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.

Quantum finite W-algebras for gl_N

A major contribution to the theory of quantum finite W-algebras in type A comes from the work of J. Brundan and A. Kleshchev who, investigating the relationship between W-algebras and Yangians, achieved important results concerning both their structure and their representation theory. In this framework, for a quantum finite W-algebra in type A, associated to any nilpotent element and arbitrary good grading, A. De Sole, V. Kac and D. Valeri constructed a matrix of Yangian type L(z) which encodes its generators and relations, generalizing the results of the same authors for classical affine W-algebras. We can then express L(z) in a nicer form: when the good grading is associated to a pyramid that is aligned to the right or to the left, we use a recursive formula to explicitly construct a matrix W(z) which provides us with a finite set of generators for the W-algebra satisfying Premet's conditions, and prove that the matrix L(z) can be obtained as a generalized quasideterminant of W(z). Finally, we explain how to generalize these results to an arbitrary good grading (and an arbitrary choice of an isotropic subspace), using fundamental results about the structure of quantum finite W-algebras due to W.L. Gan and V. Ginzburg, and J. Brundan and S. Goodwin

Points. Lack thereof

I will discuss some aspects of the concept of "point" in quantum gravity, using mainly the tool of noncommutative geometry. I will argue that at Planck's distances the very concept of point may lose its meaning. I will then show how, using the spectral action and a high momenta expansion, the connections between points, as probed by boson propagators, vanish. This discussion follows closely [1] (Kurkov-Lizzi-Vassilevich Phys. Lett. B 731 (2014) 311, [arXiv:1312.2235 [hep-th]].Comment: Proceedings of the XXII Krakow Methodological Conference: Emergence of the Classical, Copernicus Centre, 11-12 October 2018. Mostly based on arXiv:1312.2235. V2 corrects several typo

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 $U_{g}/U_d\approx-0.2$