Projective Ponzano-Regge spin networks and their symmetries

We present a novel hierarchical construction of projective spin networks of the Ponzano-Regge type from an assembling of five quadrangles up to the combinatorial 4-simplex compatible with a geometrical realization in Euclidean 4-space. The key ingrendients are the projective Desargues configuration and the incidence structure given by its space-dual, on the one hand, and the Biedenharn--Elliott identity for the 6j symbol of SU(2), on the other. The interplay between projective-combinatorial and algebraic features relies on the recoupling theory of angular momenta, an approach to discrete quantum gravity models carried out successfully over the last few decades. The role of Regge symmetry --an intriguing discrete symmetry of the $6j$ which goes beyond the standard tetrahedral symmetry of this symbol-- will be also discussed in brief to highlight its role in providing a natural regularization of projective spin networks that somehow mimics the standard regularization through a q-deformation of SU(2).Comment: 14 pages, 19 figure

Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials

The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given as a second order difference equation which, by a complex phase change, we turn into a discrete Schr\"odinger-like equation. The introduction of discrete potential-like functions reveals the surprising crucial role here of hidden symmetries, first discovered by Regge for the quantum mechanical 6j symbols; insight is provided into the underlying geometric features. The spectrum and wavefunctions of the volume operator are discussed from the viewpoint of the Hamiltonian evolution of an elementary "quantum of space", and a transparent asymptotic picture emerges of the semiclassical and classical regimes. The definition of coordinates adapted to Regge symmetry is exploited for the construction of a novel set of discrete orthogonal polynomials, characterizing the oscillatory components of torsion-like modes.Comment: 13 pages, 5 figure

3nj Morphogenesis and Semiclassical Disentangling

Recoupling coefficients (3nj symbols) are unitary transformations between binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum operators. They have been used in a variety of applications in spectroscopy, quantum chemistry and nuclear physics and quite recently also in quantum gravity and quantum computing. These coefficients, naturally associated to cubic Yutsis graphs, share a number of intriguing combinatorial, algebraic, and analytical features that make them fashinating objects to be studied on their own. In this paper we develop a bottom--up, systematic procedure for the generation of 3nj from 3(n-1)j diagrams by resorting to diagrammatical and algebraic methods. We provide also a novel approach to the problem of classifying various regimes of semiclassical expansions of 3nj coefficients (asymptotic disentangling of 3nj diagrams) for n > 2 by means of combinatorial, analytical and numerical tools

Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity

Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a “d-TST” formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena

The He + H2+ → HeH+ + H reaction: Ab initio studies of the potential energy surface, benchmark time-independent quantum dynamics in an extended energy range and comparison with experiments

The following article appeared in Journal of Chemical Physics 137.24 (2012): 244306 and may be found at http://scitation.aip.org/content/aip/journal/jcp/137/24/10.1063/1.4772651In this work we critically revise several aspects of previous ab initio quantum chemistry studies [P. Palmieri, Mol. Phys. 98, 1835 (2000); C. N. Ramachandran, et al., Chem. Phys. Lett. 469, 26 (2009)] of the HeH2+ system. New diatomic curves for the H2+ and HeH+ molecular ions, which provide vibrational frequencies at a near spectroscopic level of accuracy, have been generated to test the quality of the diatomic terms employed in the previous analytical fittings. The reliability of the global potential energy surfaces has also been tested performing benchmark quantum scattering calculations within the time-independent approach in an extended interval of energies. In particular, the total integral cross sections have been calculated in the total collision energy range 0.955-2.400 eV for the scattering of the He atom by the ortho- and para-hydrogen molecular ion. The energy profiles of the total integral cross sections for selected vibro-rotational states of H2+ (v = 0,...,5 and j = 1,... ,7) show a strong rotational enhancement for the lower vibrational states which becomes weaker as the vibrational quantum number increases. Comparison with several available experimental data is presented and discussedThe work has been performed under the HPC-EUROPA2 project (Project No.: 228398) with the support of the European Commission - Capacities Area - Research Infrastructures. D.D.F., V.A., and S.C. thank also the Italian MIUR for PRIN contracts. A.A. acknowledges support by the program CONSOLIDERINGENIO of Ministerio de Economia y Competitividad (Spain) under Grant No. CSD2009-00038, entitled “Molecular Astrophysics: the Herschel and Alma Era,” Grant No. FIS2011-29596-C02-02, and by Comunidad Autonoma de Madrid (CAM) under Grant No. S-2009/MAT/146

Quantum Dynamics and Kinetics of the F + H2 and F + D2 Reactions at Low and Ultra-Low Temperatures

Integral cross sections and rate constants for the prototypical chemical reactions of the fluorine atom with molecular hydrogen and deuterium have been calculated over a wide interval of collision energy and temperature ranging from the sub-thermal (50 K) down to the ultra-cold regimes (0.5 mK). Rigorous close coupling time-independent quantum reactive scattering calculations have been carried out on two potential energy surfaces, differing only at long-range in the reactants' channel. The results show that tunnel, resonance and virtual state effects enhance under-barrier reactivity giving rise to pronounced deviations from the Arrhenius law as temperature is lowered. Within the ultra-cold domain (below 1 mK), the reactivity is governed by virtual state effects and by tunneling through the reaction barrier; in the cold regime (1 mK–1 K), the shape resonances in the entrance channel of the potential energy surface make the quantum tunneling contribution larger so enhancing cross sections and rate constants by about one order of magnitude; at higher temperatures (above 10 K), the tunneling pathway enhanced by the constructive interference between two Feshbach resonances trapped in the reaction exit channel competes with the thermally activated mechanism, as the energy gets closer to the reaction barrier height. The results show that at low temperatures cross sections and rate constants are extremely sensitive to small changes in the long-range intermolecular interaction in the entrance channel of the potential energy surface, as well as to isotopic substitution

Subthreshold Ionization of Weakly Bound Complexes: StochasticAnalysis of the Role of the Rydberg Quasicontinuum

Recent evidence for subthreshold ionization (i.e. electron loss at energies less than anticipated from vertical transitions assuming adiabatic separation of nuclear motion) points at the role of nonadiabatic coupling of high Rydberg terms of molecules. Sinai's billiard model for the chaotic motion of the Rydberg electron, that leads to a diffusion over the energy ladder as a result of electronic–vibrational exchange, is suggested as the classical mechanism of autoionization. A quantum expression for the branching ratio between autoionization and spontaneous fluorescence is obtained and discussed with reference to experimental results on associative ionization in atomic collisions and on laser ionization of van der Waals diatomics

Double photoionization of propylene oxide: a coincidence study of the ejection of a pair of valence-shell electrons

Propylene oxide, a favorite target of experimental and theoretical studies of circular dichroism, was recently discovered in interstellar space, further amplifying the attention to its role in the current debate on protobiological homochirality. In the present work, a photoelectron-photoion-photoion coincidence technique, using an ion-imaging detector and tunable synchrotron radiation in the 18.0-37.0 eV energy range, permits us (i) to observe six double ionization fragmentation channels, their relative yields being accounted for about two-thirds by the couple (C2H4+, CH2O+) and one-fifth by (C2H3+, CH3O+); (ii) to measure thresholds for their openings as a function of photon energy; and (iii) to unravel a pronounced bimodality for a kinetic-energy-released distribution, fingerprint of competitive non-adiabatic mechanisms