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

Some generic properties of level spacing distributions of 2D real random matrices

We study the level spacing distribution $P(S)$ of 2D real random matrices both symmetric as well as general, non-symmetric. In the general case we restrict ourselves to Gaussian distributed matrix elements, but different widths of the various matrix elements are admitted. The following results are obtained: An explicit exact formula for $P(S)$ is derived and its behaviour close to S=0 is studied analytically, showing that there is linear level repulsion, unless there are additional constraints for the probability distribution of the matrix elements. The constraint of having only positive or only negative but otherwise arbitrary non-diagonal elements leads to quadratic level repulsion with logarithmic corrections. These findings detail and extend our previous results already published in a preceding paper. For the {\em symmetric} real 2D matrices also other, non-Gaussian statistical distributions are considered. In this case we show for arbitrary statistical distribution of the diagonal and non-diagonal elements that the level repulsion exponent $\rho$ is always $\rho = 1$, provided the distribution function of the matrix elements is regular at zero value. If the distribution function of the matrix elements is a singular (but still integrable) power law near zero value of $S$, the level spacing distribution $P(S)$ is a fractional exponent pawer law at small $S$. The tail of $P(S)$ depends on further details of the matrix element statistics. We explicitly work out four cases: the constant (box) distribution, the Cauchy-Lorentz distribution, the exponential distribution and, as an example for a singular distribution, the power law distribution for $P(S)$ near zero value times an exponential tail.Comment: 21 pages, no figures, submitted to Zeitschrift fuer Naturforschung

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

Interaction of Human Chorionic Gonadotropin (hCG) and Asialo-hCG with Recombinant Human Thyrotropin Receptor.

hCG is a putative thyroid stimulator. The present studies were undertaken to examine its interaction and that of its desialylated variant asialo-hCG with recombinant human TSH (hTSH) receptor (hTSHr). To this end, we transfected a human thyroid carcinoma cell line (HTC) lacking endogenous TSHr with the full-length cDNA of the hTSHr. Unlike the wild type, the transfected cells, termed HTC-TSHr cells, were able to bind bovine TSH (bTSH) with high affinity and increase cAMP production in response to bTSH stimulation. Of the hCG forms, intact hCG displayed a weak activity to inhibit [125I] bTSH binding to HTC-TSHr cells, with 100 mg/L (2.6 x 10(-6) mol/L) producing maximally a 20% inhibition, whereas asialo-hCG achieved half-maximum binding inhibition at a concentration of 8 mg/L (2.3 x 10(-7) mol/L). The inhibitory constant (Ki) of asialo-hCG for recombinant hTSHr was calculated from saturation experiments in the presence of variable doses of bTSH and a fixed concentration of asialo-hCG to be approximately 8 x 10(-8) mol/L. The interaction of asialo-hCG with TSHr was further assessed by studies of the direct binding of the radioactively labeled hormone to both HTC and HTC-TSHr cells. [125I]Asialo-hCG binding to HTC-TSHr cells was 4.7%, compared to 1.5% in the wild-type cells lacking TSHr and was displaceable by bTSH (0.1-100 IU/L), indicating specific binding of the tracer to TSHr. Functionally, hCG (up to 100 mg/L; 2.6 x 10(-6) mol/L) proved unable to evoke any significant cAMP response over basal values in HTC-TSHr cells, as did asialo-hCG. Asialo-hCG, but not hCG, inhibited bTSH-stimulated adenylate cyclase activity in the cells in a dose-dependent manner. In conclusion, the present data show that intact hCG binds only weakly to HTC-TSHr cells and produces no significant cAMP stimulation, which is at variance with data obtained in FRTL-5 and Chinese hamster ovary-TSHr cells, but in good accord with previous findings in human thyroid membranes. Asialo-hCG, on the other hand, strongly binds to recombinant TSHr and inhibits the cAMP response to bTSH in HTC-TSHr cells, indicating that the desialylated hCG variant directly interacts with the receptor and truly is an antagonist of the hTSHr

Extended phase diagram of the Lorenz model

The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz model equations for thermal convection in Rayleigh-B\'enard flow is studied. Its bifurcation structure has commonly been investigated as a function of r, the normalized Rayleigh number, at fixed Prandtl number \sigma. The present work extends the analysis to the entire (r,\sigma) parameter plane. An onion like periodic pattern is found which is due to the alternating stability of symmetric and non-symmetric periodic orbits. This periodic pattern is explained by considering non-trivial limits of large r and \sigma. In addition to the limit which was previously analyzed by Sparrow, we identify two more distinct asymptotic regimes in which either \sigma/r or \sigma^2/r is constant. In both limits the dynamics is approximately described by Airy functions whence the periodicity in parameter space can be calculated analytically. Furthermore, some observations about sequences of bifurcations and coexistence of attractors, periodic as well as chaotic, are reported.Comment: 36 pages, 20 figure

Analytic expression for Taylor-Couette stability boundary

We analyze the mechanism that determines the boundary of stability in Taylor-Couette flow. By simple physical argument we derive an analytic expression to approximate the stability line for all radius ratios and all speed ratios, for co- and counterrotating cylinders. The expression includes viscosity and so generalizes Rayleigh's criterion. We achieve agreement with linear stability theory and with experiments in the whole parameter space. Explicit formulae are given for limiting cases.Comment: 6 pages (LaTeX with REVTEX) including 4 figures (Postscript) Revised, discussion of two additional references. See also http://staff-www.uni-marburg.de/~esse

Quantifying Optimal Growth Policy

The optimal mix of growth policies is derived within a comprehensive endogenous growth model. The analysis captures important elements of the tax-transfer system and takes into account transitional dynamics. Currently, for calculating corporate taxable income US firms are allowed to deduct approximately all of their capital and R&D costs from sales revenue. Our analysis suggests that this policy leads to severe underinvestment in both R&D and physical capital. We find that firms should be allowed to deduct between 2-2.5 times their R&D costs and about 1.5-1.7 times their capital costs. Implementing the optimal policy mix is likely to entail huge welfare gains.economic growth, endogenous technical change, optimal growth policy, tax-transfer system, transitional dynamics

Why Do Some People Want to Legalize Cannabis Use?

Preferences and attitudes to illicit drug policy held by individuals are likely to be an important in uence in the development of illicit drug policy. Amongst the key factors impacting on an individuals preferences over substance use policy are their beliefs about the costs and benefits of drug use, their own drug use history, and the extent of drug use amongst their peers. We use data from the Australian National Drug Strategy's Household Surveys to study these preferences. We find that current use and past use of cannabis are a major determinants of being in favor of legalization. We also find that cannabis users are more in favor of legalization the longer they have used cannabis and, among past users, the more recent their own drug using experience. This may be re ecting the fact that experience with cannabis provides information about the costs and benefits of using this substance. We also find some evidence that peers use of cannabis impacts on preferences towards legalization.cannabis use;drugs policy

The macroeconomics of TANSTAAFL

This paper shows that dynamic inefficiency can occur in dynamic general equilibrium models with fully optimizing, infinitely-lived households even in a situation with underinvestment. We identify necessary conditions for such a possibility and illustrate it in a standard R&D-based growth model. Calibrating the model to the US, we show that a moderate increase in the R&D subsidy indeed leads to an intertemporal free lunch (i.e., an increase in per capita consumption at all times). Hence, Milton Friedman's conjecture There ain't no such thing as a free lunch (TANSTAAFL) may not apply. --intertemporal free lunch,dynamic inefficiency,R&D-based growth,transitional dynamics

Dynamically optimal R&D subsidization

Previous research on optimal R&D subsidies has focussed on the long run. This paper characterizes the optimal time path of R&D subsidization in a semi-endogenous growth model, by exploiting a recently developed numerical method. Starting from the steady state under current R&D subsidization in the US, the R&D subsidy should significantly jump upwards and then slightly decrease over time. There is a negligible loss in welfare, however, from immediately setting the R&D subsidy to its optimal long run level, compared to the case where the dynamically optimal policy is implemented. --R&D subsidy,transitional dynamics,semi-endogenous growth,welfare