The Accelerated Kepler Problem

The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem's Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the accelerated Kepler problem and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.Comment: 16 pages, 9 figures, in press at Celestial Mechanics and Dynamical Astronom

Polarization and readout of coupled single spins in diamond

We study the coupling of a single nitrogen-vacancy center in diamond to a nearby single nitrogen defect at room temperature. The magnetic dipolar coupling leads to a splitting in the electron spin resonance frequency of the nitrogen-vacancy center, allowing readout of the state of a single nitrogen electron spin. At magnetic fields where the spin splitting of the two centers is the same we observe a strong polarization of the nitrogen electron spin. The amount of polarization can be controlled by the optical excitation power. We combine the polarization and the readout in time-resolved pump-probe measurements to determine the spin relaxation time of a single nitrogen electron spin. Finally, we discuss indications for hyperfine-induced polarization of the nitrogen nuclear spin

Non-Uniqueness of Quantized Yang-Mills Theories

We consider quantized Yang-Mills theories in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S-matrix. The most general coupling which is gauge invariant in first order contains a two-parametric ambiguity in the ghost sector - a divergence- and a coboundary-coupling may be added. We prove (not completely) that the higher orders with these two additional couplings are gauge invariant, too. Moreover we show that the ambiguities of the n-point distributions restricted to the physical subspace are only a sum of divergences (in the sense of vector analysis). It turns out that the theory without divergence- and coboundary-coupling is the most simple one in a quite technical sense. The proofs for the n-point distributions containing coboundary-couplings are given up to third or fourth order only, whereas the statements about the divergence-coupling are proven in all orders.Comment: 22 pages. The paper is written in TEX. The necessary macros are include

On Gauge Invariance and Spontaneous Symmetry Breaking

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.Comment: 13 pages, latex, no figure

Investment under ambiguity with the best and worst in mind

Recent literature on optimal investment has stressed the difference between the impact of risk and the impact of ambiguity - also called Knightian uncertainty - on investors' decisions. In this paper, we show that a decision maker's attitude towards ambiguity is similarly crucial for investment decisions. We capture the investor's individual ambiguity attitude by applying alpha-MEU preferences to a standard investment problem. We show that the presence of ambiguity often leads to an increase in the subjective project value, and entrepreneurs are more eager to invest. Thereby, our investment model helps to explain differences in investment behavior in situations which are objectively identical

Thin front propagation in random shear flows

Front propagation in time dependent laminar flows is investigated in the limit of very fast reaction and very thin fronts, i.e. the so-called geometrical optics limit. In particular, we consider fronts evolving in time correlated random shear flows, modeled in terms of Ornstein-Uhlembeck processes. We show that the ratio between the time correlation of the flow and an intrinsic time scale of the reaction dynamics (the wrinkling time $t_w$) is crucial in determining both the front propagation speed and the front spatial patterns. The relevance of time correlation in realistic flows is briefly discussed in the light of the bending phenomenon, i.e. the decrease of propagation speed observed at high flow intensities.Comment: 5 Revtex4 pages, 4 figures include

Improvement of Memory by Means of Ultra-Low Doses of Antibodies to S-100B Antigen

Antigen S-100B of nervous tissue, according to the data of numerous studies, affects the mechanisms of nervous system plasticity and memory. The influence of ultralow doses of antibodies to S-100B (6C dilution, according to the homeopathic pharmacopoeia) has been studied on three learning behavioral models on Wistar rats, which were inhibitory avoidance, choosing of bowls with sucrose and feeding behavior cessation after auditory signal. For all three tasks, parameters of reproduction of the learned skills improved after per oral administration of potentiated antibodies to S-100B antigen immediately after learning. Possible mechanisms of the anti-S-100B antibodies influence on memory formation are discussed