Fundamental Aspects of Quantum Brownian Motion

With this work we elaborate on the physics of quantum noise in thermal equilibrium and in stationary non-equilibrium. Starting out from the celebrated quantum fluctuation-dissipation theorem we discuss some important consequences that must hold for open, dissipative quantum systems in thermal equilibrium. The issue of quantum dissipation is exemplified with the fundamental problem of a damped harmonic quantum oscillator. The role of quantum fluctuations is discussed in the context of both, the nonlinear generalized quantum Langevin equation and the path integral approach. We discuss the consequences of the time-reversal symmetry for an open dissipative quantum dynamics and, furthermore, point to a series of subtleties and possible pitfalls. The path integral methodology is applied to the decay of metastable states assisted by quantum Brownian noise.Comment: 13 pages, 4 figures, RevTeX, submitted to Chaos special issue "100 Years of Brownian Motion

A high-entropy wind r-process study based on nuclear-structure quantities from the new finite-range droplet model FRDM(2012)

Theoretical studies of the nucleosynthesis origin of the heavy elements in our Solar System (S.S.) by the rapid neutron-capture process (r-process) still face the entwined uncertainties in the possible astrophysical scenarios and the nuclear-physics properties far from stability. In this paper we present results from the investigation of an r-process in the high-entropy wind (HEW) of core-collapse supernovae (here chosen as one of the possible scenarios for this nucleosynthesis process), using new nuclear-data input calculated in a consistent approach, for masses and $\beta$-decay properties from the new finite-range droplet model FRDM(2012). The accuracy of the new mass model is 0.56 MeV with respect to {\sc AME2003}, to which it was adjusted. We compare the new HEW r-process abundance pattern to the latest S.S. r-process residuals and to our earlier calculations with the nuclear-structure quantities based on FRDM(1992). Substantial overall and specific local improvements in the calculated pattern of the r-process between $A\simeq 110$ and $^{209}$Bi, as well as remaining deficiencies are discussed in terms of the underlying spherical and deformed shell structure far from stability.Comment: 8 pages, 4 figure

SPINON BASIS FOR (sl2^)_k INTEGRABLE HIGHEST WEIGHT MODULES AND NEW CHARACTER FORMULAS

In this note we review the spinon basis for the integrable highest weight modules of sl2^ at levels k\geq1, and give the corresponding character formula. We show that our spinon basis is intimately related to the basis proposed by Foda et al. in the principal gradation of the algebra. This gives rise to new identities for the q-dimensions of the integrable modules.Comment: 9 pages, plain TeX + amssym.def, to appear in the proceedings of `Statistical Mechanics and Quantum Field Theory,' USC, May 16-21, 199

Detection of risk factors for obesity in early childhood with quantile regression methods for longitudinal data

This article compares and discusses three different statistical methods for investigating risk factors for overweight and obesity in early childhood by means of the LISA study, a recent German birth cohort study with 3097 children. Since the definition of overweight and obesity is typically based on upper quantiles (90% and 97%) of the age specific body mass index (BMI) distribution, our aim was to model the influence of risk factors and age on these quantiles while as far as possible taking the longitudinal data structure into account. The following statistical regression models were chosen: additive mixed models, generalized additive models for location, scale and shape (GAMLSS), and distribution free quantile regression models. The methods were compared empirically by cross-validation and for the data at hand no model could be rated superior. Motivated by previous studies we explored whether there is an age-specific skewness of the BMI distribution. The investigated data does not suggest such an effect, even after adjusting for risk factors. Concerning risk factors, our results mainly confirm results obtained in previous studies. From a methodological point of view, we conclude that GAMLSS and distribution free quantile regression are promising approaches for longitudinal quantile regression, requiring, however, further extensions to fully account for longitudinal data structures

Quantum Mechanical Propagators in Terms of Hida Distributions

We review some basic notions and results of White Noise Analysis that are used in the construction of the Feynman integrand as a generalized White Noise functional. After sketching this construction for a large class of potentials we show that the resulting Feynman integrals solve the Schroedinger equation

Delocalization and Heisenberg's uncertainty relation

In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Harper model with its quasiperiodic potential shows a transition from extended to localized states. The difference between the two models becomes particularly apparent in phase space where Heisenberg's uncertainty relation imposes a finite resolution. Our analysis points to the relevance of the coupling between momentum eigenstates at weak potential strength for the delocalization of a quantum particle.Comment: 7 pages, 2 figures, EPL class include