Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Ro?ssler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.     

Isolated exact solutions of Simple Nonadiabatic Model Hamiltonians

Simple Nonadiabatic Model Hamiltonians are treated in Bargmanns Hilbert space of analytical functions. In this formulation the Schrödinger equation is a system of two first order differential equations for two component wave functions. Algebraic equations for the eigenvalues of particularly simple isolated exact solutions can be found by a standard treatment of the solutions in the neighbourhood of the regular singular points of the system of differential equations.     

Central peak in the Takada model

Starting from a diagrammatic approach proposed by Takada et al. to the solution of the Ising model in a transverse field, a consistent approximation for the polarization function is found. A narrow central peak is obtained in a form that can be easily compared to other approaches.     

Frequency dependence of the real part of the electrical conductivity for TTF-TCNQ

The infrared data of Heeger and Garito can be qualitatively explained using expressions from polaron theory with parameters from the literature. Inclusion of intrasite Coulomb repulsion is not necessary.     

Exact solution for the dynamical Jahn-Teller effect in E ⊗ ϵ and Γ8 ⊗ τ2 systems

The analytical formulation of the dynamical J-T problem leads to a system of two ordinary linear first order differential equations, whose solutions are required to belong to the space of entire functions. This condition determines the energy eigenvalues. It can be formulated in terms of a convergent continued fraction which defines a transcendental equation between the interaction constant and the energy (with the angular momentum quantum number as parameter). For an estimate the continued fraction is approximated with high accuracy by a periodic continued fraction in which the first m partial numerators are treated exactly. In this way we derive the eigenvalue condition that had been conjectured in [14].     

Optical effects of small polarons at high frequencies with an application to reduced strontiumtitanate

Theoretical expressions for the complex electrical conductivity of small polarons are given for frequencies

     

Synthetic Studies Towards the Preparation of 2‐Benzyl‐2‐ hydroxybenzofuran‐3(2H)‐one,the Prototype of Naturally Occurring Hydrated Auronols

Various synthetic approaches were employed to prepare 2‐benzyl‐2‐hydroxybenzofuran‐3(2H)‐one ( 8 ), the prototype of naturally occurring auronols. While the base‐induced ring transformation of 3‐hydroxyflavanone ( 2 ) as well as the hydration of 2‐benzylidenebenzofuran‐3(2H)‐one (=aurone; 6 ) proved to be inappropriate, the hydrogenolytic epoxide‐ring opening of 2′‐phenylspiro[benzofuran‐2(3H),2′‐oxiran]‐3‐one ( 7 ), obtained from 6 , represents an efficient method to afford the auronol 8 .