A semi-infinite matrix analysis of the BFKL equation

The forward BFKL equation is discretised in virtuality space and it is shown that the diffusion into infrared and ultraviolet momenta can be understood in terms of a semi-infinite matrix. The square truncation of this matrix can be exponentiated leading to asymptotic eigenstates sharing many features with the BFKL gluon Green's function in the limit of large matrix size. This truncation is closely related to a representation of the XXX Heisenberg spin $= - \frac{1}{2}$ chain with SL(2) invariance where the Hamiltonian acts on a symmetric double copy of the harmonic oscillator. A simple modification of the BFKL matrix suppressing the infrared modes generates evolution with energy compatible with unitarity.Comment: Small changes, same conclusions, matching the published version in EPJ

Quantum simulation of the Anderson Hamiltonian with an array of coupled nanoresonators: delocalization and thermalization effects

The possibility of using nanoelectromechanical systems as a simulation tool for quantum many-body effects is explored. It is demonstrated that an array of electrostatically coupled nanoresonators can effectively simulate the Bose-Hubbard model without interactions, corresponding in the single-phonon regime to the Anderson tight-binding model. Employing a density matrix formalism for the system coupled to a bosonic thermal bath, we study the interplay between disorder and thermalization, focusing on the delocalization process. It is found that the phonon population remains localized for a long time at low enough temperatures; with increasing temperatures the localization is rapidly lost due to thermal pumping of excitations into the array, producing in the equilibrium a fully thermalized system. Finally, we consider a possible experimental design to measure the phonon population in the array by means of a superconducting transmon qubit coupled to individual nanoresonators. We also consider the possibility of using the proposed quantum simulator for realizing continuous-time quantum walks.Comment: Replaced with new improved version. To appear in EPJ Q

HST astrometry in the Orion Nebula Cluster: census of low-mass runaways

We present a catalog of high-precision proper motions in the Orion Nebula Cluster (ONC), based on Treasury Program observations with the Hubble Space Telescope's (HST) ACS/WFC camera. Our catalog contains 2,454 objects in the magnitude range of $14.2<m_{\rm F775W}<24.7$, thus probing the stellar masses of the ONC from $\sim$0.4 $M_\odot$ down to $\sim$0.02 $M_\odot$ over an area of $\sim$550 arcmin$^2$. We provide a number of internal velocity dispersion estimates for the ONC that indicate a weak dependence on the stellar location and mass. There is good agreement with the published velocity dispersion estimates, although nearly all of them (including ours at $\sigma_{v,x}=0.94$ and $\sigma_{v,y}=1.25$ mas yr$^{-1}$) might be biased by the overlapping young stellar populations of Orion A. We identified 4 new ONC candidate runaways based on HST and the Gaia DR2 data, all with masses less than $\sim$1 $M_\odot$. The total census of known candidate runaway sources is 10 -- one of the largest samples ever found in any Milky Way open star cluster. Surprisingly, none of them has the tangential velocity exceeding 20 km s$^{-1}$. If most of them indeed originated in the ONC, it may compel re-examination of dynamical processes in very young star clusters. It appears that the mass function of the ONC is not significantly affected by the lost runaways.Comment: 16 pages, 10 figures, 5 tables. Accepted for publication in A

Working-class royalty: bees beat the caste system

The struggle among social classes or castes is well known in humans. Here, we show that caste inequality similarly affects societies of ants, bees and wasps, where castes are morphologically distinct and workers have greatly reduced reproductive potential compared with queens. In social insects, an individual normally has no control over its own fate, whether queen or worker, as this is socially determined during rearing. Here, for the first time, we quantify a strategy for overcoming social control. In the stingless bee Schwarziana quadripunctata, some individuals reared in worker cells avoid a worker fate by developing into fully functional dwarf queens

Impact experiments in support of “Lithopanspermia”: The route from Mars to Earth

Shock recovery experiments on a Martian analogue rock (gabbro) loaded with three types of microorganisms reveal that these organisms survive the impact and ejection phase on Mars at shock pressures up to about 50 GPa with exponentially decreasing survival rates

Balance in Family Triads:How Intergenerational Relationships Affect the Adult Sibling Relationship

In order to understand the interdependency between intergenerational and adult sibling relationships, a family systems perspective is applied to identify a smaller?empirically analyzable?relational unit of analysis, that is, the sibling?parent?sibling triad. Using balance theory, triadic configurations are derived that represent enhancement, compensation, and loyalty conflicts. The hypotheses are tested for three relational dimensions: support exchange, contact, and conflict. Multilevel analyses of 549 sibling?parent?sibling triads from the Netherlands Kinship Panel data show strong evidence for enhancement, whereas some indication was obtained for sibling relationships being affected by loyalty conflicts. The results underscore and substantiate interdependency between intergenerational and adult sibling relationships

Stability of the Duality Gap in Linear Optimization

In this paper we consider the duality gap function g that measures the difference between the optimal values of the primal problem and of the dual problem in linear programming and in linear semi-infinite programming. We analyze its behavior when the data defining these problems may be perturbed, considering seven different scenarios. In particular we find some stability results by proving that, under mild conditions, either the duality gap of the perturbed problems is zero or + ∞ around the given data, or g has an infinite jump at it. We also give conditions guaranteeing that those data providing a finite duality gap are limits of sequences of data providing zero duality gap for sufficiently small perturbations, which is a generic result.This research was partially supported by MINECO of Spain and FEDER of EU, Grant MTM2014-59179-C2-01 and SECTyP-UNCuyo Res. 4540/13-R