Long-time and unitary properties of semiclassical initial value representations

We numerically compare the semiclassical ``frozen Gaussian'' Herman-Kluk propagator [Chem. Phys. 91, 27 (1984)] and the ``thawed Gaussian'' propagator put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by studying the quantum dynamics in some nonlinear one-dimensional potentials. The reasons for the lack of long time accuracy and norm conservation in the latter method are uncovered. We amend the thawed Gaussian propagator with a global harmonic approximation for the stability of the trajectories and demonstrate that this revised propagator is a true alternative to the Herman-Kluk propagator with similar accuracy.Comment: 14 pages, 4 figures, corrected typos and figure 1 (d

A Listing of Current Books

With the rapid increase in the research of promising technologies such as vehicle platooning, which are trying to find more fuel-efficient ways of operating our transportation systems, complex questions requiring creative solutions arise. Regarded as an up-and-coming technology that is expected to be highly relevant and widely applied in the near future, vehicle platooning allows the smart manipulation of the traffic by grouping two or more vehicles into a single convoy and coordinating its behavior, all the while guaranteeing a safe and fuel-efficient freight operation. This thesis tackles the specific problem in which two platoons of heavyduty vehicles (HDVs), coming from different highways, would like to be merged into a single one and remain driving as a larger platoon using the least amount of fuel possible. This can be beneficial if the HDVs need to travel a long distance after the merging point and fuel savings of up to 8% can be achieved by platooning along this trajectory. The focus lies on the calculation of the optimal input policies that minimize the fuel consumption of both platoons while completing the merging maneuver. Some theoretical background on optimal control and the minimum principle is introduced and it is consequently applied on a nonlinear model of the HDVs dynamics. The culmination of this approach is the solution of the inputconstrained, free end-time optimization problem. Due to the non-linearity of the model and the conditions set by the minimum principle numerical integration techniques, such as the shooting method, are also presented. In a final stage, this optimization tool is used together with shrinking horizon model predictive control to create a controller that is capable of accounting for disturbances, speed constraints and model uncertainties. The final result of this thesis is a control algorithm that can merge two platoons of any length, even in the presence of undesirable disturbances by correcting the optimal policies accordingly, in the most fuel-efficient manner

Clustering households by time use patterns ; an empirical investigation using the German Time Use Survey 2001/2002

Clustering individuals or households on the basis of socio-economic variables has become a widespread practice in German social research over the past few decades. This paper is part of a research project that explores results which may be obtained when time use patterns are chosen as the basis of numerical classification. Over the past few years, results relating to single households were published by the authors. The present paper extends the analysis to families. The investigation uses data from the German Time Use Survey 2001/2002. It is shown that the clustering process fulfils the criteria required by stochastic and qualitative social science. Furthermore, evidence is provided that including cluster memberships as dummy variables into a regressor set increases the predictive capabilities of a common multivariate analysis of correlations between socio-economic variables. Especially concerning health, meaningful interconnections between household styles and health state are detected. --

Entrepreneurial Innovation and Sustained Long-run Growth without Weak or Strong Scale Effects

R&D-based growth theory suggests that a larger population size raises either the long-run rate of economic growth (“strong scale effect”) or the level of per capita income (“weak scale effect”), with far-reaching policy implications. However, for modern times there is little empirical support for strong scale effects and evidence in favor of weak scale effects is mixed, at best. This paper develops a simple overlapping-generations framework with endogenous occupational choice of heterogeneous agents and entrepreneurial innovations in which any form of scale effect is absent. A higher population growth rate has a negligible, possibly negative effect on the long-run growth rate of per capita income. Long-run growth is sustained also in absence of population growth and generally is policy-dependent.economic growth, endogenous technical change, entrepreneurial skills, population growth, scale effects

Investigations on finite ideal quantum gases

Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to excited nuclei and Bose-Einstein condensation are discussed.Comment: 13 pages, 7 postscript figures, uses 'epsfig.sty'. Submitted to Physica A. More information available at http://obelix.physik.uni-osnabrueck.de/~schnack

Contest for Attention in a Quality-Ladder Model of Endogenous Growth

This paper develops a quality-ladder model of endogenous growth to study the interplay between in-house R&D and marketing expenditure. Although promotional activity is modelled as purely wasteful competition among firms for attention, it unambiguously fosters innovation activity of firms, and possibly, leads to faster growth. This result rests on two premises which are consistent with empirical evidence. First, if firms incur higher sunk costs for marketing, concentration and firm sizes rise. Second, firm size and R&D expenditure are positively related. As a result, R&D investments per firm may even become excessive, whereas being inefficiently low in the benchmark case without marketing. This has non-trivial consequences for the socially optimal policy design with respect to R&D subsidies and entry incentives.contest for attention, endogenous growth, innovation activity, marketing, R&D subsidies, scale effects

Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator

For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the propagator lead to eigenvalues of the same accuracy as WKB calculations with Langer correction. The latter are restricted to integrable systems, however, whereas the time-dependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and is extendable to arbitrary shapes of the potential.Comment: 11 pages, 1 figur

Entrepreneurial Innovation and Sustained Long-Run Growth without Weak or Strong Scale Effects

R&D-based growth theory suggests that a larger population size raises either the long-run rate of economic growth (“strong scale effect”) or the level of per capita income (“weak scale effect”), with far-reaching policy implications. However, for modern times there is little empirical support for strong scale effects and evidence in favor of weak scale effects is mixed, at best. This paper develops a simple overlapping-generations framework with endogenous occupational choice of heterogeneous agents and entrepreneurial innovations in which any form of scale effect is absent. A higher population growth rate has a negligible, possibly negative effect on the long-run growth rate of per capita income. Long-run growth is sustained also in absence of population growth and generally is policy-dependent.entrepreneurial skills, endogenous technical change, economic growth, population growth, scale effects

Firm Size and Diversification: Asymmetric Multiproduct Firms under Cournot Competition

A positive relationship between firm size and product diversification is a long-standing stylized fact. However, so far there is no appropriate theoretical model to explain the underlying forces of this observation. This paper analyzes an oligopoly model with asymmetric multiproduct frms, which is capable of addressing this issue. The model suggests that intangible assets of firms, which affect marginal costs or perceived quality of goods within a firm’s product line, play a key role for the empirical regularity that larger firms are more diversified.asymmetric equilibrium, diversification, firm size, intangible assets, multiproduct firms