We compare the Radon transform in its standard and symplectic formulations and argue that the analytical inversion of the latter is easier to perform.

If frequent measurements ascertain whether a quantum system is still in a given subspace, it remains in that subspace and a quantum Zeno effect takes place. The limiting time evolution within the projected subspace is called quantum Zeno dynamics. This phenomenon is related to the limit of a product formula obtained by intertwining the time evolution group with an orthogonal projection. By introducing a novel product formula, we will give a characterization of the quantum Zeno effect for finite-rank projections in terms of a spectral decay property of the Hamiltonian in the range of the projections. Moreover, we will also characterize its limiting quantum Zeno dynamics and exhibit its -- not necessarily bounded from below -- generator as a generalized mean value Hamiltonian.

We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed. The motion is a constant-speed interpolation of a symmetric random walk on the marked points. We study the quenched version of this process under the hypothesis that the distance between two neighboring marked points has finite mean—but possibly infinite variance—and prove the CLT and the convergence of all the accordingly rescaled moments. Thus, contrary to what is believed to hold for the annealed process, the quenched process is truly diffusive.

We consider the semiclassical limit for the Heisenberg- von Neumann equation with a potential which consists of the sum of a repulsive Coulomb potential, plus a Lipschitz potential whose gradient belongs to BV ; this assumption on the potential guarantees the well-posedness of the Liouville equation in the space of bounded integrable solutions. We find sufficient conditions on the initial data to ensure that the quantum dynamics converges to the classical one. More precisely, we consider the Husimi functions of the solution of the Heisenberg-von Neumann equation, and under suitable as- sumptions on the initial data we prove that they converge, as ε → 0, to the unique bounded solution of the Liouville equation (locally uniformly in time).

The evolution of a quantum system subjected to infinitely many measurements in a finite time interval is confined in a proper subspace of the Hilbert space. This phenomenon is called ‘quantum Zeno effect’: a particle under intensive observation which does not evolve. This effect is at variance with the classical evolution, which obviously is not affected by any observations. By a semiclassical analysis, we will show that the quantum Zeno effect vanishes at all orders, when the Planck constant tends to zero, and thus it is a purely quantum phenomenon without classical analog, at the same level of tunneling.

In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford–Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations.