%0 Journal Article
%J Annales Henri Poincare 11 (2010) 539-564
%D 2010
%T A time-dependent perturbative analysis for a quantum particle in a cloud chamber
%A Gianfausto Dell'Antonio
%A Rodolfo Figari
%A Alessandro Teta
%X We 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.
%B Annales Henri Poincare 11 (2010) 539-564
%I Springer
%G en_US
%U http://hdl.handle.net/1963/3969
%1 432
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-08-05T08:05:00Z\\nNo. of bitstreams: 1\\n0907.5503v1.pdf: 273181 bytes, checksum: 781ee2f8d4ce957ebbfbf866bcc40d2b (MD5)
%R 10.1007/s00023-010-0037-4
%0 Journal Article
%J Comm. Math. Phys. 257 (2005) 169-192
%D 2005
%T Ionization for Three Dimensional Time-dependent Point Interactions
%A Michele Correggi
%A Gianfausto Dell'Antonio
%A Rodolfo Figari
%A Andrea Mantile
%X We 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.
%B Comm. Math. Phys. 257 (2005) 169-192
%G en_US
%U http://hdl.handle.net/1963/2297
%1 1719
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-25T08:14:45Z\\nNo. of bitstreams: 1\\n0402011v2.pdf: 306766 bytes, checksum: 7efb2bcceb4c2699d662ae1af9e7dd76 (MD5)
%R 10.1007/s00220-005-1293-x
%0 Journal Article
%J Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137
%D 2004
%T Blow-up solutions for the SchrÃ¶dinger equation in dimension three with a concentrated nonlinearity
%A Riccardo Adami
%A Gianfausto Dell'Antonio
%A Rodolfo Figari
%A Alessandro Teta
%X We 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.
%B Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/2998
%1 1335
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:06:49Z\\nNo. of bitstreams: 1\\nadami.pdf: 209114 bytes, checksum: ea6a7059ff0728c6d55cdc3a16071631 (MD5)
%R 10.1016/j.anihpc.2003.01.002
%0 Journal Article
%J Annales Poincare Phys.Theor.69:413-424,1998
%D 1998
%T Diffusion of a particle in presence of N moving point sources
%A Gianfausto Dell'Antonio
%A Rodolfo Figari
%A Alessandro Teta
%B Annales Poincare Phys.Theor.69:413-424,1998
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/134
%1 75
%2 LISNU
%3 Interdisciplinary Laboratory for Advanced Studies
%$ Made available in DSpace on 2004-09-01T12:22:22Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996
%0 Journal Article
%J Lett. Math. Phys. 40 (1997), no. 3, 235-256
%D 1997
%T Statistics in space dimension two
%A Gianfausto Dell'Antonio
%A Rodolfo Figari
%A Alessandro Teta
%X We 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).
%B Lett. Math. Phys. 40 (1997), no. 3, 235-256
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/130
%1 12
%2 LISNU
%3 Interdisciplinary Laboratory for Advanced Studies
%$ Made available in DSpace on 2004-09-01T12:22:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996
%R 10.1023/A:1007361832622