TY - JOUR
T1 - A time-dependent perturbative analysis for a quantum particle in a cloud chamber
JF - Annales Henri Poincare 11 (2010) 539-564
Y1 - 2010
A1 - Gianfausto Dell'Antonio
A1 - Rodolfo Figari
A1 - Alessandro Teta
AB - 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.
PB - Springer
UR - http://hdl.handle.net/1963/3969
U1 - 432
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Ionization for Three Dimensional Time-dependent Point Interactions
JF - Comm. Math. Phys. 257 (2005) 169-192
Y1 - 2005
A1 - Michele Correggi
A1 - Gianfausto Dell'Antonio
A1 - Rodolfo Figari
A1 - Andrea Mantile
AB - 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.
UR - http://hdl.handle.net/1963/2297
U1 - 1719
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Blow-up solutions for the SchrÃ¶dinger equation in dimension three with a concentrated nonlinearity
JF - Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137
Y1 - 2004
A1 - Riccardo Adami
A1 - Gianfausto Dell'Antonio
A1 - Rodolfo Figari
A1 - Alessandro Teta
AB - 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.
PB - Elsevier
UR - http://hdl.handle.net/1963/2998
U1 - 1335
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Diffusion of a particle in presence of N moving point sources
JF - Annales Poincare Phys.Theor.69:413-424,1998
Y1 - 1998
A1 - Gianfausto Dell'Antonio
A1 - Rodolfo Figari
A1 - Alessandro Teta
PB - SISSA Library
UR - http://hdl.handle.net/1963/134
U1 - 75
U2 - LISNU
U3 - Interdisciplinary Laboratory for Advanced Studies
ER -
TY - JOUR
T1 - Statistics in space dimension two
JF - Lett. Math. Phys. 40 (1997), no. 3, 235-256
Y1 - 1997
A1 - Gianfausto Dell'Antonio
A1 - Rodolfo Figari
A1 - Alessandro Teta
AB - 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).
PB - SISSA Library
UR - http://hdl.handle.net/1963/130
U1 - 12
U2 - LISNU
U3 - Interdisciplinary Laboratory for Advanced Studies
ER -