SDLThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2018-02-25T02:40:46Z2018-02-25T02:40:46ZThe splitting theorem in non-smooth contextGigli, Nicolahttp://preprints.sissa.it/handle/1963/353062018-02-24T01:00:33Z2013-01-01T00:00:00ZThe splitting theorem in non-smooth context
Gigli, Nicola
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 $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence.
2013-01-01T00:00:00ZFractional powers and singular perturbations of differential operatorsMichelangeli, AlessandroOttolini, AndreaScandone, Raffaelehttp://preprints.sissa.it/handle/1963/353052018-02-21T07:44:45Z2018-01-01T00:00:00ZFractional powers and singular perturbations of differential operators
Michelangeli, Alessandro; Ottolini, Andrea; Scandone, Raffaele
We develop the construction of the fractional powers of singular
(point-like) perturbations of the Laplacian, and the construction of singular
perturbations of fractional powers of the Laplacian, and we compare such two
constructions focusing on their perturbative structure for resolvents and on the
local singularity structure of their domains. In application to the linear and
non-linear Schr odinger equations for the corresponding operators we outline a
programme of relevant questions that deserve being investigated.
Dedicated to Gianfausto Dell'Antonio on the occasion of his 85th birthday
2018-01-01T00:00:00ZLocal moduli of semisimple Frobenius coalescent structuresCotti, GiordanoDubrovin, BorisGuzzetti, Davidehttp://preprints.sissa.it/handle/1963/353042018-01-17T01:00:32Z2018-01-01T00:00:00ZLocal moduli of semisimple Frobenius coalescent structures
Cotti, Giordano; Dubrovin, Boris; Guzzetti, Davide
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 increasing interest for an explicit description of certain local invariants, called monodromy data, of semisimple quantum cohomologies in terms of characteristic classes of exceptional collections in the derived categories. Being intentioned to address this problem, which, to our opinion, is still not well understood, we have realized that some issues in the theory of Frobenius manifolds need to be preliminarily clarified, and that an extension of the theory itself is necessary, in view of the fact that quantum cohomologies of certain classes of homogeneous spaces may show a coalescence phenomenon.
2018-01-01T00:00:00ZSpectral Properties of the 2+1 Fermionic Trimer with Contact InteractionsBecker, SimonMichelangeli, AlessandroOttolini, Andreahttp://preprints.sissa.it/handle/1963/353032018-01-05T01:00:33Z2017-12-21T00:00:00ZSpectral Properties of the 2+1 Fermionic Trimer with Contact Interactions
Becker, Simon; Michelangeli, Alessandro; Ottolini, Andrea
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 different
species, with two-body interaction of zero range. For arbitrary magnitude of
the interaction, and arbitrary value of the mass parameter (the ratio between
the mass of the third particle and that of each fermion) above the stability
threshold, we identify the essential spectrum, localise and prove the finiteness
of the discrete spectrum, qualify the angular symmetry of the eigenfunctions,
and prove the monotonicity of the eigenvalues with respect to the mass parameter.
We also demonstrate the existence of bound states in a physically
relevant regime of masses.
Partially supported by the 2014-2017 MIUR-FIR grant \Cond-Math: Condensed Matter and
Mathematical Physics" code RBFR13WAET (S.B., A.M., A.O.), by the DAAD International
Trainership Programme (S.B.), and by a 2017 visiting research fellowship at the International Center for Mathematical Research CIRM, Trento (A.M.).
2017-12-21T00:00:00Z