Scaling analyses based on wavelet transforms for the Talbot effect

The fractal properties of the transverse Talbot images are analysed with two well-known scaling methods, the wavelet transform modulus maxima (WTMM) and the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). We use the widths of the singularity spectra, Delta alpha=alpha_H-alpha_min, as a characteristic feature of these Talbot images. The tau scaling exponents of the q moments are linear in q within the two methods, which proves the monofractality of the transverse diffractive paraxial field in the case of these imagesComment: 9 pages, 6 figures, version accepted at Physica

Supersymmetric Fokker-Planck strict isospectrality

I report a study of the nonstationary one-dimensional Fokker-Planck solutions by means of the strictly isospectral method of supesymmetric quantum mechanics. The main conclusion is that this technique can lead to a space-dependent (modulational) damping of the spatial part of the nonstationary Fokker-Planck solutions, which I call strictly isospectral damping. At the same time, using an additive decomposition of the nonstationary solutions suggested by the strictly isospectral procedure and by an argument of Englefield [J. Stat. Phys. 52, 369 (1988)], they can be normalized and thus turned into physical solutions, i.e., Fokker-Planck probability densities. There might be applications to many physical processes during their transient periodComment: revised version, scheduled for PRE 56 (1 August 1997) as a B

Signatures of the Unruh effect from electrons accelerated by ultra-strong laser fields

We calculate the radiation resulting from the Unruh effect for strongly accelerated electrons and show that the photons are created in pairs whose polarizations are maximally entangled. Apart from the photon statistics, this quantum radiation can further be discriminated from the classical (Larmor) radiation via the different spectral and angular distributions. The signatures of the Unruh effect become significant if the external electromagnetic field accelerating the electrons is not too far below the Schwinger limit and might be observable with future facilities. Finally, the corrections due to the birefringent nature of the QED vacuum at such ultra-high fields are discussed. PACS: 04.62.+v, 12.20.Fv, 41.60.-m, 42.25.Lc.Comment: 4 pages, 1 figur

Ermakov Systems with Multiplicative Noise

Using the Euler-Maruyama numerical method, we present calculations of the Ermakov-Lewis invariant and the dynamic, geometric, and total phases for several cases of stochastic parametric oscillators, including the simplest case of the stochastic harmonic oscillator. The results are compared with the corresponding numerical noiseless cases to evaluate the effect of the noise. Besides, the noiseless cases are analytic and their analytic solutions are briefly presented. The Ermakov-Lewis invariant is not affected by the multiplicative noise in the three particular examples presented in this work, whereas there is a shift effect in the case of the phasesComment: 12 pages, 4 figures, 22 reference