Fluorescence antibunching microscopy

Breaking the diffraction limit in microscopy by utilizing quantum properties of light has been the goal of intense research in the recent years. We propose a quantum superresolution technique based on non-classical emission statistics of fluorescent markers, routinely used as contrast labels for bio-imaging. The technique can be readily implemented using standard fluorescence microscopy equipment

Could the classical relativistic electron be a strange attractor?

We review the formulation of the problem of the electromagnetic self-interaction of a relativistic charged particle in the framework of the manifestly covariant classical mechanics of Stueckelberg, Horwitz and Piron. The gauge fields of this theory, in general, cause the mass of the particle to change. We show that the non-linear Lorentz force equation for the self-interaction resulting from the expansion of the Green's function has chaotic solutions. We study the autonomous equation for the off-shell particle mass here, for which the effective charged particle mass achieves a macroscopic average value determined by what appears to be a strange attractor.Comment: 19 pages PLain TeX, 1 page Captions, 18 figure (.eps files

Eikonal Approximation to 5D Wave Equations as Geodesic Motion in a Curved 4D Spacetime

We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the symplectic structure of the corresponding mechanics. We then apply an analogous method to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics to demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. Finally we discuss the case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg-Schr\"odinger equation. This construction provides a model for an underlying quantum mechanical structure for classical dynamical motion along geodesics on a pseudo-Riemannian manifold. The locally symplectic structure which emerges is that of Stueckelberg's covariant mechanics on this manifold.Comment: TeX file. 17 pages. Rewritten for clarit

Stripes Disorder and Correlation lengths in doped antiferromagnets

For stripes in doped antiferromagnets, we find that the ratio of spin and charge correlation lenghts, $\xi_{s}/\xi_{c}$, provide a sharp criterion for determining the dominant form of disorder in the system. If stripes disorder is controlled by topological defects then $\xi_{s}/\xi_{c}\lesssim 1$. In contast, if stripes correlations are disordered primarily by non-topological elastic deformations (i.e., a Bragg-Glass type of disorder) then $1<\xi _{s}/\xi_{c}\lesssim 4$ is expected. Therefore, the observation of $\xi _{s}/\xi_{c}\approx 4$ in $(LaNd)_{2-x}Sr_{x}CuO_{4}$ and $\xi_{s}/\xi _{c}\approx 3$ in $La_{2/3}Sr_{1/3}NiO_{4}$ invariably implies that the stripes are in a Bragg glass type state, and topological defects are much less relevant than commonly assumed. Expected spectral properties are discussed. Thus, we establish the basis for any theoretical analysis of the experimentally obsereved glassy state in these material.Comment: 4 pages, 2 figure

Contact Line Instability and Pattern Selection in Thermally Driven Liquid Films

Liquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability of the flow can be altered, or patterns selected, using feedback control. We show that thermal perturbations of certain spatial structure imposed behind the contact line and proportional to the deviation of the contact line from its mean position can completely suppress the instability. Due to the presence of mean flow and a spatially nonuniform nature of spreading liquid films the dynamics of disturbances is governed by a nonnormal evolution operator, opening up a possibility of transient amplification and nonlinear instabilities. We show that in the case of thermal driving the nonnormality can be significant, especially for small wavenumber disturbances, and trace the origin of transient amplification to a close alignment of a large group of eigenfunctions of the evolution operator. However, for values of noise likely to occur in experiments we find that the transient amplification is not sufficiently strong to either change the predictions of the linear stability analysis or invalidate the proposed control approach.Comment: 13 pages, 14 figure