The linear conductivity tensor for generic homogeneous, microscopic quantum models was
formulated as a noncommutative Kubo formula in Refs.[,,]. This formula was derived directly …

We derive a general upper bound on the spreading rate of wavepackets in the framework of
Schrödinger time evolution. Our result consists of showing that a portion of the wavepacket …

We exhibit an intermittency phenomenon in quantum dynamics. More precisely, we derive
new lower bounds for the moments of order p associated to the state ψ(t)=e^-itHψ and …

A method is presented for proving upper bounds on the moments of the position operator
when the dynamics of quantum wavepackets is governed by a random (possibly correlated) …

We exhibit a class of Hamiltonians in dimension D≥ 3, describing a quantum particle in an
aperiodic medium with absolutely continuous spectrum and subdiffusive behavior. The …

Let H be a self-adjoint operator on a separable Hilbert space H, ψ∈ H,|| ψ||= 1. Given an
orthonormal basis B={en} of H, we consider the time-averaged moments〈| X| ψp〉(T) of the …

We study the connections between dynamical properties of Schrödinger operators H on
separable Hilbert space H and the properties of corresponding spectral measures. Our main …

We review the main rigorous results accumulated during the last 5 years concerning the
theory of transport in aperiodic media. Motivated by the transport properties of quasicrystals …

For a class of discrete quasi-periodic Schrödinger operators defined by covariant
representations of the rotation algebra, a lower bound on phase-averaged transport in terms …

We study generalized fractal dimensions of measures, called the Hentschel–Procaccia
dimensions and the generalized Rényi dimensions. We consider compactly supported Borel …