We report a general method for the calculation of Jahn-Teller coupling constants by ab initio methods widely available today in standard packages. The vibrational frequencies corresponding to those obtained experimentally are calculated at the symmetric position using a generalized restricted Hartree-Fock (GRHF) wavefunction. The energy of the symmetric configuration is calculated as a conical ...

We report the bright solitons of the generalized Gross-Pitaevskii (GP) equation with some types of physically relevant parity-time- ( PT-) and non- PT-symmetric potentials. We find that the constant momentum coefficient Γ can modulate the linear stability and complicated transverse power-flows (not always from the gain toward loss) of nonlinear modes. However, the varying momentum coefficient Γ...

Coherent coupling of optical resonances in spherical microcavities results in the formation of so called photonic molecules. The name originates from the analogy to chemical molecules. The coupled optical modes are similar to the atomic orbitals of a chemical molecule. In this work, we studied the resonance spectrum of the symmetric photonic molecules. Furthermore, symmetric directional emissio...

We present a combined finite-difference time-domain/linear response approach for modeling plasmon/molecule systems. The self-interaction of the molecule is avoided by splitting the fields and currents into two parts: those due to the molecule and those from everything else. This approach is suitable for describing surface plasmons on metal nanostructures interacting in the near field with nearb...

Various attempts to find a proper generalization of the notion of Lie algebra associated to a vector space V endowed with a non symmetric braiding c appeared in the literature. In this direction, we introduce and investigate a notion of braided Lie algebra (and the associated universal enveloping algebra) which turns out to be effective for the class of braided vector spaces (V, c) whose Nichol...

We know from Littlewood (1968) that the moments of order 4 of the classical Rudin–Shapiro polynomials Pn(z) satisfy a linear recurrence of degree 2. In a previous article, we developed a new approach, which enables us to compute exactly all the moments Mq(Pn) of even order q for q 32. We were also able to check a conjecture on the asymptotic behavior of Mq(Pn), namely Mq(Pn) ∼ Cq2, where Cq = 2...

The algebra Sym of symmetric functions is a proper subalgebra of QSym: for example, M11 and M12 +M21 are symmetric, but M12 is not. As an algebra, QSym is generated by those monomial symmetric functions corresponding to Lyndon words in the positive integers [11, 6]. The subalgebra of QSym ⊂ QSym generated by all Lyndon words other than M1 has the vector space basis consisting of all monomial sy...