Generation of rectangular optical waves by relativistic clipping

Theoretical results are reported, concerning the reflection and transmission of few-cycle laser pulses on a very thin conducting layer, which may represent the surface current density of the massless charges of graphene. It is shown that the pulse may undergo violent distortions, even at moderate intensities, to that extent, that the scattered radiation contains rectangular trains, which are approximate realizations of Rademacher functions in the optical or terahertz regime.Comment: 10 pages, 3 figures. Talk 2.7.5 presented at Seminar 2 of the 21th International Laser Physics Workshop (LPHYS'12) July 23-27, 2012, Calgary, Canada. The present manuscript is ment to be associated to the Proceedings of LPHYS'1

A study on black-body radiation: classical and binary photons

The present study gives a detailed analysis of the black-body radiation based on classical random variables. It is shown that the energy of a mode of a chaotic radiation field (Gauss variable) can be uniquely decomposed into a sum of a discrete variable (Planck variable having the Planck-Bose distribution) and a continuous dark variable (with a truncated exponential distribution of finite support). The Planck variable is decomposed, on one hand, into a sum of binary variables representing the binary photons of energies 2^s*h*nu with s=0,1,2,etc. In this way the black-body radiation can be viewed as a mixture of thermodinamically independent fermion gases. The Planck variable can also be decomposed into a sum of independent Poisson components representing the classical photo-molecules of energies m*h*nu with m=1,2,3,etc. These classical photons have only particle-like fluctuations, on the other hand, the binary photons have wave-particle fluctuations of fermionic character.Comment: 20 page

Isotope separation using tuned laser and electron beam

The apparatus comprises means for producing an atomic beam containing the isotope of interest and other isotopes. Means are provided for producing a magnetic field traversing the path of the atomic beam of an intensity sufficient to broaden the energy domain of the various individual magnetic sublevels of the isotope of interest and having the atomic beam passing therethrough. A laser beam is produced of a frequency and polarization selected to maximize the activation of only individual magnetic sublevels of the isotope of interest with the portion of its broadened energy domain most removed from other isotopes with the stream. The laser beam is directed so as to strike the atomic beam within the magnetic field and traverse the path of the atomic beam whereby only the isotope of interest is activated by the laser beam. The apparatus further includes means for producing a collimated and high intensity beam of electrons of narrow energy distribution within the magnetic field which is aimed so as to strike the atomic beam while the atomic beam is simultaneously struck by the laser beam and at an energy level selected to ionize the activated isotope of interest but not ground state species included therewith. Deflection means are disposed in the usual manner to collect the ions

On Certain Arithmetic Functions

In the recent book there appear certain arithmetic functions which are similar to the Smarandache function. In a recent paper we have considered certain generalization or duals of the Smarandache function. In this note we wish to point out that the arithmetic functions introduced all are particular cases of our function Fj, defined in the following manner

Lectures on renormalization and asymptotic safety

A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross-Neveu model, the nonlinear $\sigma$ model, the sine-Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behaviorof the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase whichcreates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method.Comment: 34 pages, 21 figures. Based on the talk presented at the Theoretical Physics School on Quantum Gravity, Szeged, Hungary, 27-31 August 2012. Final version, to appear in Annals of Physic

On certain new inequalities and limits for the Smarandache function

On certain new inequalities and limits for the Smarandache function