Surprises in the suddenly-expanded infinite well

I study the time-evolution of a particle prepared in the ground state of an infinite well after the latter is suddenly expanded. It turns out that the probability density $|\Psi(x, t)|^{2}$ shows up quite a surprising behaviour: for definite times, {\it plateaux} appear for which $|\Psi(x, t)|^{2}$ is constant on finite intervals for $x$. Elements of theoretical explanation are given by analyzing the singular component of the second derivative $\partial_{xx}\Psi(x, t)$. Analytical closed expressions are obtained for some specific times, which easily allow to show that, at these times, the density organizes itself into regular patterns provided the size of the box in large enough; more, above some critical time-dependent size, the density patterns are independent of the expansion parameter. It is seen how the density at these times simply results from a construction game with definite rules acting on the pieces of the initial density.Comment: 24 pages, 14 figure

Hyperfine interaction and electronic spin fluctuation study on Sr2−x_{2-x}Lax_xFeCoO6_6 (x = 0, 1, 2) by high-resolution back-scattering neutron spectroscopy

The study of hyperfine interaction by high-resolution inelastic neutron scattering is not very well known compared to the other competing techniques viz. NMR, M\"ossbauer, PACS etc. Also the study is limited mostly to magnetically ordered systems. Here we report such study on Sr$_{2-x}$La$_x$FeCoO$_6$ (x = 0, 1, 2) of which first (Sr$_2$FeCoO$_6$ with x = 0) has a canonical spin spin glass, the second (SrLaFeCoO$_6$ with x = 1) has a so-called magnetic glass and the third (La$_2$FeCoO$_6$ with x = 2) has a magnetically ordered ground state. Our present study revealed clear inelastic signal for SrLaFeCoO$_6$, possibly also inelastic signal for Sr$_2$FeCoO$_6$ below the spin freezing temperatures $T_{sf}$ but no inelastic signal at all for for the magnetically ordered La$_2$FeCoO$_6$ in the neutron scattering spectra. The broadened inelastic signals observed suggest hyperfine field distribution in the two disordered magnetic glassy systems and no signal for the third compound suggests no or very small hyperfine field at the Co nucleus due to Co electronic moment. For the two magnetic glassy system apart from the hyperfine signal due only to Co, we also observed electronic spin fluctuations probably from both Fe and Co electronic moments. \end{abstract

Quantum coherence and carriers mobility in organic semiconductors

We present a model of charge transport in organic molecular semiconductors based on the effects of lattice fluctuations on the quantum coherence of the electronic state of the charge carrier. Thermal intermolecular phonons and librations tend to localize pure coherent states and to assist the motion of less coherent ones. Decoherence is thus the primary mechanism by which conduction occurs. It is driven by the coupling of the carrier to the molecular lattice through polarization and transfer integral fluctuations as described by the hamiltonian of Gosar and Choi. Localization effects in the quantum coherent regime are modeled via the Anderson hamiltonian with correlated diagonal and non-diagonal disorder leading to the determination of the carrier localization length. This length defines the coherent extension of the ground state and determines, in turn, the diffusion range in the incoherent regime and thus the mobility. The transfer integral disorder of Troisi and Orlandi can also be incorporated. This model, based on the idea of decoherence, allowed us to predict the value and temperature dependence of the carrier mobility in prototypical organic semiconductors that are in qualitative accord with experiments

A modified parallel tree code for N-body simulation of the Large Scale Structure of the Universe

N-body codes to perform simulations of the origin and evolution of the Large Scale Structure of the Universe have improved significantly over the past decade both in terms of the resolution achieved and of reduction of the CPU time. However, state-of-the-art N-body codes hardly allow one to deal with particle numbers larger than a few 10^7, even on the largest parallel systems. In order to allow simulations with larger resolution, we have first re-considered the grouping strategy as described in Barnes (1990) (hereafter B90) and applied it with some modifications to our WDSH-PT (Work and Data SHaring - Parallel Tree) code. In the first part of this paper we will give a short description of the code adopting the Barnes and Hut algorithm \cite{barh86} (hereafter BH), and in particular of the memory and work distribution strategy applied to describe the {\it data distribution} on a CC-NUMA machine like the CRAY-T3E system. In the second part of the paper we describe the modification to the Barnes grouping strategy we have devised to improve the performance of the WDSH-PT code. We will use the property that nearby particles have similar interaction list. This idea has been checked in B90, where an interaction list is builded which applies everywhere within a cell C_{group} containing a little number of particles N_{crit}. B90 reuses this interaction list for each particle $p \in C_{group}$ in the cell in turn. We will assume each particle p to have the same interaction list. Thus it has been possible to reduce the CPU time increasing the performances. This leads us to run simulations with a large number of particles (N ~ 10^7/10^9) in non-prohibitive times.Comment: 13 pages and 7 Figure

Equations over free inverse monoids with idempotent variables

We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEXPTIME) whether a system of equations in idempotent variables over a free inverse monoid has a solution. The result is proved by a direct reduction to solve language equations with one-sided concatenation and a known complexity result by Baader and Narendran: Unification of concept terms in description logics, 2001. We also show that the problem becomes DEXPTIME hard , as soon as the quotient group of the free inverse monoid has rank at least two. Decidability for systems of typed equations over a free inverse monoid with one irreducible variable and at least one unbalanced equation is proved with the same complexity for the upper bound. Our results improve known complexity bounds by Deis, Meakin, and Senizergues: Equations in free inverse monoids, 2007. Our results also apply to larger families of equations where no decidability has been previously known.Comment: 28 pages. The conference version of this paper appeared in the proceedings of 10th International Computer Science Symposium in Russia, CSR 2015, Listvyanka, Russia, July 13-17, 2015. Springer LNCS 9139, pp. 173-188 (2015

Effects of disorder on two coupled Hubbard chains at half-filling

We investigate the effects of quenched disorder on two chain Hubbard models at half-filling by using bosonization and renormalization group methods. It is found that the sufficiently strong forward scattering due to impurities and the random gauge field, which is generated by impurity backward scattering, destroy the charge gaps as well as the spin gaps. Random backward scattering due to impurities then drives the resulting massless phase to the Anderson localization phase. For intermediate strength of random forward scattering, however, the spin gaps still survive, and only one of the charge gaps is collapsed. In this parameter region, one of the charge degrees of freedom is in the Anderson localized state, while the other one is still in the massive state.Comment: 10 pages, RevTex, 3 eps figure

Charge transfer and coherence dynamics of tunnelling system coupled to a harmonic oscillator

We study the transition probability and coherence of a two-site system, interacting with an oscillator. Both properties depend on the initial preparation. The oscillator is prepared in a thermal state and, even though it cannot be considered as an extended bath, it produces decoherence because of the large number of states involved in the dynamics. In the case in which the oscillator is intially displaced a coherent dynamics of change entangled with oscillator modes takes place. Coherency is however degraded as far as the oscillator mass increases producing a increasingly large recoherence time. Calculations are carried on by exact diagonalization and compared with two semiclassical approximations. The role of the quantum effects are highlighted in the long-time dynamics, where semiclassical approaches give rise to a dissipative behaviour. Moreover, we find that the oscillator dynamics has to be taken into account, even in a semiclassical approximation, in order to reproduce a thermally activated enhancement of the transition probability

Experimental Study of the Radiative Decays K+ -> mu+ nu e+e- and K+ -> e+ nu e+e-

Experiment 865 at the Brookhaven AGS obtained 410 K+ -> e+ nu e+e- and 2679 K+ -> mu+ nu e+e- events including 10% and 19% background. The branching ratios were measured to be (2.48+-0.14(stat.)+-0.14(syst.))x10^-8 (m_ee>150 MeV) and (7.06+-0.16+-0.26)x10^-8 (m_ee>145 MeV), respectively. Results for the decay form factors are presented.Comment: 4 pages, 3 figures, RevTeX

dtwSat: Time-Weighted Dynamic Time Warping for Satellite Image Time Series Analysis in R

The opening of large archives of satellite data such as LANDSAT, MODIS and the SENTINELs has given researchers unprecedented access to data, allowing them to better quantify and understand local and global land change. The need to analyse such large data sets has lead to the development of automated and semi-automated methods for satellite image time series analysis. However, few of the proposed methods for re mote sensing time series analysis are available as open source software. In this paper we present the R package dtwSat . This package provides an implementation of the Time-Weighted Dynamic Time Warping method for land cover mapping using sequence of multi-band satellite images. Methods based on dynamic time warping are flexible to handle irregular sampling and out-of-phase time series, and they have achieved significant result s in time series analysis. dtwSat is available from the Comprehensive R Archive Network and contributes to making methods for satellite time series analysis available to a larger audience. The package supports the full cycle of land cover classification using image time series, ranging from selecting temporal patterns to visualising and assessing the results