Non-equilibrium dynamics of a system with Quantum Frustration

Using flow equations, equilibrium and non-equilibrium dynamics of a two-level system are investigated, which couples via non-commuting components to two independent oscillator baths. In equilibrium the two-level energy splitting is protected when the TLS is coupled symmetrically to both bath. A critical asymmetry angle separates the localized from the delocalized phase. On the other hand, real-time decoherence of a non-equilibrium initial state is for a generic initial state faster for a coupling to two baths than for a single bath.Comment: 22 pages, 9 figure

First-Order Type Effects in YBa2_2Cu3_3O6+x_{6+x} at the Onset of Superconductivity

We present results of Raman scattering experiments on tetragonal ${\rm (Y_{1-y}Ca_{y})Ba_{2}Cu_{3}O_{6+x}}$ for doping levels $p(x,y)$ between 0 and 0.07 holes/CuO$_2$. Below the onset of superconductivity at $p_{\rm sc1} \approx 0.06$, we find evidence of a diagonal superstructure. At $p_{\rm sc1}$, lattice and electron dynamics change discontinuously with the charge and spin properties being renormalized at all energy scales. The results indicate that charge ordering is intimately related to the transition at $p_{\rm sc1}$ and that the maximal transition temperature to superconductivity at optimal doping $T_{c}^{\rm max}$ depends on the type of ordering at $p>p_{\rm sc1}$.Comment: 4 pages, 4 figure

Raman scattering from a superconductivity-induced bound state in MgB2MgB_2

It is shown that the sharp peak in the $E_{2g}$ Raman spectrum of superconducting $MgB_2$ is due to a bound state caused by the electron-phonon coupling. Our theory explains why this peak appears only in the spectra with $E_{2g}$ symmetry and only in the $\sigma$ but not $\pi$ bands. The properties of the bound state and the Raman spectrum are investigated, also in the presence of impurity scattering.Comment: 4 pages, 4 figures, will appear in PR

Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory

We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its non-equilibrium spin dynamics.Comment: Final version as accepted for publication in Phys. Rev. B (4 pages, 3 figures

Statistical Analysis of "Structural Change" - An Annotated Bibliography

Within the framework of the Economic Structural Change Program, a cooperative research activity of IIASA and the University of Bonn, FRG, a project is carried out on "Statistical and Econometric Identification of Structural Change"; the project involves studies on the formal aspects of the analysis of structural changes. On the one hand, they include statistical methods to detect non-constancies, such as stability tests, detection criteria, etc., and on the other hand, methods which are suitable for models which incorporate nonconstancy of the parameters, such as estimation techniques for time-varying parameters, adaptive methods, etc. The present paper provides a documentation of the state of the art in the form of a bibliography

On kk-Gons and kk-Holes in Point Sets

We consider a variation of the classical Erd\H{o}s-Szekeres problems on the existence and number of convex $k$-gons and $k$-holes (empty $k$-gons) in a set of $n$ points in the plane. Allowing the $k$-gons to be non-convex, we show bounds and structural results on maximizing and minimizing their numbers. Most noteworthy, for any $k$ and sufficiently large $n$, we give a quadratic lower bound for the number of $k$-holes, and show that this number is maximized by sets in convex position