Numerical approaches to time evolution of complex quantum systems

We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev polynomials. The Chebyshev approach benefits from two advantages over the standard time-integration Crank-Nicholson scheme: speedup and efficiency. Potential competitors are semiclassical methods such as the Wigner-Moyal or quantum tomographic approaches. We outline the basic concepts of these techniques and benchmark their performance against the Chebyshev approach by monitoring the time evolution of a Gaussian wave packet in restricted one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes and the motion in anharmonic potentials. Finally we apply the prominent Chebyshev technique to two highly non-trivial problems of current interest: (i) the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the spatiotemporal evolution of polaron states in finite quantum systems. Here, depending on the disorder/electron-phonon coupling strength and the device dimensions, we observe transmission or localisation of the matter wave.     

Foundations of continuous-time recursive utility: differentiability and normalization of certainty equivalents

This paper relates recursive utility in continuous time to its discrete-time origins and provides an alternative to the approach presented in Duffie and Epstein (Econometrica 60:353–394, 1992), who define recursive utility in continuous time via backward stochastic differential equations (stochastic differential utility). We show that the notion of Gâteaux differentiability of certainty equivalents used in their paper has to be replaced by a different concept. Our approach allows us to address the important issue of normalization of aggregators in non-Brownian settings. We show that normalization is always feasible if the certainty equivalent of the aggregator is of the expected utility type. Conversely, we prove that in general Lévy frameworks this is essentially also necessary, i.e. aggregators that are not of the expected utility type cannot be normalized in general. Besides, for these settings we clarify the relationship of our approach to stochastic differential utility and, finally, establish dynamic programming results.     

The structure group of an alternative algebra

The structure group of an alternative algebra and various canonical subgroups are defined and investigated. Using the principle of triality, natural sets of generators for these groups in the case of octonion algebras are exhibited. Horst Tietz zur Vollendung des achtzigsten Lebensjahres gewidmet     

The Rotational Spectrum of ClClO2 in Its v4=1 and v6=1 Vibrationally Excited States: An Example of Strong Coriolis Interaction

The two lowest vibrational states of ³⁵Cl³⁵ClO₂, v₄=1 (A′) and v₆=1 (A″), were investigated between 223 and 500 GHz. More than 250 rotational transitions were recorded with J and K_a up to 71 and 34, respectively. The spectra are heavily perturbed by strong c-type and weaker a-type Coriolis interactions. Near degeneracies of rotational levels of the two vibrational states having ΔJ=0, ΔK_a=5 to 1, and ΔK_a+ΔK_c= odd cause moderate to severe perturbations in the rotational structure, preventing the states from being fit as isolated ones. Distortions in the hyperfine structure facilitated the assignment of rotational quantum numbers. Several resonantly interacting levels with ΔK_a=5 to 2 were accessed, and a number of transitions between the states were observed. While resonant Coriolis interaction with ΔK_a=1 occurs only at K_a>40, the effects of this interaction are so severe that nonresonant interaction considerably perturbs the highest K_aQ-branches observed. The observed transitions could be fit to within experimental uncertainties employing the first-order Coriolis coupling constants fixed to those from the harmonic force field, sextic distortion constants fixed to those of the ground state, and some higher order Coriolis terms. The energy difference calculated from the fit agrees well with that obtained from the matrix-isolation infrared spectrum. Quadrupole coupling constants were determined for both Cl nuclei and both vibrational states.     

Synthesis,characterization, and bonding properties of polymeric fullerides AC70.nNH3 (A = Ca,Sr, Ba,Eu, Yb)

Reduction of C70 with alkaline earth and rare earth metals dissolved in liquid ammonia results in metal fulleride solvates AC70.nNH3 (A = Ca, Sr, Ba, Eu, Yb) containing linear polymeric, anionic chains infinity 1 [C70(2-)]. The compounds were characterised by means of Raman spectroscopy and single-crystal structure determination. The accurate crystal structure of [Sr(NH3)8]C70.3NH3, determined with atomic resolution, allowed for a comparison with results of quantum chemical calculations. The nature of the C-C bonds in the fulleride is analysed in detail leading to a model explaining the unexpected polymerisation of C70(2-).     

3,4-Dihydroxy-7,8-dihydro-beta-ionone 3-O-beta-D-glucopyranoside and other glycosidic constituents from apple leaves

3,4-Dihydroxy-7,8-dihydro-beta-ionone 3-O-beta-D-glucopyranoside 1 has been isolated from a methanolic extract of apple (Malus domestica) leaves by XAD-2 adsorption chromatography and subsequent purification by high speed countercurrent chromatography (HSCCC) and HPLC. Under acidic conditions this glycoside gives rise to a number of volatile compounds including 1,1,6-trimethyl-1,2-dihydronaphthalene (TDN) 2, which is known as an off-flavor compound in wine. In the course of the study, six additional glycoconjugates were isolated from apple leaves, i.e. roseoside 3, 3-oxo-alpha-ionol beta-D-glucopyranoside 4, benzoic acid beta-D-glucose ester 5, kaempferol 3-O-rhamnoside 6, (+)-syringaresinol beta-D-glucopyranoside 7 and 4-hydroxy-5-(3'-methyl-2'-butenyl)-benzoic acid methylester 3-beta-D-glucopyranoside 8. The latter compound has been isolated for the first time in nature. In order to avoid the 'kerosene-off-flavor' caused by TDN, the methanolic extract has been subjected to yeast fermentation. This treatment reduced the amount of TDN formed and resulted in an improved flavor impression of the methanolic extract.