Finite Group Discretization of Yang-Mills and Einstein Actions

Discrete versions of the Yang-Mills and Einstein actions are proposed for any finite group. These actions are invariant respectively under local gauge transformations and under the analogues of Lorentz and general coordinate transformations. The case Z_n×Z_n×···×Z_n is treated in some detail, recovering the Wilson action for Yang-Mills theories and a new discretized action for gravity.     

A distinctive example of the cooperative interplay of structure and environment in tuning of intramolecular charge transfer in second-order nonlinear optical chromophores

The strongly enhanced cooperative influence of medium polarity and organic structural design on the first hyperpolarizability beta of a novel family of highly polarizable azinium-(CH=CH-thienyl)-dicyanomethanido chromophores 1-3 is described. The dyes can be efficiently synthesized by regioselective protonation/alkylation of the corresponding bidentate anion precursors. Consecutive annelation of the pyridyl ring of 1 (pyridine-->quinoline-->acridine) and medium polarity effects are responsible for an extraordinarily variable range of intramolecular charge transfer (ICT), leading to a large set of pi-electron distribution patterns. Accordingly, systems with remarkably different zwitterionic/quinoid character in the ground and excited states present beta values in a broad range, eventually switching from negative to positive. Our investigation is based on a combination of experimental (UV/Vis spectroscopy, multinuclear NMR spectroscopy, and electrooptical absorption measurements) and computational (ab initio) approaches. It is shown that: 1) beta and mubeta are dramatically influenced, even by orders of magnitude, by a complex, non-monotonic interplay of structure and medium action, which in turn affects molecular ICT and bond length alternation (BLA), 2) the computations, validated by different experimental data, are to be recommended as an extremely useful tool in the search for a greatly improved set of molecular nonlinear optical (NLO) responses (in the case of 1-3 they show that such conditions may be attained only in a narrow and limited range of dielectric constants in which the annelation effect operates most efficiently), and 3) the search for the most favorable molecular NLO response of a highly polarizable chromophore both in solution and in solid matrices should simultaneously take into account not only the molecular design supplemented by annelation effects but also the polarity of the medium.     

Entanglement,superselection rules and supersymmetric quantum mechanics

In this paper we show that the energy eigenstates of supersymmetric quantum mechanics (SUSYQM) with non-definite “fermion” number are entangled states. They are “physical states” of the model provided that observables with odd number of spin variables are allowed in the theory like it happens in the Jaynes–Cummings model. Those states generalize the so-called “spin-spring” states of the Jaynes–Cummings model which have played an important role in the study of entanglement.     

Regioselective synthesis of 1,2- vs 1,3-squaraines

Squaraines have been known for many decades as very stable and versatile vis-NIR absorbing dyes. They have found applications for example as sensitizers in organic photovoltaics and photodetectors. The most common squaraine structure is the 1,3-regioisomer. Their 1,2-regioisomers are seldom mentioned and unanimously regarded as side products. A facile direct synthesis of 1,2-squaraines, highlighting the role played by reaction conditions and electronic factors, is described. The first electrochemical characterization of these dyes is also shown.     

Multipolar symmetric squaraines with large two-photon absorption cross-sections in the NIR region

The two-photon absorption (TPA) properties of two extended symmetric squaraine dyes are thoroughly characterized from the experimental and quantum-chemical point of view. The two molecules are specially engineered to have a multipolar structure with increasing complexity, D-π-A-π-D and A'-π-D-π-A-π-D-π-A', respectively. The experimental TPA spectra, measured by means of the Z-scan technique in the femtoseconds regime, display considerably high values of TPA cross sections (σ(TPA)) for both molecules. In particular, the squaraine with the more extended structure shows the highest value of σ(TPA) ever reported for this class of molecules. CIS and TDDFT calculations of the one and two-photon absorption properties are carried out to clarify the origin of the observed TPA properties and fully characterize the electronic properties of these compounds. The calculations, in good agreement with the experimental data, suggest that the origin of this exceptionally high σ(TPA) can be ascribed to the presence of a peripheral A' group, that increases the density of excited states involved in the TPA process.