Radiation Damping and Quantum Excitation for Longitudinal Charged Particle Dynamics in the Thermal Wave Model

On the basis of the recently proposed {\it Thermal Wave Model (TWM) for particle beams}, we give a description of the longitudinal charge particle dynamics in circular accelerating machines by taking into account both radiation damping and quantum excitation (stochastic effect), in presence of a RF potential well. The longitudinal dynamics is governed by a 1-D Schr\"{o}dinger-like equation for a complex wave function whose squared modulus gives the longitudinal bunch density profile. In this framework, the appropriate {\it r.m.s. emittance} scaling law, due to the damping effect, is naturally recovered, and the asymptotic equilibrium condition for the bunch length, due to the competition between quantum excitation (QE) and radiation damping (RD), is found. This result opens the possibility to apply the TWM, already tested for protons, to electrons, for which QE and RD are very important.Comment: 10 pages, plain LaTeX; published in Phys. Lett. A194 (1994) 113-11

Investigation of the transverse beam dynamics in the thermal wave model with a functional method

We investigated the transverse beam dynamics in a thermal wave model by using a functional method. It can describe the beam optical elements separately with a kernel for a component. The method can be applied to general quadrupole magnets beyond a thin lens approximation as well as drift spaces. We found that the model can successfully describe the PARMILA simulation result through an FODO lattice structure for the Gaussian input beam without space charge effects.Comment: 12 pages, 6 figure

Full Phase-Space Analysis of Particle Beam Transport in the Thermal Wave Model

Within the Thermal Wave Model framework a comparison among Wigner function, Husimi function, and the phase-space distribution given by a particle tracking code is made for a particle beam travelling through a linear lens with small aberrations. The results show that the quantum-like approach seems to be very promising.Comment: 15 pages, plain LaTeX, + 3 uuencoded figures, to be published in Phys. Lett.

Geometric phases of water waves

Recently, Banner et al. (2014) highlighted a new fundamental property of open ocean wave groups, the so-called crest slowdown. For linear narrowband waves, this is related to the geometric and dynamical phase velocities $U_d$ and $U_g$ associated with the parallel transport through the principal fiber bundle of the wave motion with $\mathit{U}(1)$ symmetry. The theoretical predictions are shown to be in fair agreement with ocean field observations, from which the average crest speed $c=U_d+U_g$ with $c/U_d\approx0.8$ and $U_{g}/U_d\approx-0.2$

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Dimensional Deception from Noncommutative Tori: An alternative to Horava-Lifschitz

We study the dimensional aspect of the geometry of quantum spaces. Introducing a physically motivated notion of the scaling dimension, we study in detail the model based on a fuzzy torus. We show that for a natural choice of a deformed Laplace operator, this model demonstrates quite non-trivial behaviour: the scaling dimension flows from 2 in IR to 1 in UV. Unlike another model with the similar property, the so-called Horava-Lifshitz model, our construction does not have any preferred direction. The dimension flow is rather achieved by a rearrangement of the degrees of freedom. In this respect the number of dimensions is deceptive. Some physical consequences are discussed.Comment: 20 pages + extensive appendix. 3 figure

Matrix Bases for Star Products: a Review

We review the matrix bases for a family of noncommutative $\star$ products based on a Weyl map. These products include the Moyal product, as well as the Wick-Voros products and other translation invariant ones. We also review the derivation of Lie algebra type star products, with adapted matrix bases. We discuss the uses of these matrix bases for field theory, fuzzy spaces and emergent gravity

Quantum corrected electron holes

The theory of electron holes is extended into the quantum regime. The Wigner--Poisson system is solved perturbatively based in lowest order on a weak, standing electron hole. Quantum corrections are shown to lower the potential amplitude and to increase the number of deeply trapped electrons. They, hence, tend to bring this extreme non--equilibrium state closer to thermodynamic equilibrium, an effect which can be attributed to the tunneling of particles in this mixed state system.Comment: 12 pages, 3 figure

Projective Systems of Noncommutative Lattices as a Pregeometric Substratum

We present an approximation to topological spaces by {\it noncommutative} lattices. This approximation has a deep physical flavour based on the impossibility to fully localize particles in any position measurement. The original space being approximated is recovered out of a projective limit.Comment: 30 pages, Latex. To appear in `Quantum Groups and Fundamental Physical Applications', ISI Guccia, Palermo, December 1997, D. Kastler and M. Rosso Eds., (Nova Science Publishers, USA

Scaling Limits for Multispecies Statistical Mechanics Mean-Field Models

We study the limiting thermodynamic behavior of the normalized sums of spins in multi-species Curie-Weiss models. We find sufficient conditions for the limiting random vector to be Gaussian (or to have an exponential distribution of higher order) and compute the covariance matrix in terms of model parameters.Comment: 21 page