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

Surgical treatment of tertiary hyperparathyroidism: does one fit for all?

Background Tertiary hyperparathyroidism (3HPT) is defined as a condition of excessive autonomous excretion of intact parathyroid hormone (iPTH) with persistent hypercalcemia (>10.5 mg/dL) that lasts for more than 12 months after a successful kidney transplantation, in the context of a long course secondary hyperparathyroidism (2HPT). The chronic high levels of iPTH cause a worsening of graft function, accompanied by systemic symptoms of hypercalcemia. The only curative therapy is parathyroidectomy (PTX). It remains unclear whether total parathyroidectomy with autotransplantation (TPTX-AT) or subtotal parathyroidectomy (SPTX) lead to better outcomes.Aims The aim of this retrospective, single-institution cohort study is to evaluate the rate of persistent or recurrent disease and postoperative calcium/iPTH disturbances in patients treated with TPTX-AT or SPTX for 3HPT.Methods A single-center retrospective analysis of 3HPT patients submitted to TPTX-AT or SPTX between 2007-2020 with at least 24 months follow-up was conducted. The outcome parameters included persistence/recurrence of disease, incidence of transitory hypocalcemia, and temporary/permanent hypoparathyroidism.Results A cohort of 52 patients was analyzed and divided in two groups: 38 (73%) were submitted for TPTX-AT, and 14 patients (27%) were submitted for SPTX. The TPTX-AT population showed lower plasmatic calcium concentrations compared with the SPTX group during the entire follow-up period (p<0.001). There were eight cases (21%) of transitory hypocalcemia in the TPTX-AT group and none in the SPTX group, with p=0.065. Two cases (5%) of temporary hypoparathyroidism occurred in the TPTX-AT group and none in the SPTX group, with p= 0.530. There were no cases of permanent hypoparathyroidism and no cases of persistent disease. No statistical difference was assessed for the recurrence of 3HPT between the TPTX-AT group and the SPTX group (N=1, 3% vs N=1, 7%) (p=0.470).Conclusion No significative difference was registered between the TPTX-AT and SPTX groups in terms of persistence/recurrence of disease, incidence of transitory hypocalcemia, and temporary/permanent hypoparathyroidism. Mean calcium levels iPTH values were statistically lower among the TPTX-AT group compared with the SPTX group while remaining always in the range of normality

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