Quantum quench in the transverse-field Ising chain

We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.     

Magnesium nanoparticles with transition metal decoration for hydrogen storage

We report on the hydrogen storage behaviour of Mg nanoparticles (NPs) (size range 100 nm–1 μm) with metal-oxide core–shell morphology synthesized by inert gas condensation and decorated by transition metal (TM) (Pd or Ti) clusters via in situ vacuum deposition. The structure and morphology of the as-prepared and hydrogenated NPs is studied by electron microscopy, X-ray diffraction including in situ experiments and X-ray absorption spectroscopy, in order to investigate the relationships with the hydrogen storage kinetics measured by the volumetric Sieverts method. With both Pd and Ti, the decoration deeply improves the hydrogen sorption properties: previously inert NPs exhibit complete hydrogenation with fast transformation kinetics, good stability and reversible gravimetric capacity that can attain 6 wt%. In the case of Pd-decoration, the occurrence of Mg–Pd alloying is observed at high temperatures and in dependence of the hydrogen pressure conditions. These structural transformations modify both the kinetics and thermodynamics of hydride formation, while Ti-decoration has an effect only on the kinetics. The experimental results are discussed in relation with key issues such as the amount of decoration, the heat of mixing between TM and Mg and the binding energy between TM and hydrogen.     

A binary algorithm with low divergence for modular inversion on SIMD architectures

When performing modular arithmetic the most computationally expensive operation is the modular inversion of an integer. Its cost might be a problem for cryptanalytical applications (like the transformation from projective to affine coordinates within a Pollard rho algorithm implementation to solve the discrete logarithm problem on an elliptic curve) where performances constitute a key aspect. Good platforms for such operations are single-instruction multiple-data architectures, like graphic processing units (GPUs) because of their extremely competitive performance/price ratio. Unfortunately, when a single thread computes a single inversion, the whole computation on GPUs can be significantly slowed down in the presence of divergent threads. In this paper we describe a new algorithm to compute modular inversion on GPUs based on Stein’s Binary GCD. By exploiting the De Bruijn sequences and the Montgomery arithmetic, our version of Stein’s algorithm better fits GPUs, since it reduces the divergence among threads of the original algorithm. The paper includes a brief report on tests of our algorithm in six prime fields with characteristics of size ranging from 109 to 359 bits and in the two prime fields associated to the Mersenne primes \(2^{521} - 1\) and \(2^{607} - 1\).     

Exclusively Heteronuclear NMR Experiments to Obtain Structural and Dynamic Information on Proteins

Provided that ¹³C‐detected NMR experiments are either preferable or complementary to ¹H detection, we report here tools to determine C^α? C′, C′? N, and C^α? H^α residual dipolar couplings on the basis of the CON experiment. The coupling constants determined on ubiquitin are consistent with the subset measured with the ¹H‐detected HNCO sequences. Since the utilization of residual dipolar couplings may depend on the mobility of the involved nuclei, we also provide tools to measure longitudinal and transverse relaxation rates of N and C′. This new set of experiments is a further development of a whole strategy based on ¹³C direct‐detection NMR spectroscopy for the study of biological macromolecules.     

A new synthetic entry to 3-carboxamido-4-carboxylic acid derivatives of isoxazole and pyrazole

Ethyl 2-amino-3-methoxycarbonyl-4-oxo-2-pentenoate (3) reacts with hydroxylamine or hydrazines to give isoxazole and pyrazole ortho-dicarboxylic acid esters 4 and 5, respectively. Partial hydrolysis of diesters 4 and 5 afforded the corresponding dicarboxylic acid monoesters 6 and 7. Amidation of the intermediate acid chlorides 8,9 followed by hydrolysis of 4-methylesters 10, 11 gave the title compounds 1 and 2, respectively.     

Double resonance with Landesman-Lazer conditions for planar systems of ordinary differential equations

We prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman-Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer-Fu?ik spectrum.     

Diffusion reproduction processes

Interesting physics emerges from studying a population of reproducing individuals. Each can be regarded as a random walker, but it can either duplicate or die. Novel features of the collective behavior are quite surprising: if individuals reproduce or die freely, the life expectation is proportional to the size of the population, and if it is kept constant, the center of mass moves in space as if it were a single walker (i.e., the diffusion constant is independent of population's size). Biology-inspired interactions are also considered.