SISSA Preprints: Recent submissions

  • Michelangeli, Alessandro; Scandone, Raffaele (SISSA, 2018-03)
    We construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger operators with regular potentials centred ...
  • Michelangeli, Alessandro; Thanh Nam, Phan; Olgiati, Alessandro (2018-03)
    We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order ...
  • Michelangeli, Alessandro; Olgiati, Alessandro (2018-03)
    We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which ...
  • Dal Maso, Gianni; Franzina, Giovanni; Zucco, Davide (2018-03)
    We study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise ...
  • Cagnetti, Filippo; Dal Maso, Gianni; Scardia, Lucia; Zeppieri, Caterina Ida (2018-03)
    In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity ...
  • Dal Maso, Gianni; Larsen, Christopher J.; Toader, Rodica (2018-03)
    We consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, ...
  • Caponi, Maicol (2018)
    We propose a phase-field model of dynamic crack propagation based on the Ambrosio-Tortorelli approximation, which takes in account dissipative effects due to the speed of the crack tips. In particular, adapting the time ...
  • Gigli, Nicola (2013)
    We prove that an infinitesimally Hilbertian $CD(0,N)$ space containing a line splits as the product of $R$ and an infinitesimally Hilbertian $CD(0,N −1)$ space. By ‘infinitesimally Hilbertian’ we mean that the Sobolev space ...
  • Michelangeli, Alessandro; Ottolini, Andrea; Scandone, Raffaele (SISSA, 2018-01)
    We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their ...
  • Cotti, Giordano; Dubrovin, Boris; Guzzetti, Davide (SISSA, 2018-01)
    There is a conjectural relation, formulated by the second author, between the enumerative geometry of a wide class of smooth projective varieties and their derived category of coherent sheaves. In particular, there is an ...
  • Becker, Simon; Michelangeli, Alessandro; Ottolini, Andrea (SISSA, 2017-12-21)
    We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of ...
  • Lazzaroni, Giuliano; Nardini, Lorenzo (SISSA, 2017)
    Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we ...
  • Michelangeli, Alessandro; Olgiati, Alessandro; Scandone, Raffaele (2017)
    We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where ...
  • Gallone, Matteo; Michelangeli, Alessandro (2017)
    The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished ...
  • Bianchini, Stefano; Bonicatto, Paolo (2017)
  • Erceg, Marco; Michelangeli, Alessandro (2017)
    We realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators ...
  • Bellazzini, Brando; Riva, Francesco; Serra, Javi; Sgarlata, Francesco (2017)
    We constrain effective feld theories by going beyond the familiar positivity bounds that follow from unitarity, analyticity, and crossing symmetry of the scattering amplitudes. As interesting examples, we discuss the ...
  • Baldi, Pietro; Berti, Massimiliano; Haus, Emanuele; Montalto, Riccardo (2017)
    We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with ...
  • Bruzzo, Ugo; Lanza, Valeriano; Lo Giudice, Alessio (2017)
    We provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifold. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the ...
  • Antonelli, Paolo; Michelangeli, Alessandro; Scandone, Raffaele (2017)
    We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not ...