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

Parameterized Inapproximability of Target Set Selection and Generalizations

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex $v$ is activated during the propagation process if at least $thr(v)$ of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions $f$ and $\rho$ this problem cannot be approximated within a factor of $\rho(k)$ in $f(k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results

The Extraordinary Infrared Spectrum of NGC 1222 (Mkn 603)

The infrared spectra of starburst galaxies are dominated by the low-excitation lines of [NeII] and [SIII], and the stellar populations deduced from these spectra appear to lack stars larger than about 35 Msun. The only exceptions to this result until now were low metallicity dwarf galaxies. We report our analysis of the mid-infrared spectra obtained with IRS on Spitzer of the starburst galaxy NGC 1222 (Mkn 603). NGC 1222 is a large spheroidal galaxy with a starburst nucleus that is a compact radio and infrared source, and its infrared emission is dominated by the [NeIII] line. This is the first starburst of solar or near-solar metallicity, known to us, which is dominated by the high-excitation lines and which is a likely host of high mass stars. We model the emission with several different assumptions as to the spatial distibution of the high- and low-excitation lines and find that the upper mass cutoff in this galaxy is 40-100 Msun.Comment: accepted, Astronomical Journal. 29 pp, 4 figures. In replacement version an acknowledgment to NRAO is adde

Addressing student models of energy loss in quantum tunnelling

We report on a multi-year, multi-institution study to investigate student reasoning about energy in the context of quantum tunnelling. We use ungraded surveys, graded examination questions, individual clinical interviews, and multiple-choice exams to build a picture of the types of responses that students typically give. We find that two descriptions of tunnelling through a square barrier are particularly common. Students often state that tunnelling particles lose energy while tunnelling. When sketching wave functions, students also show a shift in the axis of oscillation, as if the height of the axis of oscillation indicated the energy of the particle. We find inconsistencies between students' conceptual, mathematical, and graphical models of quantum tunnelling. As part of a curriculum in quantum physics, we have developed instructional materials to help students develop a more robust and less inconsistent picture of tunnelling, and present data suggesting that we have succeeded in doing so.Comment: Originally submitted to the European Journal of Physics on 2005 Feb 10. Pages: 14. References: 11. Figures: 9. Tables: 1. Resubmitted May 18 with revisions that include an appendix with the curriculum materials discussed in the paper (4 page small group UW-style tutorial

Melting of Colloidal Molecular Crystals on Triangular Lattices

The phase behavior of a two-dimensional colloidal system subject to a commensurate triangular potential is investigated. We consider the integer number of colloids in each potential minimum as rigid composite objects with effective discrete degrees of freedom. It is shown that there is a rich variety of phases including ``herring bone'' and ``Japanese 6 in 1'' phases. The ensuing phase diagram and phase transitions are analyzed analytically within variational mean-field theory and supplemented by Monte Carlo simulations. Consequences for experiments are discussed.Comment: 10 pages, 4 figure

The time of the Roma in times of crisis: Where has European neoliberal capitalism failed?

This paper argues that the economic and financial crisis that has ensnared Europe from the late 2000s has been instrumental in reshaping employment and social relations in a detrimental way for the majority of the European people. It argues that the crisis has exacerbated the socio-economic position of most Roma people, immigrants as well as of other vulnerable groups. This development is approached here as an outcome of the widening structural inequalities that underpin the crisis within an increasingly neoliberalised Europe. Through recent policy developments and public discourses from a number of European countries I show how rising inequalities nurture racialised social tensions. My account draws on classic and contemporary theoretical propositions that have been propounded about the nature of capitalism, its contemporary re-articulation as well as its ramification for the future of Europe

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.Comment: Revtex 4-1, 14 pages, 2 figures. Final published versio

Voltage and temperature dependence of the grain boundary tunneling magnetoresistance in manganites

We have performed a systematic analysis of the voltage and temperature dependence of the tunneling magnetoresistance (TMR) of grain boundaries (GB) in the manganites. We find a strong decrease of the TMR with increasing voltage and temperature. The decrease of the TMR with increasing voltage scales with an increase of the inelastic tunneling current due to multi-step inelastic tunneling via localized defect states in the tunneling barrier. This behavior can be described within a three-current model for magnetic tunnel junctions that extends the two-current Julliere model by adding an inelastic, spin-independent tunneling contribution. Our analysis gives strong evidence that the observed drastic decrease of the GB-TMR in manganites is caused by an imperfect tunneling barrier.Comment: to be published in Europhys. Lett., 8 pages, 4 figures (included