Spectrum and diffusion for a class of tight-binding models on hypercubes

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.Comment: 5 pages Late

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

Double butterfly spectrum for two interacting particles in the Harper model

We study the effect of interparticle interaction $U$ on the spectrum of the Harper model and show that it leads to a pure-point component arising from the multifractal spectrum of non interacting problem. Our numerical studies allow to understand the global structure of the spectrum. Analytical approach developed permits to understand the origin of localized states in the limit of strong interaction $U$ and fine spectral structure for small $U$.Comment: revtex, 4 pages, 5 figure

Urticaria and hyposideremia: a case report

The authors report the case of an 86-year-old man with a six-month history of chronic idiopathic urticaria, refractory to standard treatments. The patient did not report concomitant diseases and all clinical tests performed were normal. Laboratory tests showed only mild anemia and low serum iron (31 mcg/dl, normal value 59-158). After oral iron supplementation (105 mg/day of elemental iron, taken as ferrous sulphate) for two months, normal serum iron levels and complete remission of urticaria were observed. No further episodes of urticaria were reported at follow-up visits, six and twelve months later. The possible link between hyposideremia and urticaria is also discussed. In vitro experimental data suggest that transferrin inhibits histamine release from mast cells, and a direct correlation exists between the level of transferrin saturation and the degree of inhibition of histamine release. Reduced transferrin saturation due to hyposideremia could lower the threshold of stimulation required for mast cell degranulation, thus increasing the risk of urticaria in response to endogenous and/or exogenous pathogenic stimuli, even minimal. Further studies are necessary to better understand frequency and pathogenic mechanism(s) of “sideropenic urticaria” (chronic urticaria associated with hyposideremia and favourably responding to iron supplementation). From a clinical point of view, evaluation of serum iron levels in selected patients appears advisable, in the light of the relatively low cost and possible significant benefit

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