Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states

We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read-Rezayi state whose effective theory is the SU(2)_K Chern-Simons theory. As a generalization of the Pfaffian (K = 2) and the Fibonacci (K = 3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we propose a method to compute the entanglement entropy skein-theoretically. We find that the entanglement entropy has a nontrivial contribution called the topological entanglement entropy which depends on the quantum dimension of non-Abelian quasi-particle intertwining two subsystems.     

Experimental and theoretical spectroscopic studies of ortho derivatives of methyl p-dimethylaminobenzoate

Steady-state spectroscopic studies of two ortho (-OCH₃ and -OH) derivatives of methyl p-dimethylaminobenzoate have been performed. The absorption spectra of molecules under study are analyzed taking into consideration results of quantum chemical semiempirical calculations. The fluorescence spectra of these molecules possess in polar solvents two bands, i.e., the locally excited and intramolecular charge transfer (ICT) fluorescence band. Their intensity ratio as well as the fluorescence/phosphorescence intensity ratio determined at 77 K depends on the solvent polarity. Theoretical studies of the TICT phenomenon have been made in order to explain the dual emission of molecules under study. Calculated electric dipole moments of these molecules in the ground, S₀, and excited, S₁(LE) and S₁(ICT) states, have been compared with experimentally determined data. Theoretically determined transition energies, ΔE_i, oscillator strengths, f_i, and electric dipole moments μ_S0, μ_S1(LE) and μ_S1(ICT) of the planar donor-acceptor (D/A) conformer agree with experimental data. According to Marcus theory inner- and outer-solvatation sphere reorganization energies (λ_out, λ_in) are calculated using the determined spectroscopic properties of molecules under study.     

Lower excited states of 7-azaindole dimer with a C2h(M) symmetry

The title subjects (in the vapor phase) were assessed to be in the weak-coupling limit as Frenkel-type excitons of a L_a-type excited state, by examining reported data on these systems: (1) L_b/L_a interconversion by dimerization (in the solution) just like what happens in the monomer by the change of solvent polarity, e.g., from 3-methylpentane to ethanol. (2) Good correspondence between the monophotonic excitation spectrum of the tautomer fluorescence (after excited-state double proton-transfer reaction of the dimer) and mass-selected (2 + 2) photoionization spectrum of the dimer, as is predicted theoretically. (3) Potential minima for locally excited configurations, as were predicted by ab initio calculations. Comments on the current controversy about the mechanism of its excited-state tautomerization, i.e., whether it is of one step or two steps, are made as well.