Zobrazeno 1 - 10
of 308
pro vyhledávání: '"Finco D"'
In this paper we consider the NLS equation with power nonlinearity and a point interaction (a "$\delta$-potential" in the physical literature) in dimension two and three. We will show that for low power nonlinearities there is failure of scattering t
Externí odkaz:
http://arxiv.org/abs/2212.14216
In the present note we study the NLS equation in dimension two with a point interaction and in the supercritical regime, showing two results. After obtaining the (nonstandard) virial formula, we exhibit a set of initial data that blow-up. Moreover we
Externí odkaz:
http://arxiv.org/abs/2209.09537
Publikováno v:
Ann. H. Poincar\'e 20 (2019), 2899-2935
We consider a quantum model of two-channel scattering to describe the mechanism of a Feshbach resonance. We perform a rigorous analysis in order to count and localize the energy resonances in the perturbative regime, i.e., for small inter-channel cou
Externí odkaz:
http://arxiv.org/abs/1901.08282
Publikováno v:
Math. Phys. Anal. Geom. 18 (2015), 1-36
We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $ m $, where each fermion interacts via a zero-range force with the different particle. In particular we study the unit
Externí odkaz:
http://arxiv.org/abs/1505.04132
In this paper we give the complete classification of solitons for a cubic NLS equation on the simplest network with a non-trivial topology: the tadpole graph, i.e. a ring with a half-line attached to it and free boundary conditions at the junction. T
Externí odkaz:
http://arxiv.org/abs/1405.3465
In the present paper we study the following scaled nonlinear Schr\"odinger equation (NLS) in one space dimension: \[ i\frac{d}{dt} \psi^{\varepsilon}(t) =-\Delta\psi^{\varepsilon}(t) + \frac{1}{\epsilon}V\left(\frac{x}{\epsilon}\right)|\psi^{\varepsi
Externí odkaz:
http://arxiv.org/abs/1403.1401
We consider a nonlinear Schr\"odinger equation with focusing nonlinearity of power type on a star graph ${\mathcal G}$, written as $ i \partial_t \Psi (t) = H \Psi (t) - |\Psi (t)|^{2\mu}\Psi (t)$, where $H$ is the selfadjoint operator which defines
Externí odkaz:
http://arxiv.org/abs/1211.1515
We study standing waves for a nonlinear Schr\"odinger equation on a star graph {$\mathcal{G}$} i.e. $N$ half-lines joined at a vertex. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\alpha\leqslant
Externí odkaz:
http://arxiv.org/abs/1206.5201
Publikováno v:
Rev. Math. Phys. 24 (2012), 1250017
We study the stability problem for a non-relativistic quantum system in dimension three composed by $ N \geq 2 $ identical fermions, with unit mass, interacting with a different particle, with mass $ m $, via a zero-range interaction of strength $ \a
Externí odkaz:
http://arxiv.org/abs/1201.5740
Autor:
Cacciapuoti, C., Finco, D.
We discuss the limit of small width for the Laplacian defined on a waveguide with Robin boundary conditions. Under suitable hypothesis on the scaling of the curvature, we prove the convergence of the Robin Laplacian to the Laplacian on the correspond
Externí odkaz:
http://arxiv.org/abs/0803.4314