Analytic quasi-perodic cocycles with singularities and the Lyapunov Exponent of Extended Harper's Model

We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic $M_2(\mathbb{C})$-cocycles. This includes rational approximation of the frequency, which so far has not been available

Trends and Cycles : an Historical Review of the Euro Area.

We analyze the euro area business cycle in a medium scale DSGE model where we assume two stochastic trends: one on total factor productivity and one on the inflation target of the central bank. To justify our choice of integrated trends, we test alternative specifications for both of them. We do so, estimating trends together with the model's structural parameters, to prevent estimation biases. In our estimates, business cycle fluctuations are dominated by investment specific shocks and preference shocks of households. Our results cast doubts on the view that cost push shocks dominate economic fluctuations in DSGE models and show that productivity shocks drive fluctuations on a longer term. As a conclusion, we present our estimation's historical reading of the business cycle in the euro area. This estimation gives credible explanations of major economic events since 1985.New Keynesian model, Business Cycle, Bayesian estimation.

Transport and Noise Characteristics of Submicron High-Temperature Superconductor Grain-Boundary Junctions

We have investigated the transport and noise properties of submicron YBCO bicrystal grain-boundary junctions prepared using electron beam lithography. The junctions show an increased conductance for low voltages reminiscent of Josephson junctions having a barrier with high transmissivity. The voltage noise spectra are dominated by a few Lorentzian components. At low temperatures clear two-level random telegraph switching (RTS) signals are observable in the voltage vs time traces. We have investigated the temperature and voltage dependence of individual fluctuators both from statistical analysis of voltage vs time traces and from fits to noise spectra. A transition from tunneling to thermally activated behavior of individual fluctuators was clearly observed. The experimental results support the model of charge carrier traps in the barrier region.Comment: 4 pages, 4 figures, to be published in Appl. Phys. Let

Singular components of spectral measures for ergodic Jacobi matrices

For ergodic 1d Jacobi operators we prove that the random singular components of any spectral measure are almost surely mutually disjoint as long as one restricts to the set of positive Lyapunov exponent. In the context of extended Harper's equation this yields the first rigorous proof of the Thouless' formula for the Lyapunov exponent in the dual regions.Comment: to appear in the Journal of Mathematical Physics, vol 52 (2011