Level attraction in a microwave optomechanical circuit

Level repulsion - the opening of a gap between two degenerate modes due to coupling - is ubiquitous anywhere from solid state theory to quantum chemistry. In contrast, if one mode has negative energy, the mode frequencies attract instead. They converge and develop imaginary components, leading to an instability; an exceptional point marks the transition. This, however, only occurs if the dissipation rates of the two modes are comparable. Here we expose a theoretical framework for the general phenomenon and realize it experimentally through engineered dissipation in a multimode superconducting microwave optomechanical circuit. Level attraction is observed for a mechanical oscillator and a superconducting microwave cavity, while an auxiliary cavity is used for sideband cooling. Two exceptional points are demonstrated that could be exploited for their topological properties.Comment: 5 pages, 4 figures; includes Supplementary informatio

Searching for electromagnetic counterpart of LIGO gravitational waves in the Fermi GBM data with ADWO

The Fermi collaboration identified a possible electromagnetic counterpart of the gravitational wave event of September 14, 2015. Our goal is to provide an unsupervised data analysis algorithm to identify similar events in Fermi's Gamma-ray Burst Monitor CTTE data stream. We are looking for signals that are typically weak. Therefore, they can only be found by a careful analysis of count rates of all detectors and energy channels simultaneously. Our Automatized Detector Weight Optimization (ADWO) method consists of a search for the signal, and a test of its significance. We developed ADWO, a virtual detector analysis tool for multi-channel multi-detector signals, and performed successful searches for short transients in the data-streams. We have identified GRB150522B, as well as possible electromagnetic candidates of the transients GW150914 and LVT151012. ADWO is an independently developed, unsupervised data analysis tool that only relies on the raw data of the Fermi satellite. It can therefore provide a strong, independent test to any electromagnetic signal accompanying future gravitational wave observations.Comment: 4 pages and 4 figures, A&A Letters accepte

The Flip Diameter of Rectangulations and Convex Subdivisions

We study the configuration space of rectangulations and convex subdivisions of $n$ points in the plane. It is shown that a sequence of $O(n\log n)$ elementary flip and rotate operations can transform any rectangulation to any other rectangulation on the same set of $n$ points. This bound is the best possible for some point sets, while $\Theta(n)$ operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of $n$ points in the plane.Comment: 17 pages, 12 figures, an extended abstract has been presented at LATIN 201

On the asymmetry of the forward and reverse martensitic transformations in shape memory alloys

Differential Scanning Calorimetric, DSC, runs taken during martensitic phase transformations in shape memory alloys, often look differently during cooling and heating. Similar asymmetry is observed e.g. for the numbers of hits or the critical exponents of energy and amplitude distributions (\epsilon and \alpha, respectively) in acoustic emission measurements. It is illustrated that, in accordance with empirical correlations, the above asymmetry of acoustic noises can be classified into two groups: the relative changes of the exponents during cooling and heating (\gamma \epsilon=(\epsilon h-\epsilon c)/\epsilon c as well as \gamma \alpha=(\alpha h-\alpha c)/\alpha c)) are either positive or negative. For positive \gamma values the number of hits and the total energy of acoustic emission are larger for cooling, and the situation is just the reverse for negative asymmetry. Our interpretation is based on the different ways of relaxation of the elastic strain energy during cooling as well as heating. It is illustrated that if the relaxed fraction of the total elastic strain energy (which would be stored without relaxations) during cooling is larger than the corresponding relaxed fraction during heating, then the asymmetry is positive. Magnetic emission noises, accompanied with martensitic phase transformations in ferromagnetic alloys, show similar asymmetry than those observed for thermal (DSC) and acoustic noises and depends on the constant external magnetic field too