Nicola Cufaro Petroni

Stochastic collective dynamics of charged-particle beams in the stability regime

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time-reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by lambda(c)sqrt[N], where N is the number of particles in the beam and lambda(c) the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schrödinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so-called quantum-like approaches to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.

Stochastic-hydrodynamic model of halo formation in charged particle beams

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 stochastic- hydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance. This leads to a linearized theory that describes the collective dynamics of the beam in terms of a classical Schrodinger equation. Taking into account space-charge effects, we derive a set of coupled nonlinear hydrodynamic equations. These equations define a collective dynamics of self-interacting systems much in the same spirit as in the Gross-Pitaevskii and Landau-Ginzburg theories of the collective dynamics for interacting quantum many-body systems. Self-consistent solutions of the dynamical equations lead to quasistationary beam configurations with enhanced transverse dispersion and transverse emittance growth. In the limit of a frozen space-charge core it is then possible to determine and study the properties of stationary, stable core-plus-halo beam distributions. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution.

Controlled quantum evolutions and transitions

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. As a first signficant application we present a detailed treatment of the transition probabilities and of the controlling time-dependent potentials associated to the transitions between the stationary, the coherent, and the squeezed states of the harmonic oscillator.

Entangled states in stochastic mechanics

An axiomatization of the core part of stochastic mechanics (SM) is proposed and this scheme is discussed as a hidden variables theory. We work out in detail an example with entanglement and rigorously prove that SM and quantum mechanics agree in predicting all the observed correlations at different times.

Lévy–Schrödinger wave packets

We analyze the time--dependent solutions of the pseudo--differential Levy--Schrodinger wave equation in the free case, and we compare them with the associated Levy processes. We list the principal laws used to describe the time evolutions of both the Levy process densities, and the Levy--Schrodinger wave packets. To have self--adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible Levy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the Levy--Schrodinger wave packets, and in particular of the bi-modality arising in their evolutions: a feature at variance with the typical diffusive uni--modality of both the Levy process densities, and the usual Schrodinger wave functions.

Remarks on Observed Superluminal Light Propagation

A recent experiment [1] shows evidence for strong superluminal group and energy propagation, albeit not for superluminal signal velocity, in light pulses. A few remarks are in order about its implications on the quantum theory of light.

DYNAMICAL CONTROL OF THE HALO IN PARTICLE BEAMS: A STOCHASTIC HYDRODYNAMIC APPROACH

In this paper we describe the beam distribution in particle accelerators in the framework of a stochastic{hydrodynamic scheme. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution. The relaxation time toward the halo is estimated, and a few examples of controlled transitions toward a permanent halo elimination are discussed.

MASS SPECTRUM FROM STOCHASTIC LÉVY-SCHRÖDINGER RELATIVISTIC EQUATIONS: POSSIBLE QUALITATIVE PREDICTIONS IN QCD

Starting from the relation between the kinetic energy of a free Levy–Schrodinger particle and the logarithmic characteristic of the underlying stochastic process, we show that it is possible to get a precise relation between renormalizable field theories and a specific Levy process. This subsequently leads to a particular cutoff in the perturbative diagrams and can produce a phenomenological mass spectrum that allows an interpretation of quarks and leptons distributed in the three families of the standard model.