Sampling Distributions of Random Electromagnetic Fields in Mesoscopic or Dynamical Systems

We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or static statistically inhomogeneous. The results allow for the estimation of field statistics and confidence intervals when a single spatial or temporal stochastic process produces randomization of the field. Results for both coherent and incoherent detection techniques are derived, for Cartesian, planar and full-vectorial fields. We show that the functional form of the sampling pdf depends on whether the random variable is dimensioned (e.g., the sampled electric field proper) or is expressed in dimensionless standardized or normalized form (e.g., the sampled electric field divided by its sampled standard deviation). For dimensioned quantities, the electric field, its amplitude and intensity exhibit different types of Bessel $K$ sampling pdfs, which differ significantly from the asymptotic Gauss normal and $\chi^{(2)}_{2p}$ ensemble pdfs when $\nu$ is relatively small. By contrast, for the corresponding standardized quantities, Student $t$, Fisher-Snedecor $F$ and root-$F$ sampling pdfs are obtained that exhibit heavier tails than comparable Bessel $K$ pdfs. Statistical uncertainties obtained from classical small-sample theory for dimensionless quantities are shown to be overestimated compared to dimensioned quantities. Differences in the sampling pdfs arising from de-normalization versus de-standardization are obtained.Comment: 12 pages, 15 figures, accepted for publication in Phys. Rev. E, minor typos correcte

Semiclassical dynamics of a spin-1/2 in an arbitrary magnetic field

The spin coherent state path integral describing the dynamics of a spin-1/2-system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical approximation leads to a continuous minimal action path with jumps at the endpoints. The resulting semiclassical propagator is shown to coincide with the exact quantum mechanical propagator. A non-linear transformation of the angle variables allows for a determination of the semiclassical path and the jumps without solving a boundary-value problem. The semiclassical spin dynamics is thus readily amenable to numerical methods.Comment: 16 pages, submitted to Journal of Physics

Strings with Negative Stiffness and Hyperfine Structure

We propose a new string model by adding a higher-order gradient term to the rigid string, so that the stiffness can be positive or negative without loosing stability. In the large-D approximation, the model has three phases, one of which with a new type of generalized "antiferromagnetic" orientational correlations. We find an infrared-stable fixed point describing world-sheets with vanishing tension and Hausdorff dimension D_H=2. Crumpling is prevented by the new term which suppresses configurations with rapidly changing extrinsic curvature.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re27

Photon mixing in universes with large extra-dimensions

In presence of a magnetic field, photons can mix with any particle having a two-photon vertex. In theories with large compact extra-dimensions, there exists a hierachy of massive Kaluza-Klein gravitons that couple to any photon entering a magnetic field. We study this mixing and show that, in comparison with the four dimensional situation where the photon couples only to the massless graviton, the oscillation effect may be enhanced due to the existence of a large number of Kaluza-Klein modes. We give the conditions for such an enhancement and then investigate the cosmological and astrophysical consequences of this phenomenon; we also discuss some laboratory experiments. Axions also couple to photons in the same way; we discuss the effect of the existence of bulk axions in universes with large extra-dimensions. The results can also be applied to neutrino physics with extra-dimensions.Comment: 41 pages, LaTex, 6 figure