A Modified Approach to Single-Spin Detection Using Magnetic Resonance Force Microscopy

The magnetic moment of a single spin interacting with a cantilever in magnetic resonance force microscopy (MRFM) experiences quantum jumps in orientation rather than smooth oscillations. These jumps cannot be detected by a conventional MRFM based on observation of driven resonant oscillations of a cantilever. In this paper, we propose a method which will allow detection of the magnetic signal from a single spin using a modification of a conventional MRFM. We estimate the opportunity to detect the magnetic signal from a single proton.Comment: 4 pages LaTex, 4 figures in GIF forma

On separable Fokker-Planck equations with a constant diagonal diffusion matrix

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe

Bound-States of the Spinless Salpeter Equation for the PT-Symmetric Generalized Hulthen Potential by the Nikiforov-Uvarov Method

The one-dimensional spinless Salpeter equation has been solved for the PT-symmetric generalized Hulth\'{e}n potential. The Nikiforov-Uvarov {NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthen potentials.Comment: 24 page

Alternative analysis to perturbation theory

We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function, additionally we can analyze the time evolution of the system. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained.Comment: 12 pages, no figure

Phase transitions on the surface of a carbon nanotube

A suspended carbon nanotube can act as a nanoscale resonator with remarkable electromechanical properties and the ability to detect adsorption on its surface at the level of single atoms. Understanding adsorption on nanotubes and other graphitic materials is key to many sensing and storage applications. Here we show that nanotube resonators offer a powerful new means of investigating fundamental aspects of adsorption on carbon, including the collective behaviour of adsorbed matter and its coupling to the substrate electrons. By monitoring the vibrational resonance frequency in the presence of noble gases, we observe the formation of monolayers on the cylindrical surface and phase transitions within these monolayers, and simultaneous modification of the electrical conductance. The monolayer observations also demonstrate the possibility of studying the fundamental behaviour of matter in cylindrical geometry.Comment: Unpublished; 7 pages with 4 figures plus 3 pages of supplementary materia

Optical extinction, refractive index, and multiple scattering for suspensions of interacting colloidal particles

We provide a general microscopic theory of the scattering cross-section and of the refractive index for a system of interacting colloidal particles, exact at second order in the molecular polarizabilities. In particular: a) we show that the structural features of the suspension are encoded into the forward scattered field by multiple scattering effects, whose contribution is essential for the so-called "optical theorem" to hold in the presence of interactions; b) we investigate the role of radiation reaction on light extinction; c) we discuss our results in the framework of effective medium theories, presenting a general result for the effective refractive index valid, whatever the structural properties of the suspension, in the limit of particles much larger than the wavelength; d) by discussing strongly-interacting suspensions, we unravel subtle anomalous dispersion effects for the suspension refractive index.Comment: Submitted to Journal of Chemical Physics 37 pages, 4 figure

Green functions and propagation of waves in strongly inhomogeneous media

We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of Green functions of operators with bounded coefficients. We discuss some consequences of such an anomalous short or long distance behaviour for a diffusion and wave propagation in an inhomogeneous medium

Hydrodynamic object recognition using pressure sensing

Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing