What determines the spreading of a wave packet?

The multifractal dimensions D2^mu and D2^psi of the energy spectrum and eigenfunctions, resp., are shown to determine the asymptotic scaling of the width of a spreading wave packet. For systems where the shape of the wave packet is preserved the k-th moment increases as t^(k*beta) with beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound. Furthermore, we show that in d dimensions asymptotically in time the center of any wave packet decreases spatially as a power law with exponent D_2^psi - d and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure

Decay of Quantum Accelerator Modes

Experimentally observable Quantum Accelerator Modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable states, analogous to the Wannier-Stark resonances. Different regimes of tunneling, marked by different quantitative dependence of the lifetimes on 1/hbar, are identified, depending on the resolution of KAM substructures that is achieved on the scale of hbar. The theory of Resonance Assisted Tunneling introduced by Brodier, Schlagheck, and Ullmo [9], is revisited, and found to well describe decay whenever applicable.Comment: 16 pages, 11 encapsulated postscript figures (figures with a better resolution are available upon request to the authors); added reference for section

Arnol'd Tongues and Quantum Accelerator Modes

The stable periodic orbits of an area-preserving map on the 2-torus, which is formally a variant of the Standard Map, have been shown to explain the quantum accelerator modes that were discovered in experiments with laser-cooled atoms. We show that their parametric dependence exhibits Arnol'd-like tongues and perform a perturbative analysis of such structures. We thus explain the arithmetical organisation of the accelerator modes and discuss experimental implications thereof.Comment: 20 pages, 6 encapsulated postscript figure

Dynamics of a quantum particle in low-dimensional disordered systems with extended states

We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some special energies. We provide a consistent picture for two well-known one-dimensional examples: the chain with off-diagonal disorder and the random-dimer model. In both cases the quantum motion exhibits a peculiar kind of anomalous diffusion which can be referred to as bi-fractality. The disorder-averaged density profile of the particle becomes critical in the long-time regime. The $q$-th moment of the position of the particle diverges with time whenever $q$ exceeds some $q_0$. We obtain $q_0=2$ for off-diagonal disorder on the chain (and conjecturally on two-dimensional bipartite lattices as well). For the random-dimer model, our result $q_0=1/2$ corroborates known rigorous results.Comment: 20 pages, 12 figures, 1 table. Note added on the recent work by Lepri et a

Autologous micrografts and methotrexate in plantar erosive lichen planus: healing and pain control. A case report

Erosive lichen planus is an uncommon variant of lichen planus. We report a case of long-standing and refractory plantar ELPs causing disabling and opiate-resistant pain treated with 'classic' meshed skin graft combined with RigeneraVR micrografts. After approximately 9 months follow-up, no clinical recurrence or pain were observed. Erosive lichen planus (ELP) is an uncommon variant of lichen planus, involving oral cavity and genitalia and, less often plantar areas, where it usually presents with chronic erosions of the soles, along with intense, disabling pain and progressive loss of toenails. An abnormal immune cellular response (CD8+ lymphocytes and macrophages) and the consequent altered production of multiple mediators (interleukin-12, interferon-gamma, tumor necrosis factor-alpha, RANTES and MMP-9), seem to play a crucial role in the pathogenesis, although the etiology remains uncertain. From a histological point of view, ELP shows keratinocyte apoptosis, intense inflammatory response and basal epithelial keratinocytes TNF-alpha overexpression. Several therapies have been proposed, with variable and controversial results. While topical corticosteroids and topical calcineurin inhibitors are the treatments of choice for localized forms, short pulses of systemic glucocorticoids, phototherapy, and systemic immunosuppressants are recommended for generalized cases. Surgery has been reported as a possible therapeutic option in refractory and stable cases with localized lesions, either alone or with cyclosporine. Herein, we report a case of longstanding and refractory plantar ELPS causing disabling and opiate-resistant pain treated with 'classic' meshed skin graft combined with RigeneraVR micrografts

Distinct roles for strigolactones in cyst nematode parasitism of Arabidopsis roots

Phytohormones play an essential role in different stages of plant-nematode interactions. Strigolactones (SLs) are a novel class of plant hormones which play an important role in plant development. Furthermore, certain soil-inhabiting organisms exploit this plant molecule as allelochemical. However, whether SLs play a role in plant parasitism by nematodes is as yet unknown. This prompted us to investigate the potential role of SLs in different stages of the nematode life cycle using the beet cyst nematode Heterodera schachtii and Arabidopsis as a model system. We analyzed the effect of SLs on cyst nematode hatching, host attraction and invasion, and the establishment of a feeding relation upon infection of the SL deficient mutant max4-1 and the SL signaling mutant max2-1. In addition, infection assays were performed under phosphate shortage to enhance SL production and in the presence of the synthetic SL analog GR24. From this study, we can conclude that SLs do not contribute to cyst nematode hatching at the levels tested but that they do play a role in host attraction and subsequent invasion in a MAX2 dependent manner. Furthermore, we observed that increased levels of exogenous and endogenous SLs change the root invasion zone. Upon root infection, cyst nematode development was enhanced in both the max2-1 and max4-1 mutants due to the formation of enlarged feeding cells. These data provide evidence for distinct roles of SLs during cyst nematode parasitism of plant roots

On the spacing distribution of the Riemann zeros: corrections to the asymptotic result

It has been conjectured that the statistical properties of zeros of the Riemann zeta function near z = 1/2 + \ui E tend, as $E \to \infty$, to the distribution of eigenvalues of large random matrices from the Unitary Ensemble. At finite $E$ numerical results show that the nearest-neighbour spacing distribution presents deviations with respect to the conjectured asymptotic form. We give here arguments indicating that to leading order these deviations are the same as those of unitary random matrices of finite dimension $N_{\rm eff}=\log(E/2\pi)/\sqrt{12 \Lambda}$, where $\Lambda=1.57314 ...$ is a well defined constant.Comment: 9 pages, 3 figure