On the approach to equilibrium for a polymer with adsorption and repulsion

We consider paths of a one-dimensional simple random walk conditioned to come back to the origin after L steps (L an even integer). In the 'pinning model' each path \eta has a weight \lambda^{N(\eta)}, where \lambda>0 and N(\eta) is the number of zeros in \eta. When the paths are constrained to be non-negative, the polymer is said to satisfy a hard-wall constraint. Such models are well known to undergo a localization/delocalization transition as the pinning strength \lambda is varied. In this paper we study a natural 'spin flip' dynamics for these models and derive several estimates on its spectral gap and mixing time. In particular, for the system with the wall we prove that relaxation to equilibrium is always at least as fast as in the free case (\lambda=1, no wall), where the gap and the mixing time are known to scale as L^{-2} and L^2\log L, respectively. This improves considerably over previously known results. For the system without the wall we show that the equilibrium phase transition has a clear dynamical manifestation: for \lambda \geq 1 the relaxation is again at least as fast as the diffusive free case, but in the strictly delocalized phase (\lambda < 1) the gap is shown to be O(L^{-5/2}), up to logarithmic corrections. As an application of our bounds, we prove stretched exponential relaxation of local functions in the localized regime.Comment: 43 pages, 5 figures; v2: corrected typos, added Table

On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature

We obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $\Lambda$, both under the infinite volume measure and under the measure with zero boundary conditions around $\Lambda$, this probability turns out to behave like $\exp(-\tau_\beta(0) L \log L )$, with $\tau_\beta(0)$ the surface tension at zero tilt, also called step free energy, and $L$ the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models.Comment: 21 pages, 6 figure

Deformed quons and bi-coherent states

We discuss how a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons. This deformation involves interesting mathematical problems and suggests possible applications to pseudo-hermitian quantum mechanics. We construct bi-coherent states associated to \D-pseudo-quons, and we show that they share many of their properties with ordinary coherent states. In particular, we find conditions for these states to exist, to be eigenstates of suitable annihilation operators and to give rise to a resolution of the identity. Two examples are discussed in details, one connected to an unbounded similarity map, and the other to a bounded map.Comment: in press in Proceedings of the Royal Society

Matrix computations for the dynamics of fermionic systems

In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and lowering operators play a relevant role in this analysis. The technical problem of our approach stands in the difficulty of solving the equations of motion, which are, first of all, {\em operator-valued} and, secondly, quite often nonlinear. In this paper we construct a general procedure which significantly simplifies the treatment for those systems which can be described in terms of fermionic operators. The proposed procedure allows to get an analytic solution, both for quadratic and for more general hamiltonians.Comment: In press in International Journal of Theoretical Physic

Heavy-flavor correlations and multiplicity dependence in pp and p--Pb collisions with ALICE

The production of heavy quarks in pp collisions at the LHC energies provides a reliable test of perturbative QCD calculations. Comparisons of pp and \pPb measurements of their hadronization products allow us to investigate how cold nuclear matter effects affect the heavy-quark production. We present ALICE measurements of azimuthal correlations of prompt D mesons with charged hadrons in pp collisions at \s = 7 TeV and \pPb collisions at \sNN = 5.02 TeV. We also show the per-event D-meson yields as a function of the charged-particle multiplicity in pp collisions at \s = 7 TeV.Comment: Proceedings of Quark Matter 2015 conferenc

On some properties of transitions operators

We study a general transition operator, generated by a random walk on a graph $X$; in particular we give necessary and sufficient condition on the matrix coefficient (1-step transition probablilities) to be a bounded operator from $l^\infty(X)$ into itself. Moreover we characterize compact operators and we relate this property to the behaviour of the associated random walk. We give a necessary and sufficient condition for the pre-adjoint of the discrete Laplace operator to be an injective map.Comment: 9 page

Complementary results for the spectral analysis of matrices in Galerkin methods with GB-splines

We collect some new results relative to the study of the spectral analysis of matrices in Galerkin methods based on generalized B-splines with high smoothness

Legal Fictions and the Essence of Robots: Thoughts on Essentialism and Pragmatism in the Regulation of Robotics

The purpose of this paper is to offer some critical remarks on the so-called pragmatist approach to the regulation of robotics. To this end, the article mainly reviews the work of Jack Balkin and Joanna Bryson, who have taken up such ap- proach with interestingly similar outcomes. Moreover, special attention will be paid to the discussion concerning the legal fiction of ‘electronic personality’. This will help shed light on the opposition between essentialist and pragmatist methodologies. After a brief introduction (1.), in 2. I introduce the main points of the methodological debate which opposes pragmatism and essentialism in the regulation of robotics and I examine how legal fictions are framed from a pragmatist, functional perspective. Since this approach entails a neat separation of ontological analysis and legal rea- soning, in 3. I discuss whether considerations on robots’ essence are actually put into brackets when the pragmatist approach is endorsed. Finally, in 4. I address the problem of the social valence of legal fictions in order to suggest a possible limit of the pragmatist approach. My conclusion (5.) is that in the specific case of regulating robotics it may be very difficult to separate ontological considerations from legal reasoning—and vice versa—both on an epistemological and social level. This calls for great caution in the recourse to anthropomorphic legal fictions