 00431 Barbaroux J.M., Germinet F., Tcheremchantsev S.
 Quantum diffusion and generalized fractal dimensions:
The continuous case $L^2(\R^d)$
(46K, LaTeX)
Nov 6, 00

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We estimate the spreading of the solution of the Schr\"odinger
equation asymptotically in time, in term of the fractal properties of
the associated spectral measures. For this, we exhibit a lower bound
for the moments of order $p$ at time $T$, for the state $\psi$,
defined by
$$
\frac{1}{T}\int_0^T \ X^{p/2} {\rm e}^{itH}\psi\^2 dt\ .
$$
We show that this lower bound can be expressed in term of the
generalized fractal dimensions of the spectral measure $\mu_\psi$
associated to the Hamiltonian $H$ and the state $\psi$. We especially
focus on continuous models.
 Files:
00431.tex