Crossover trimers connecting continuous and discrete scaling regimes

For a system of two identical fermions and one distinguishable particle interacting via a short-range potential with a large s-wave scattering length, the Efimov trimers and Kartavtsev-Malykh trimers exist in different regimes of the mass ratio. The Efimov trimers are known to exhibit a discrete scaling invariance, while the Kartavtsev-Malykh trimers feature a continuous scaling invariance. We point out that a third type of trimers, "crossover trimers", exist universally regardless of short-range details of the potential. These crossover trimers have neither the discrete nor continuous scaling invariance. We show that the crossover trimers continuously connect the discrete and continuous scaling regimes as the mass ratio and the scattering length are varied. We identify the regions for the Kartavtsev-Malykh trimers, Efimov trimers, crossover trimers, and non-universal trimers as a function of the mass ratio and the s-wave scattering length by investigating the scaling property and model-independence of the trimers.Comment: 14 pages, 9 figure

Binary Patterns in Binary Cube-Free Words: Avoidability and Growth

The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper bounds. Finally, a new example of a pattern-avoiding language of polynomial growth is given.Comment: 18 pages, 2 tables; submitted to RAIRO TIA (Special issue of Mons Days 2012

Nurturing the young shoots of talent: Using action research for exploration and theory building

This is an Author's Accepted Manuscript of an article published in European Early Childhood Education Research Journal, 19(4), 433-450, 2011, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/1350293X.2011.623515.This paper reports the outcomes of a set of action research projects carried out by teacher researchers in 14 local education authorities in England, working collaboratively with university tutors, over a period of three years. The common aim of all the projects was to explore practical ways of nurturing the gifts and talents of children aged four–seven years. The project was funded by the Department of Education and Skills in England as part of the government's gifted and talented programme. The project teachers felt that their understanding of issues relating to nurturing the gifts and talents of younger children was enhanced through their engagement in the project. It was possible to map the findings of the projects to the English government's National Quality Standards for gifted and talented education which include: (1) identification; (2) effective provision in the classroom; (3) enabling curriculum entitlement and choice; (4) assessment for learning; (5) engaging with community, families and beyond. The findings are also analysed within the framework of good practice in educating children in the first years of schooling. Participating practitioners felt that action research offered them a suitable methodology to explore the complexity of the topic of giftedness through cycles of planning, action and reflection and personal theory building

Dispersive Response of a Disordered Superconducting Quantum Metamaterial

We consider a disordered quantum metamaterial formed by an array of superconducting flux qubits coupled to microwave photons in a cavity. We map the system on the Tavis-Cummings model accounting for the disorder in frequencies of the qubits. The complex transmittance is calculated with the parameters taken from state-of-the-art experiments. We demonstrate that photon phase shift measurements allow to distinguish individual resonances in the metamaterial with up to 100 qubits, in spite of the decoherence spectral width being remarkably larger than the effective coupling constant. Our simulations are in agreement with the results of the recently reported experiment.Comment: 10 pages, 4 figure

Non-universal Efimov Atom-Dimer Resonances in a Three-Component Mixture of 6Li

We observed an enhanced atom-dimer relaxation due to the existence of Efimov states in a three-component mixture of 6Li atoms. We measured the magnetic-field dependence of the atom-dimer loss coefficient in the mixture of atoms in state |1> and dimers formed in states |2> and |3>, and found two peaks corresponding to the degeneracy points of the |23> dimer energy level and energy levels of Efimov trimers. We found that the locations of these peaks disagree with universal theory predictions, in a way that cannot be explained by non-universal two-body properties. We constructed theoretical models that characterize the non-universal three-body physics of three-component 6Li atoms in the low energy domain.Comment: 5 pages, 3 figure

Control of Andreev bound state population and related charge-imbalance effect

Motivated by recent experimental research, we study the processes in an ac driven superconducting constriction whereby one quasiparticle is promoted to the delocalized states outside the superconducting gap. We demonstrate that with these processes one can control the population of the Andreev bound states in the constriction. We stress an interesting charge asymmetry of these processes that may produce a charge imbalance of accumulated quasiparticles, which depends on the phase

A possible Efimov trimer state in a 3-component lithium-6 mixture

We consider the Efimov trimer theory as a possible framework to explain recently observed losses by inelastic three-body collisions in a three-hyperfine-component ultracold mixture of lithium 6. Within this framework, these losses would arise chiefly from the existence of an Efimov trimer bound state below the continuum of free triplets of atoms, and the loss maxima (at certain values of an applied magnetic field) would correspond to zero-energy resonances where the trimer dissociates into three free atoms. Our results show that such a trimer state is indeed possible given the two-body scattering lengths in the three-component lithium mixture, and gives rise to two zero-energy resonances. The locations of these resonances appear to be consistent with observed losses.Comment: 4 pages, 2 figures. Updated figures, equations and references as in the published version. Note that there is a 1/2 factor missing in Eq. (6) of the published versio

Frequency Division Multiplexing Readout and Simultaneous Manipulation of an Array of Flux Qubits

An important desired ingredient of superconducting quantum circuits is a readout scheme whose complexity does not increase with the number of qubits involved in the measurement. Here, we present a readout scheme employing a single microwave line, which enables simultaneous readout of multiple qubits. Consequently, scaling up superconducting qubit circuits is no longer limited by the readout apparatus. Parallel readout of 6 flux qubits using a frequency division multiplexing technique is demonstrated, as well as simultaneous manipulation and time resolved measurement of 3 qubits. We discuss how this technique can be scaled up to read out hundreds of qubits on a chip.Comment: 4 pages, 4 figure

Cross-correlations of coherent multiple Andreev reflections

We use the Landauer-B\"uttiker scattering theory for electronic transport to calculate the current cross-correlations in a voltage-biased three-terminal junction with all superconducting leads. At low bias voltage, when charge transport is due to coherent multiple Andreev reflections, we find large cross-correlations compared with their normal-state value. Furthermore, depending on the parameters that characterize the properties of the scattering region between the leads, the cross-correlations can reverse their sign with respect to the case of non-interacting fermionic systems.Comment: 10 pages, 5 figures, Contribution for the special issue of Physica E in memory of Markus B\"uttike