Magnetic field dependence of the energy of negatively charged excitons in semiconductor quantum wells

A variational calculation of the spin-singlet and spin-triplet state of a negatively charged exciton (trion) confined to a single quantum well and in the presence of a perpendicular magnetic field is presented. We calculated the probability density and the pair correlation function of the singlet and triplet trion states. The dependence of the energy levels and of the binding energy on the well width and on the magnetic field strength was investigated. We compared our results with the available experimental data on GaAs/AlGaAs quantum wells and find that in the low magnetic field region (B<18 T) the observed transition are those of the singlet and the dark triplet trion (with angular momentum $L_z=-1$), while for high magnetic fields (B>25 T) the dark trion becomes optically inactive and possibly a transition to a bright triplet trion (angular momentum $L_z=0$) state is observed.Comment: 9 pages, 10 figures submitted to Phys. Rev.

Signals of Inflation in a Friendly String Landscape

Following Freivogel {\it et al} we consider inflation in a predictive (or `friendly') region of the landscape of string vacua, as modeled by Arkani-Hamed, Dimopoulos and Kachru. In such a region the dimensionful coefficients of super-renormalizable operators unprotected by symmetries, such as the vacuum energy and scalar mass-squareds are freely scanned over, and the objects of study are anthropically or `environmentally' conditioned probability distributions for observables. In this context we study the statistical predictions of (inverted) hybrid inflation models, where the properties of the inflaton are probabilistically distributed. We derive the resulting distributions of observables, including the deviation from flatness $|1-\Omega|$, the spectral index of scalar cosmological perturbations $n_s$ (and its scale dependence $dn_s/d\log k$), and the ratio of tensor to scalar perturbations $r$. The environmental bound on the curvature implies a solution to the $\eta$-problem of inflation with the predicted distribution of $(1-n_s)$ indicating values close to current observations. We find a relatively low probability ($<3$) of `just-so' inflation with measurable deviations from flatness. Intermediate scales of inflation are preferred in these models.Comment: 20 pages, 11 figure

Excitons and charged excitons in semiconductor quantum wells

A variational calculation of the ground-state energy of neutral excitons and of positively and negatively charged excitons (trions) confined in a single-quantum well is presented. We study the dependence of the correlation energy and of the binding energy on the well width and on the hole mass. The conditional probability distribution for positively and negatively charged excitons is obtained, providing information on the correlation and the charge distribution in the system. A comparison is made with available experimental data on trion binding energies in GaAs-, ZnSe-, and CdTe-based quantum well structures, which indicates that trions become localized with decreasing quantum well width.Comment: 9 pages, 11 figure

Active shape correction of a thin glass/plastic X-ray mirror

Optics for future X-ray telescopes will be characterized by very large aperture and focal length, and will be made of lightweight materials like glass or plastic in order to keep the total mass within acceptable limits. Optics based on thin slumped glass foils are currently in use in the NuSTAR telescope and are being developed at various institutes like INAF/OAB, aiming at improving the angular resolution to a few arcsec HEW. Another possibility would be the use of thin plastic foils, being developed at SAO and the Palermo University. Even if relevant progresses in the achieved angular resolution were recently made, a viable possibility to further improve the mirror figure would be the application of piezoelectric actuators onto the non-optical side of the mirrors. In fact, thin mirrors are prone to deform, so they require a careful integration to avoid deformations and even correct forming errors. This however offers the possibility to actively correct the residual deformation. Even if other groups are already at work on this idea, we are pursuing the concept of active integration of thin glass or plastic foils with piezoelectric patches, fed by voltages driven by the feedback provided by X-rays, in intra-focal setup at the XACT facility at INAF/OAPA. In this work, we show the preliminary simulations and the first steps taken in this project

Mind the Gap: Essentially Optimal Algorithms for Online Dictionary Matching with One Gap

We examine the complexity of the online Dictionary Matching with One Gap Problem (DMOG) which is the following. Preprocess a dictionary D of d patterns, where each pattern contains a special gap symbol that can match any string, so that given a text that arrives online, a character at a time, we can report all of the patterns from D that are suffixes of the text that has arrived so far, before the next character arrives. In more general versions the gap symbols are associated with bounds determining the possible lengths of matching strings. Online DMOG captures the difficulty in a bottleneck procedure for cyber-security, as many digital signatures of viruses manifest themselves as patterns with a single gap. In this paper, we demonstrate that the difficulty in obtaining efficient solutions for the DMOG problem, even in the offline setting, can be traced back to the infamous 3SUM conjecture. We show a conditional lower bound of Omega(delta(G_D)+op) time per text character, where G_D is a bipartite graph that captures the structure of D, delta(G_D) is the degeneracy of this graph, and op is the output size. Moreover, we show a conditional lower bound in terms of the magnitude of gaps for the bounded case, thereby showing that some known offline upper bounds are essentially optimal. We also provide matching upper-bounds (up to sub-polynomial factors), in terms of the degeneracy, for the online DMOG problem. In particular, we introduce algorithms whose time cost depends linearly on delta(G_D). Our algorithms make use of graph orientations, together with some additional techniques. These algorithms are of practical interest since although delta(G_D) can be as large as sqrt(d), and even larger if G_D is a multi-graph, it is typically a very small constant in practice. Finally, when delta(G_D) is large we are able to obtain even more efficient solutions