Mixed symmetry localized modes and breathers in binary mixtures of Bose-Einstein condensates in optical lattices

We study localized modes in binary mixtures of Bose-Einstein condensates embedded in one-dimensional optical lattices. We report a diversity of asymmetric modes and investigate their dynamics. We concentrate on the cases where one of the components is dominant, i.e. has much larger number of atoms than the other one, and where both components have the numbers of atoms of the same order but different symmetries. In the first case we propose a method of systematic obtaining the modes, considering the "small" component as bifurcating from the continuum spectrum. A generalization of this approach combined with the use of the symmetry of the coupled Gross-Pitaevskii equations allows obtaining breather modes, which are also presented.Comment: 11 pages, 16 figure

Correlated Component Analysis for diffuse component separation with error estimation on simulated Planck polarization data

We present a data analysis pipeline for CMB polarization experiments, running from multi-frequency maps to the power spectra. We focus mainly on component separation and, for the first time, we work out the covariance matrix accounting for errors associated to the separation itself. This allows us to propagate such errors and evaluate their contributions to the uncertainties on the final products.The pipeline is optimized for intermediate and small scales, but could be easily extended to lower multipoles. We exploit realistic simulations of the sky, tailored for the Planck mission. The component separation is achieved by exploiting the Correlated Component Analysis in the harmonic domain, that we demonstrate to be superior to the real-space application (Bonaldi et al. 2006). We present two techniques to estimate the uncertainties on the spectral parameters of the separated components. The component separation errors are then propagated by means of Monte Carlo simulations to obtain the corresponding contributions to uncertainties on the component maps and on the CMB power spectra. For the Planck polarization case they are found to be subdominant compared to noise.Comment: 17 pages, accepted in MNRA

Base sequence dependent sliding of proteins on DNA

The possibility that the sliding motion of proteins on DNA is influenced by the base sequence through a base pair reading interaction, is considered. Referring to the case of the T7 RNA-polymerase, we show that the protein should follow a noise-influenced sequence-dependent motion which deviate from the standard random walk usually assumed. The general validity and the implications of the results are discussed.Comment: 12 pages, 3 figure

Quantum signatures of breather-breather interactions

The spectrum of the Quantum Discrete Nonlinear Schr\"odinger equation on a periodic 1D lattice shows some interesting detailed band structure which may be interpreted as the quantum signature of a two-breather interaction in the classical case. We show that this fine structure can be interpreted using degenerate perturbation theory.Comment: 4 pages, 4 fig

Hereditary neuropathy with liability to pressure palsy (HNPP): Report of a family with a new point mutation in PMP22 gene

Background: Hereditary neuropathy with liability to pressure palsy (HNPP) is an autosomal dominant disorder most commonly presenting with acute-onset, non-painful focal sensory and motor mononeuropathy. Approximately 80% of patients carry a 1.5 Mb deletion of chromosome 17p11.2 involving the peripheral myelin protein 22 gene (PMP22), the same duplicated in Charcot-Marie-Tooth 1A patients. In a small proportion of patients the disease is caused by PMP22 point mutations. Case presentation: We report on a familial case harbouring a new point mutation in the PMP22 gene. The proband is a 4-years-old girl with acute onset of focal numbness and weakness in her right hand. Electroneurography demonstrated transient sensory and motor radial nerves involvement. In her father, reporting chronic symptoms (cramps and exercise-induced myalgia), we uncovered mild atrophy and areflexia on clinical examination and a mixed (predominantly demyelinating) polyneuropathy with sensory-motor involvement on electrophysiological study. Both carried a nucleotidic substitution c.178 + 2 T > C on intron 3 of the PMP22 gene, involving the splicing donor site, not reported on databases but predicted to be likely pathogenic. Conclusions: We described a previously unreported point mutation in PMP22 gene, which led to the development of a HNPP phenotype in a child and her father. In children evaluated for a sensory and motor transient episode, HNPP disorder due to PMP22 mutations should be suspected. Clinical and electrophysiological studies should be extended to all family members even in the absence of previous episodes suggestive for HNPP

Three dimensional imaging of short pulses

We exploit a slightly noncollinear second-harmonic cross-correlation scheme to map the 3D space-time intensity distribution of an unknown complex-shaped ultrashort optical pulse. We show the capability of the technique to reconstruct both the amplitude and the phase of the field through the coherence of the nonlinear interaction down to a resolution of 10 $\mu$m in space and 200 fs in time. This implies that the concept of second-harmonic holography can be employed down to the sub-ps time scale, and used to discuss the features of the technique in terms of the reconstructed fields.Comment: 16 pages, 6 figure

Multi-component gap solitons in spinor Bose-Einstein condensates

We model the nonlinear behaviour of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or anti-ferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional optical lattice potential. We show that both types of BECs exhibit dynamical instabilities and may form spatially localized multi-component structures. The localized states of the spinor matter waves take the form of vector gap solitons and self-trapped waves that exist only within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are the nonlinear localized states that do not exhibit a common spatial density profile shared by all condensate components, and consequently cannot be described by the single mode approximation (SMA), frequently employed within the framework of the mean-field treatment. We show that the non-SMA states can exhibits Josephson-like internal oscillations and self-magnetisation, i.e. intrinsic precession of the local spin. Finally, we demonstrate that non-stationary states of a spinor BEC in a lattice exhibit coherent undamped spin-mixing dynamics, and that their controlled conversion into a stationary state can be achieved by the application of an external magnetic field.Comment: 12 pages, 13 figure