01175nas a2200133 4500008004300000245008500043210006900128260001300197520072500210100002900935700002000964700002100984856003601005 2010 en_Ud 00aA time-dependent perturbative analysis for a quantum particle in a cloud chamber0 atimedependent perturbative analysis for a quantum particle in a bSpringer3 aWe consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/396901006nas a2200133 4500008004300000245007100043210006900114520056200183100002200745700002900767700002000796700002000816856003600836 2005 en_Ud 00aIonization for Three Dimensional Time-dependent Point Interactions0 aIonization for Three Dimensional Timedependent Point Interaction3 aWe study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the ``strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aMantile, Andrea uhttp://hdl.handle.net/1963/229700908nas a2200145 4500008004300000245010400043210007000147260001300217520040600230100002000636700002900656700002000685700002100705856003600726 2004 en_Ud 00aBlow-up solutions for the SchrÃ¶dinger equation in dimension three with a concentrated nonlinearity0 aBlowup solutions for the SchrÃ¶dinger equation in dimension three bElsevier3 aWe present some results on the blow-up phenomenon for the Schroedinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetry of the equation and construct a family of explicit blow up solutions.1 aAdami, Riccardo1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/299800418nas a2200121 4500008004100000245006600041210006600107260001800173100002900191700002000220700002100240856003500261 1998 en d00aDiffusion of a particle in presence of N moving point sources0 aDiffusion of a particle in presence of N moving point sources bSISSA Library1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/13401073nas a2200133 4500008004100000245003800041210003800079260001800117520069900135100002900834700002000863700002100883856003500904 1997 en d00aStatistics in space dimension two0 aStatistics in space dimension two bSISSA Library3 aWe construct as a selfadjoint operator the Schroedinger hamiltonian for a system of $N$ identical particles on a plane, obeying the statistics defined by a representation $\\\\pi_1$ of the braid group. We use quadratic forms and potential theory, and give details only for the free case; standard arguments provide the extension of our approach to the case of potentials which are small in the sense of forms with respect to the laplacian. We also comment on the relation between the analysis given here and other approaches to the problem, and also on the connection with the description of a quantum particle on a plane under the influence of a shielded magnetic field (Aharanov-Bohm effect).1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/130