Quantum slow motion

We simulate the center of mass motion of cold atoms in a standing, amplitude modulated, laser field as an example of a system that has a classical mixed phase-space. We show a simple model to explain the momentum distribution of the atoms taken after any distinct number of modulation cycles. The peaks corresponding to a classical resonance move towards smaller velocities in comparison to the velocities of the classical resonances. We explain this by showing that, for a wave packet on the classical resonances, we can replace the complicated dynamics in the quantum Liouville equation in phase-space by the classical dynamics in a modified potential. Therefore we can describe the quantum mechanical motion of a wave packet on a classical resonance by a purely classical motion

Operations between sets in geometry

An investigation is launched into the fundamental characteristics of operations on and between sets, with a focus on compact convex sets and star sets (compact sets star-shaped with respect to the origin) in $n$-dimensional Euclidean space $\R^n$. For example, it is proved that if $n\ge 2$, with three trivial exceptions, an operation between origin-symmetric compact convex sets is continuous in the Hausdorff metric, GL(n) covariant, and associative if and only if it is $L_p$ addition for some $1\le p\le\infty$. It is also demonstrated that if $n\ge 2$, an operation * between compact convex sets is continuous in the Hausdorff metric, GL(n) covariant, and has the identity property (i.e., $K*\{o\}=K=\{o\}*K$ for all compact convex sets $K$, where $o$ denotes the origin) if and only if it is Minkowski addition. Some analogous results for operations between star sets are obtained. An operation called $M$-addition is generalized and systematically studied for the first time. Geometric-analytic formulas that characterize continuous and GL(n)-covariant operations between compact convex sets in terms of $M$-addition are established. The term "polynomial volume" is introduced for the property of operations * between compact convex or star sets that the volume of $rK*sL$, $r,s\ge 0$, is a polynomial in the variables $r$ and $s$. It is proved that if $n\ge 2$, with three trivial exceptions, an operation between origin-symmetric compact convex sets is continuous in the Hausdorff metric, GL(n) covariant, associative, and has polynomial volume if and only if it is Minkowski addition

Intrinsic volumes of random polytopes with vertices on the boundary of a convex body

Let $K$ be a convex body in $\R^d$, let $j\in\{1, ..., d-1\}$, and let $\varrho$ be a positive and continuous probability density function with respect to the $(d-1)$-dimensional Hausdorff measure on the boundary $\partial K$ of $K$. Denote by $K_n$ the convex hull of $n$ points chosen randomly and independently from $\partial K$ according to the probability distribution determined by $\varrho$. For the case when $\partial K$ is a $C^2$ submanifold of $\R^d$ with everywhere positive Gauss curvature, M. Reitzner proved an asymptotic formula for the expectation of the difference of the $j$th intrinsic volumes of $K$ and $K_n$, as $n\to\infty$. In this article, we extend this result to the case when the only condition on $K$ is that a ball rolls freely in $K$

Reentrant transitions in colloidal or dusty plasma bilayers

The phase diagram of crystalline bilayers of particles interacting via a Yukawa potential is calculated for arbitrary screening lengths and particle densities. Staggered rectangular, square, rhombic and triangular structures are found to be stable including a first-order transition between two different rhombic structures. For varied screening length at fixed density, one of these rhombic phases exhibits both a single and even a double reentrant transition. Our predictions can be verified experimentally in strongly confined charged colloidal suspensions or dusty plasma bilayers.Comment: 4 pages, 3 eps figs - revtex4. PRL - in pres

Role of interface coupling inhomogeneity in domain evolution in exchange bias

Models of exchange-bias in thin films have been able to describe various aspects of this technologically relevant effect. Through appropriate choices of free parameters the modelled hysteresis loops adequately match experiment, and typical domain structures can be simulated. However, the use of these parameters, notably the coupling strength between the systems' ferromagnetic (F) and antiferromagnetic (AF) layers, obscures conclusions about their influence on the magnetization reversal processes. Here we develop a 2D phase-field model of the magnetization process in exchange-biased CoO/(Co/Pt)xn that incorporates the 10 nm-resolved measured local biasing characteristics of the antiferromagnet. Just three interrelated parameters set to measured physical quantities of the ferromagnet and the measured density of uncompensated spins thus suffice to match the experiment in microscopic and macroscopic detail. We use the model to study changes in bias and coercivity caused by different distributions of pinned uncompensated spins of the antiferromagnet, in application-relevant situations where domain wall motion dominates the ferromagnetic reversal. We show the excess coercivity can arise solely from inhomogeneity in the density of biasing- and anti-biasing pinned uncompensated spins in the antiferromagnet. Counter to conventional wisdom, irreversible processes in the latter are not essential

Halbach arrays at the nanoscale from chiral spin textures

Mallinson's idea that some spin textures in planar magnetic structures could produce an enhancement of the magnetic flux on one side of the plane at the expense of the other gave rise to permanent magnet configurations known as Halbach magnet arrays. Applications range from wiggler magnets in particle accelerators and free electron lasers, to motors, to magnetic levitation trains, but exploiting Halbach arrays in micro- or nanoscale spintronics devices requires solving the problem of fabrication and field metrology below 100 {\mu}m size. In this work we show that a Halbach configuration of moments can be obtained over areas as small as 1 x 1 {\mu}m^2 in sputtered thin films with N\'eel-type domain walls of unique domain wall chirality, and we measure their stray field at a controlled probe-sample distance of 12.0 x 0.5 nm. Because here chirality is determined by the interfacial Dyzaloshinkii-Moriya interaction the field attenuation and amplification is an intrinsic property of this film, allowing for flexibility of design based on an appropriate definition of magnetic domains. 100 nm-wide skyrmions illustrate the smallest kind of such structures, for which our measurement of stray magnetic fields and mapping of the spin structure shows they funnel the field toward one specific side of the film given by the sign of the Dyzaloshinkii-Moriya interaction parameter D.Comment: 12 pages, 4 figure

Stability of the reverse Blaschke–Santaló inequality for zonoids and applications

AbstractAn important GL(n) invariant functional of centred (origin symmetric) convex bodies that has received particular attention is the volume product. For a centred convex body A⊂Rn it is defined by P(A):=|A|⋅|A∗|, where |⋅| denotes volume and A∗ is the polar body of A. If A is a centred zonoid, then it is known that P(A)⩾P(Cn), where Cn is a centred affine cube, i.e. a Minkowski sum of n linearly independent centred segments. Equality holds in the class of centred zonoids if and only if A is a centred affine cube. Here we sharpen this uniqueness statement in terms of a stability result by showing in a quantitative form that the Banach–Mazur distance of a centred zonoid A from a centred affine cube is small if P(A) is close to P(Cn). This result is then applied to strengthen a uniqueness result in stochastic geometry

Intestinal current measurements to diagnose cystic fibrosis

AbstractElectrophysiological techniques are essential for the diagnosis of cystic fibrosis. In the past ten years intestinal current measurements has emerged as valuable tool for this purpose. This overview highlights the objectives, methodology and current protocols to diagnose cystic fibrosis by intestinal current measurement on rectal biopsies