arXiv subjects

G. F. Dell'Antonio

Publications and source records attributed to G. F. Dell'Antonio.

3 recordsLinked to original sources

arXiv2004

Ionization for Three Dimensional Time-dependent Point Interactions

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 (α(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (α(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.

math-ph↗

arXiv2004

Semiclassical analysis of constrained quantum systems

We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order hbar^(1/2), by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system.

math-ph↗

arXiv1999

Schrodinger Equation with Moving Point Interactions in Three Dimensions

We consider the motion of a non relativistic quantum particle in R^3 subject to n point interactions which are moving on given smooth trajectories. Due to the singular character of the time-dependent interaction, the corresponding Schrodinger equation does not have solutions in a strong sense and, moreover, standard perturbation techniques cannot be used. Here we prove that, for smooth initial data, there is a unique weak solution by reducing the problem to the solution of a Volterra integral equation involving only the time variable. It is also shown that the evolution operator uniquely extends to a unitary operator in $L^{2}(R^{3})$.

math-ph↗