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

The Epstein-Glaser approach to pQFT: graphs and Hopf algebras

The paper aims at investigating perturbative quantum field theory (pQFT) in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one associated with a special combination of physical concepts such as normalization, localization, pseudo-unitarity, causality and an associated regularization, and renormalization. The algebraic structures, representing the perturbative expansion of the S-matrix, are imposed on the operator-valued distributions which are equipped with appropriate graph indices. Translation invariance ensures the algebras to be analytically well-defined and graded total symmetry allows to formulate bialgebras. The algebraic results are given embedded in the physical framework, which covers the two recent EG versions by Fredenhagen and Scharf that differ with respect to the concrete recursive implementation of causality. Besides, the ultraviolet divergences occuring in Feynman's representation are mathematically reasoned. As a final result, the change of the renormalization scheme in the EG framework is modeled via a HA which can be seen as the EG-analog of Kreimer's HA.Comment: 52 pages, 5 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

Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures

This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in (relatively) hyperbolic groups". We study there the existential theory of torsion free hyperbolic and relatively hyperbolic groups, in particular those with virtually abelian parabolic subgroups. We show that the satisfiability of systems of equations and inequations is decidable in these groups. In the second part, called "Finding relative hyperbolic structures", we provide a general algorithm that recognizes the class of groups that are hyperbolic relative to abelian subgroups.Comment: Two independant parts 23p + 9p, revised. To appear separately in Israel J. Math, and Bull. London Math. Soc. respectivel

Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?

The most promising source of gravitational waves for the planned detectors LIGO and VIRGO are merging compact binaries, i.e., neutron star/neutron star (NS/NS), neutron star/black hole (NS/BH), and black hole/black-hole (BH/BH) binaries. We investigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the gravitational wave signals by the three detector LIGO/VIRGO network using ``advanced detectors'' (those present a few years after initial operation). The combination ${\cal M} \equiv (M_1 M_2)^{3/5}(M_1 +M_2)^{-1/5}$ of the masses of the two bodies is measurable with an accuracy $\approx 0.1\%-1\%$. The reduced mass is measurable to $\sim 10\%-15\%$ for NS/NS and NS/BH binaries, and $\sim 50\%$ for BH/BH binaries (assuming $10M_\odot$ BH's). Measurements of the masses and spins are strongly correlated; there is a combination of $\mu$ and the spin angular momenta that is measured to within $\sim 1\%$. We also estimate that distance measurement accuracies will be $\le 15\%$ for $\sim 8\%$ of the detected signals, and $\le 30\%$ for $\sim 60\%$ of the signals, for the LIGO/VIRGO 3-detector network.Comment: 103 pages, 20 figures, submitted to Phys Rev D, uses revtex macros, Caltech preprint GRP-36

Existence of the Bogoliubov S(g) operator for the (:ϕ4:)2(:\phi^4:)_2 quantum field theory

We prove the existence of the Bogoliubov S(g) operator for the $(:\phi^4:)_2$ quantum field theory for coupling functions $g$ of compact support in space and time. The construction is nonperturbative and relies on a theorem of Kisy\'nski. It implies almost automatically the properties of unitarity and causality for disjoint supports in the time variable.Comment: LaTeX, 24 pages, minor modifications, typos correcte

Electron-ion interaction in doped conducting polymers

The discovery of electric-field effect for conducting polymers in transistor structures aroused a number of questions about structure, mechanism of charge transport, and a role of ions in conducting polymers. We present here the model of an electrochemical transistor whose resistance is governed by the gate potential through bulk ionic charging/discharging of the conducting polymer-based active channel. The predicted I(V) characteristics do not agree with the measured experimental dependencies for highly doped conducting polymer-based transistors. We suggest that the observable electric-field effect in conducting polymers is related to their structural peculiarities. The large free volume within the conductive polymer chain network enables ions to easily move into and out of the polymers. The main effect of ion insertion is breaking of the percolation network for the conductivity by removing critical hoping sites and, as a result, producing a conductor-nonconductor transition