3,001 research outputs found
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 -dimensional
Euclidean space . For example, it is proved that if , 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 addition for some . It is also
demonstrated that if , an operation * between compact convex sets is
continuous in the Hausdorff metric, GL(n) covariant, and has the identity
property (i.e., for all compact convex sets , where
denotes the origin) if and only if it is Minkowski addition. Some analogous
results for operations between star sets are obtained. An operation called
-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 -addition are
established. The term "polynomial volume" is introduced for the property of
operations * between compact convex or star sets that the volume of ,
, is a polynomial in the variables and . It is proved that if
, 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 be a convex body in , let , and let
be a positive and continuous probability density function with
respect to the -dimensional Hausdorff measure on the boundary of . Denote by the convex hull of points chosen randomly and
independently from according to the probability distribution
determined by . For the case when is a submanifold
of with everywhere positive Gauss curvature, M. Reitzner proved an
asymptotic formula for the expectation of the difference of the th intrinsic
volumes of and , as . In this article, we extend this
result to the case when the only condition on is that a ball rolls freely
in
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
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