Ionization of Coulomb systems in $\RR^3$ by time periodic forcings of arbitrary size

Details Ionization of Coulomb systems in $\RR^3$ by time periodic forcings of arbitrary size Ionization of Coulomb systems in $\RR^3$ by time periodic forcings of arbitrary size

2006-11-27

arxiv.org/abs/math/0611818v3

Mathematics

Analysis of PDEs

Scientific paper

We analyze the long time behavior of solutions of the Schr\"odinger equation $i\psi_t=(-\Delta-b/r+V(t,x))\psi$, $x\in\RR^3$, $r=|x|$, describing a Coulomb system subjected to a spatially compactly supported time periodic potential $V(t,x)=V(t+2\pi/\omega,x)$ with zero time average. We show that, for any $V(t,x)$ of the form $2\Omega(r)\sin (\omega t-\theta)$, with $\Omega(r)$ nonzero on its support, Floquet bound states do not exist. This implies that the system ionizes, {\em i.e.} $P(t,K)=\int_K|\psi(t,x)|^2dx\to 0$ as $t\to\infty$ for any compact set $K\subset\RR^3$. Furthermore, if the initial state is compactly supported and has only finitely many spherical harmonic modes, then $P(t,K)$ decays like $t^{-5/3}$ as $t \to \infty $. To prove these statements, we develop a rigorous WKB theory for infinite systems of ordinary differential equations.

Affiliated with

Also associated with

No associations

Rating

Ionization of Coulomb systems in $\RR^3$ by time periodic forcings of arbitrary size does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ionization of Coulomb systems in $\RR^3$ by time periodic forcings of arbitrary size, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ionization of Coulomb systems in $\RR^3$ by time periodic forcings of arbitrary size will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-23587