Multifractal wave functions of simple quantum maps

We study numerically multifractal properties of two models of one-dimensional quantum maps, a map with pseudointegrable dynamics and intermediate spectral statistics, and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting method and wavelet method). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects.Comment: 15 pages, 21 figure

A numerical study of interactions and stellar bars

For several decades it has been known that stellar bars in disc galaxies can be triggered by interactions, or by internal processes such as dynamical instabilities. In this work, we explore the differences between these two mechanisms using numerical simulations. We perform two groups of simulations based on isolated galaxies, one group in which a bar develops naturally, and another group in which the bar could not develop in isolation. The rest of the simulations recreate 1:1 coplanar fly-by interactions computed with the impulse approximation. The orbits we use for the interactions represent the fly-bys in groups or clusters of different masses accordingly to the velocity of the encounter. In the analysis we focus on bars' amplitude, size, pattern speed and their rotation parameter, ${\cal R}=R_{CR}/R_{bar}$. The latter is used to define fast (${\cal R}1.4$). Compared with equivalent isolated galaxies we find that bars affected or triggered by interactions: (i) remain in the slow regime for longer; (ii) are more boxy in face-on views; (iii) they host kinematically hotter discs. Within this set of simulations we do not see strong differences between retrograde or prograde fly-bys. We also show that slow interactions can trigger bar formation.Comment: 12 pages, 7 figures. Accepted for publication in MNRA

D=11 Supermembrane wrapped on calibrated submanifolds

We construct the Hamiltonian of the D=11 Supermembrane with topological conditions on configuration space. It may be interpreted as a supermembrane theory where all configurations are wrapped in an irreducible way on a calibrated submanifold of a compact sector of the target space. We prove that the spectrum of its Hamiltonian is discrete with finite multiplicity. The construction is explicitly perfomed for a compact sector of the target space being a $2g$ dimensional flat torus and the base manifold of the Supermembrane a genus $g$ compact Riemann surface. The topological conditions on configuration space work in such a way that the $g=2$ case may be interpreted as the intersection of two D=11 Supermembranes over $g=1$ surfaces, with their corresponding topological conditions. The discreteness of the spectrum is preserved by the intersection procedure. Between the configurations satisfying the topological conditions there are minimal configurations which describe minimal immersions from the base manifold to the compact sector of the target space. They allow to map the D=11 Supermembrane with topological conditions to a symplectic noncommutative Yang-Mills theory. We analyze geometrical properties of these configurations in the context of Supermembranes and D-branes theories. We show that this class of configurations also minimizes the Hamiltonian of D-branes theories.Comment: 24 page

Quantum simulation of Anderson and Kondo lattices with superconducting qubits

We introduce a mapping between a variety of superconducting circuits and a family of Hamiltonians describing localized magnetic impurities interacting with conduction bands. This includes the Anderson model, the single impurity one- and two-channel Kondo problem, as well as the 1D Kondo lattice. We compare the requirements for performing quantum simulations using the proposed circuits to those of universal quantum computation with superconducting qubits, singling out the specific challenges that will have to be addressed.Comment: Longer versio

Anderson localization in a periodic photonic lattice with a disordered boundary

We investigate experimentally the light evolution inside a two-dimensional finite periodic array of weakly- coupled optical waveguides with a disordered boundary. For a completely localized initial condition away from the surface, we find that the disordered boundary induces an asymptotic localization in the bulk, centered around the initial position of the input beam.Comment: 3 pages, 4 figure

Overview of progress in European medium sized tokamaks towards an integrated plasma-edge/wall solution

Integrating the plasma core performance with an edge and scrape-off layer (SOL) that leads to tolerable heat and particle loads on the wall is a major challenge. The new European medium size tokamak task force (EU-MST) coordinates research on ASDEX Upgrade (AUG), MAST and TCV. This multi-machine approach within EU-MST, covering a wide parameter range, is instrumental to progress in the field, as ITER and DEMO core/pedestal and SOL parameters are not achievable simultaneously in present day devices. A two prong approach is adopted. On the one hand, scenarios with tolerable transient heat and particle loads, including active edge localised mode (ELM) control are developed. On the other hand, divertor solutions including advanced magnetic configurations are studied. Considerable progress has been made on both approaches, in particular in the fields of: ELM control with resonant magnetic perturbations (RMP), small ELM regimes, detachment onset and control, as well as filamentary scrape-off-layer transport. For example full ELM suppression has now been achieved on AUG at low collisionality with n = 2 RMP maintaining good confinement HH(98,y2) 0.95. Advances have been made with respect to detachment onset and control. Studies in advanced divertor configurations (Snowflake, Super-X and X-point target divertor) shed new light on SOL physics. Cross field filamentary transport has been characterised in a wide parameter regime on AUG, MAST and TCV progressing the theoretical and experimental understanding crucial for predicting first wall loads in ITER and DEMO. Conditions in the SOL also play a crucial role for ELM stability and access to small ELM regimes.European Commission (EUROfusion 633053

Stereoisomeric semiconducting radical cation salts of chiral bis(2-hydroxypropylthio)ethylenedithioTTF with tetrafluoroborate anions

The new chiral TTF-based donor molecule bis(2-hydroxypropylthio)ethylenedithiotetrathiafulvalene has produced enantiopure R,R and S,S radical cation salts with the tetrafluoroborate anion as well as the nearly isostructural meso/racemate mixture. The enantiopure R,R or S,S salts are both 1:1 semiconducting salts with activation energies of 0.19–0.24 eV, both crystallising in the orthorhombic space group C2221. The semiconducting salt containing both meso and racemic donor cations has a very similar crystal structure but crystallising in the monoclinic space group C2/c (β = 91.39°) with similar S⋯S interactions but a smaller activation energy of 0.15–0.17 eV. This is in contrast to previous families of this type where the disordered racemate has a larger activation energy than its enantiopure salts

Implementation of Spin Hamiltonians in Optical Lattices

We propose an optical lattice setup to investigate spin chains and ladders. Electric and magnetic fields allow us to vary at will the coupling constants, producing a variety of quantum phases including the Haldane phase, critical phases, quantum dimers etc. Numerical simulations are presented showing how ground states can be prepared adiabatically. We also propose ways to measure a number of observables, like energy gap, staggered magnetization, end-chain spins effects, spin correlations and the string order parameter