SISSA PreprintsThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2020-04-02T15:49:01Z2020-04-02T15:49:01ZSelf-adjoint extensions with Friedrichs lower boundGallone, MatteoMichelangeli, Alessandrohttp://preprints.sissa.it:8180/xmlui/handle/1963/353472020-03-28T00:20:24Z2020-01-01T00:00:00ZSelf-adjoint extensions with Friedrichs lower bound
Gallone, Matteo; Michelangeli, Alessandro
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 lower bound as the Friedrichs extension. Applications of this abstract result to a few instructive examples are then discussed.
2020-01-01T00:00:00ZGeometric Confinement and Dynamical Transmission of a Quantum Particle in Grushin CylinderGallone, MatteoMichelangeli, AlessandroPozzoli, Eugeniohttp://preprints.sissa.it:8180/xmlui/handle/1963/353462020-03-27T11:02:48Z2019-01-01T00:00:00ZGeometric Confinement and Dynamical Transmission of a Quantum Particle in Grushin Cylinder
Gallone, Matteo; Michelangeli, Alessandro; Pozzoli, Eugenio
We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally deﬁned on an inﬁnite cylinder equipped with an incom-plete Riemannian metric of Grushin type, in the non-trivial class of metrics yielding an inﬁnite deﬁciency index. Such realisations are naturally interpreted as Hamiltonians governing the geometric conﬁnement of a Schr¨odinger quan-tum particle away from the singularity, or the dynamical transmission across the singularity. In particular, we characterise all physically meaningful exten-sions qualiﬁed by explicit local boundary conditions at the singularity. Within our general classiﬁcation we retrieve those distinguished extensions previously identiﬁed in the recent literature, namely the most conﬁning and the most transmitting one.
69 p.
2019-01-01T00:00:00ZZero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactionsScandone, Raffaelehttp://preprints.sissa.it:8180/xmlui/handle/1963/353452020-03-10T00:20:28Z2019-01-01T00:00:00ZZero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactions
Scandone, Raffaele
We study the low energy behavior of the resolvent of Schrodinger operators with finitely many point interactions in three dimensions. We also discuss the occurrence and the multiplicity of zero energy obstructions.
2019-01-01T00:00:00ZDeformations of holomorphic pairs and 2d-4d wall-crossingFantini, Veronicahttp://preprints.sissa.it:8180/xmlui/handle/1963/353442020-03-10T00:20:27Z2019-01-01T00:00:00ZDeformations of holomorphic pairs and 2d-4d wall-crossing
Fantini, Veronica
We show how wall-crossing formulas in coupled 2d-4d systems, introduced by Gaiotto, Moore and Neitzke, can be interpreted geometrically in terms of the deformation theory of holomorphic pairs, given by a complex manifold together with a holomorphic vector bundle. The main part of the paper studies the relation between scattering diagrams and deformations of holomorphic pairs, building on recent work by Chan, Conan Leung and Ma.
2019-01-01T00:00:00Z