Quantum Return Probability for Substitution Potentials

We propose an effective exponent ruling the algebraic decay of the average quantum return probability for discrete Schrodinger operators. We compute it for some non-periodic substitution potentials with different degrees of randomness, and do not find a complete qualitative agreement with the spectral type of the substitution sequences themselves, i.e., more random the sequence smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics

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

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

Upper bounds on wavepacket spreading for random Jacobi matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.Comment: final version, to appear in CM

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

The presence of dominant follicles and corpora lutea does not perturb response to controlled ovarian stimulation in random start protocols

The advent of random start protocols to shorten the time needed to store oocytes in women with malignancies has represented an important improvement in the field of fertility preservation. However, Randomized Controlled Trials are difficult to implement in this area and available evidence that supports this approach remains modest. To shed more light on this issue, we compared the follicular development between the ovary carrying the dominant follicle or the corpus luteum and the contralateral resting ovary in 90 women who underwent random start controlled ovarian stimulation (COS). In fact, ovarian response did not differ between the two ovaries. Subgroup analyses according to the phase of the cycle at the initiation of COS, the type of malignancy, the use of letrozole and the magnitude of the ovarian response did not allow to identify any condition showing a difference in the follicular response between the active and the resting ovaries. In conclusion, follicular growth does not seem to be perturbed by the presence of a dominant follicle or a corpus luteum

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