The dispersion relation for noninteracting excitons and the influence of perturbative corrections are examined in the case of pentacene structure. The values of exchange integrals are determined by nonlinear fits to the experimental dispersion data, obtained by the inelastic electron scattering reported in recent experiments. We obtain theoretical dispersion curves along four different directions in the Brillouin zone which possess the same periodicity as the experimental data. We also show that perturbative corrections are negligible since the exciton gap in the dispersion relation is huge in comparison to the exchange integrals.

The response function and largest Lyapunov exponent analysis were applied to the driven overdamped Frenkel-Kontorova model with two types of anharmonic convex interparticle potentials. In both cases model reduces to a single particle model for integer values of winding number. It is shown that the mirror image of the amplitude dependence of critical depinning force and largest Lyapunov exponent observed recently in the standard Frenkel-Kontorova model (Odavić et al 2017 Commun. Nonlinear Sci. Numer. Simul. 47, 100) is not retained generally. Behaviour of systems with relatively strong interparticle force was examined and evidence for the appearance of mode-locking phenomenon in both directions of particles’ motion is presented.

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Recently, there has been an increased interest in studying quantum entanglement and quantum coherence. Since both of these properties are attributed to the existence of quantum superposition, it would be useful to determine if some type of correlation between them exists. Hence, the purpose of this paper is to explore the type of the correlation in several systems with different types of anisotropy. The focus will be on the XY spin chains with the Dzyaloshinskii-Moriya interaction and the type of the mentioned bond will be explored using the quantum renormalization group method.

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