of-mass energies ranging up to 13.6 TeV and in simplified model scenarios. We find slightly increased total cross section values, accompanied by a significant decrease of the associated theoretical uncertainties. Furthermore, we explore the dependence of the results on the squark masses.Comment: 30 pages, 5 figure

Dynamics of Charge-Transfer Processes with Time-Dependent Density Functional Theory

We show that as an electron transfers between closed-shell molecular fragments at large separation, the exact correlation potential of time-dependent density functional theory gradually develops a step and peak structure in the bonding region. This structure has a density-dependence that is non-local both in space and time, and even the exact ground-state exchange-correlation functional fails to cap- ture it. In the complementary case of charge-transfer between open-shell fragments, an initial step and peak vanish as the charge-transfer state is reached. Lack of these structures in usual approxima- tions leads to inaccurate charge-transfer dynamics. This is dramatically illustrated by the complete lack of Rabi oscillations in the dipole moment under conditions of resonant charge-transfer

An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold

It is well known that the inequivalent unitary irreducible representations (UIR's) of the mapping class group $G$ of a 3-manifold give rise to ``theta sectors'' in theories of quantum gravity with fixed spatial topology. In this paper, we study several families of UIR's of $G$ and attempt to understand the physical implications of the resulting quantum sectors. The mapping class group of a three-manifold which is the connected sum of $\R^3$ with a finite number of identical irreducible primes is a semi-direct product group. Following Mackey's theory of induced representations, we provide an analysis of the structure of the general finite dimensional UIR of such a group. In the picture of quantized primes as particles (topological geons), this general group-theoretic analysis enables one to draw several interesting qualitative conclusions about the geons' behavior in different quantum sectors, without requiring an explicit knowledge of the UIR's corresponding to the individual primes.Comment: 52 pages, harvmac, 2 postscript figures, epsf required. Added an appendix proving the semi-direct product structure of the MCG, corrected an error in the characterization of the slide subgroup, reworded extensively. All our analysis and conclusions remain as befor

Unravelling small world networks

New classes of random graphs have recently been shown to exhibit the small world phenomenon - they are clustered like regular lattices and yet have small average pathlengths like traditional random graphs. Small world behaviour has been observed in a number of real life networks, and hence these random graphs represent a useful modelling tool. In particular, Grindrod [Phys. Rev. E 66 (2002) 066702-1] has proposed a class of range dependent random graphs for modelling proteome networks in bioinformatics. A property of these graphs is that, when suitably ordered, most edges in the graph are short-range, in the sense that they connect near-neighbours, and relatively few are long-range. Grindrod also looked at an inverse problem - given a graph that is known to be an instance of a range dependent random graph, but with vertices in arbitrary order, can we reorder the vertices so that the short-range/long-range connectivity structure is apparent? When the graph is viewed in terms of its adjacency matrix, this becomes a problem in sparse matrix theory: find a symmetric row/column reordering that places most nonzeros close to the diagonal. Algorithms of this general nature have been proposed for other purposes, most notably for reordering to reduce fill-in and for clustering large data sets. Here, we investigate their use in the small world reordering problem. Our numerical results suggest that a spectral reordering algorithm is extremely promising, and we give some theoretical justification for this observation via the maximum likelihood principle