47 citations · 426 across the 46 of their papers we have counts for
49 papers
Scattering for Short-Range Mass-Subcritical Choquard Equations
Alessandro Michelangeli, Mirko Tarulli
We study scattering for the defocusing inhomogeneous generalized Choquard equation with data in the conformal energy space. In the full short-range mass-subcritical regime, a key e…
Complexity scaling and optimal policy degeneracy in quantum reinforcement learning via analytically solvable unitary-control-then-measure models
Andrea Cintio, Alessandro Michelangeli, Dmitrii Tsutskov
We propose and analyse a class of analytically solvable models of quantum reinforcement learning (QRL), formulated as finite-horizon Markov decision processes in finite-dimensional…
The Dynamical Landscape of Beggar-My-Neighbour: Ultra-long Matches, Loops, and Infinite Matches
Nicolas Andorno, Giulio Cernoia, Simone Duiz +1
We present a rigorous mathematical and computational analysis of the deterministic card game \emph{Beggar-My-Neighbour}. By establishing a formal state-space framework, we investig…
Non-relativistic limit of Dirac Hamiltonians with Aharonov-Bohm fields
Matteo Gallone, Alessandro Michelangeli, Diego Noja
We characterise the families of self-adjoint Dirac and Schrödinger operators with Aharonov-Bohm magnetic field, and we exploit the non-relativistic limit of infinite light speed to…
Open problems and perspectives on solving Friedrichs systems by Krylov approximation
Noe Angelo Caruso, Alessandro Michelangeli
We set up, at the abstract Hilbert space setting, the general question on when an inverse linear problem induced by an operator of Friedrichs type admits solutions belonging to (th…
On creating new essential spectrum by self-adjoint extension of gapped operators
Alessandro Michelangeli
Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily prescribed portions of the gap a…
On a comparison between absolute and relative self-adjoint extension schemes
Noè Angelo Caruso, Alessandro Michelangeli, Andrea Ottolini
The problem of connecting the operator parameters that label the same self-adjoint extension of a given symmetric operator, respectively, within the 'absolute' von Neumann extensio…
On the characterisation of fragmented Bose-Einstein condensation and its emergent effective evolution
Jinyeop Lee, Alessandro Michelangeli
Fragmented Bose-Einstein condensates are large systems of identical bosons displaying \emph{multiple} macroscopic occupations of one-body states, in a suitable sense. The quest for…
Generalised solutions to linear and non-linear Schrödinger-type equations with point defect: Colombeau and non-Colombeau regimes
N. Dugandžija, A. Michelangeli, I. Vojnović
For a semi-linear Schrödinger equation of Hartree type in three spatial dimensions, various approximations of singular, point-like perturbations are considered, in the form of pote…
Standing waves and global well-posedness for the 2d Hartree equation with a point interaction
Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone
We study a class of two-dimensional non-linear Schrödinger equations with point-like singular perturbation and Hartree non-linearity. The point-like singular perturbation of the fr…
Self-adjoint extension schemes and modern applications to quantum Hamiltonians
Matteo Gallone, Alessandro Michelangeli
This monograph contains revised and enlarged materials from previous lecture notes of undergraduate and graduate courses and seminars delivered by both authors over the last years…
Lieb-Robinson bounds and growth of correlations in Bose mixtures
Alessandro Michelangeli, Nicola Santamaria
For a mixture of interacting Bose gases initially prepared in a regime of condensation (uncorrelation), it is proved that in the course of the the time evolution observables of dis…
Heat equation with inverse-square potential of bridging type across two half-lines
Matteo Gallone, Alessandro Michelangeli, Eugenio Pozzoli
The heat equation with inverse square potential on both half-lines of is discussed in the presence of \emph{bridging} boundary conditions at the origin. The problem is…
Inverse linear problems on Hilbert space and their Krylov solvability
Noe Angelo Caruso, Alessandro Michelangeli
This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the line…
Krylov solvability under perturbations of abstract inverse linear problems
Noe Angelo Caruso, Alessandro Michelangeli
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum a…
Self-adjointness in Quantum Mechanics: a pedagogical path
Andrea Cintio, Alessandro Michelangeli
Observables in quantum mechanics are represented by self-adjoint operators on Hilbert space. Such ubiquitous, well-known, and very foundational fact, however, is traditionally subt…
Quantum particle across Grushin singularity
Matteo Gallone, Alessandro Michelangeli
A class of models is considered for a quantum particle constrained on degenerate Riemannian manifolds known as Grushin cylinders, and moving freely subject only to the underlying g…
Models of zero-range interaction for the bosonic trimer at unitarity
Alessandro Michelangeli
We present the mathematical construction of the physically relevant quantum Hamiltonians for a three-body systems consisting of identical bosons mutually coupled by a two-body inte…
Faber-Krahn inequalities for Schrödinger operators with point and with Coulomb interactions
Vladimir Lotoreichik, Alessandro Michelangeli
We obtain new Faber-Krahn-type inequalities for certain perturbations of the Dirichlet Laplacian on a bounded domain. First, we establish a two- and three-dimensional Faber-Krahn i…
Self-adjoint extensions with Friedrichs lower bound
Matteo Gallone, Alessandro Michelangeli
We produce a simple criterion and a constructive recipe to identify those self-adjoint extensions of a lower semi-bounded symmetric operator on Hilbert space which have the same lo…
Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder
Matteo Gallone, Alessandro Michelangeli, Eugenio Pozzoli
We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder equipped with an incomplete Riemannian metric of Grushin type,…
On real resonances for three-dimensional Schrödinger operators with point interactions
Alessandro Michelangeli, Raffaele Scandone
We prove the absence of positive real resonances for Schrödinger operators with finitely many point interactions in and we discuss such a property from the perspecti…
Krylov solvability of unbounded inverse linear problems
Noe Caruso, Alessandro Michelangeli
The abstract issue of 'Krylov solvability' is extensively discussed for the inverse problem where is a (possibly unbounded) linear operator on an infinite-dimensional…
Convergence of the conjugate gradient method with unbounded operators
Noe Caruso, Alessandro Michelangeli
In the framework of inverse linear problems on infinite-dimensional Hilbert space, we prove the convergence of the conjugate gradient iterates to an exact solution to the inverse p…