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We study the nonstationary solutions of Fokker–Planck equations associated to either stationary or non stationary quantum states. In particular, we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows arbitrary evolutions ruled by these equations to account for controlled quantum transitions.… (More)

- Massimo Blasone, Fabio Dell’Anno, Silvio De Siena, Fabrizio Illuminati
- 2009

Flavor oscillations in elementary particle physics are related to multi-mode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in… (More)

- Fabio Dell’Anno, Silvio De Siena, Fabrizio Illuminati
- 2007

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum… (More)

The algebraic structure of Thermo Field Dynamics lies in the q-deformation of the algebra of creation and annihilation operators. Doubling of the degrees of freedom, tilde-conjugation rules, and Bogoliubov transformation for bosons and fermions are recognized as algebraic properties of hq(1) and of hq(1|1), respectively. PACS: 03.70.+k, 03.65.F, 11.10.-z

It is shown that uncertainty relations, as well as coherent and squeezed states, are structural properties of stochastic processes with Fokker-Planck dynamics. The quantum mechanical coherent and squeezed states are explicitly constructed via Nelson stochastic quantization. The method is applied to derive new minimum uncertainty states in time-dependent… (More)

We demonstrate that to all large scale cosmological structures where gravitation is the only overall relevant interaction assembling the system (e.g. galaxies), there is associated a characteristic unit of action per particle whose order of magnitude coincides with the Planck action constant h. This result extends the class of physical systems for which… (More)

We show that the characteristic sizes of astrophysical and cosmological structures, where gravity is the only overall relevant interaction assembling the system, have a phenomenological relation to the microscopic scales whose order of magnitude is essentially ruled by the Compton wavelength of the proton. This result agrees with the absence of screening… (More)

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the stochastic mechanics which produces time reversal invariant diffusion processes. In this paper we analyze the consequences of introducing the generalized Student laws, namely non-Gaussian, Lévy infinitely divisible (but not stable)… (More)

The formation of the beam halo in charged particle accelerators is studied in the framework of a stochastic-hydrodynamic model for the collective motion of the particle beam. In such a stochastichydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance.… (More)

We analyse the non-stationary solutions of the Fokker1Planck equations associated to quantum states by stochastic mechanics. In particular we study the exact solutions for the stationary states of the harmonic oscillator and the potentials which realize new possible evolutions ruled by the same equations. c © 1998 Published by Elsevier Science B.V.