311 research outputs found
Nonparametric estimation of multivariate convex-transformed densities
We study estimation of multivariate densities of the form
for and for a fixed monotone function and an unknown
convex function . The canonical example is for ; in this case, the resulting class of densities [\mathcal
{P}(e^{-y})={p=\exp(-g):g is convex}] is well known as the class of log-concave
densities. Other functions allow for classes of densities with heavier
tails than the log-concave class. We first investigate when the maximum
likelihood estimator exists for the class for
various choices of monotone transformations , including decreasing and
increasing functions . The resulting models for increasing transformations
extend the classes of log-convex densities studied previously in the
econometrics literature, corresponding to . We then establish
consistency of the maximum likelihood estimator for fairly general functions
, including the log-concave class and many others. In
a final section, we provide asymptotic minimax lower bounds for the estimation
of and its vector of derivatives at a fixed point under natural
smoothness hypotheses on and . The proofs rely heavily on results from
convex analysis.Comment: Published in at http://dx.doi.org/10.1214/10-AOS840 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Domain wall motion in ferromagnetic nanowires driven by arbitrary time-dependent fields: An exact result
We address the dynamics of magnetic domain walls in ferromagnetic nanowires
under the influence of external time-dependent magnetic fields. We report a new
exact spatiotemporal solution of the Landau-Lifshitz-Gilbert equation for the
case of soft ferromagnetic wires and nanostructures with uniaxial anisotropy.
The solution holds for applied fields with arbitrary strength and time
dependence. We further extend this solution to applied fields slowly varying in
space and to multiple domain walls.Comment: 3 pages, 1 figur
Domain wall motion in thin ferromagnetic nanotubes: Analytic results
Dynamics of magnetization domain walls (DWs) in thin ferromagnetic nanotubes subject to weak longitudinal external fields is addressed analytically in the regimes of strong and weak penalization. Exact solutions for the DW profiles and formulas for the DW propagation velocity are derived in both regimes. In particular, the DW speed is shown to depend nonlinearly on the nanotube radius
Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents
We study fidelity decay in classically chaotic microwave billiards for a local, piston-like boundary perturbation. We experimentally verify a predicted non-monotonic cross-over from the Fermi Golden Rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation. In particular, we observe pronounced oscillations of the decay rate as a function of the piston position which quantitatively agree with corresponding theoretical results based on a refined semiclassical approach for local boundary perturbations
Influence of boundary conditions on quantum escape
It has recently been established that quantum statistics can play a crucial
role in quantum escape. Here we demonstrate that boundary conditions can be
equally important - moreover, in certain cases, may lead to a complete
suppression of the escape. Our results are exact and hold for arbitrarily many
particles.Comment: 6 pages, 3 figures, 1 tabl
Long-time saturation of the Loschmidt echo in quantum chaotic billiards
The Loschmidt echo (LE) (or fidelity) quantifies the sensitivity of the time
evolution of a quantum system with respect to a perturbation of the
Hamiltonian. In a typical chaotic system the LE has been previously argued to
exhibit a long-time saturation at a value inversely proportional to the
effective size of the Hilbert space of the system. However, until now no
quantitative results have been known and, in particular, no explicit expression
for the proportionality constant has been proposed. In this paper we perform a
quantitative analysis of the phenomenon of the LE saturation and provide the
analytical expression for its long-time saturation value for a semiclassical
particle in a two-dimensional chaotic billiard. We further perform extensive
(fully quantum mechanical) numerical calculations of the LE saturation value
and find the numerical results to support the semiclassical theory.Comment: 5 pages, 2 figure
Wave packet autocorrelation functions for quantum hard-disk and hard-sphere billiards in the high-energy, diffraction regime
We consider the time evolution of a wave packet representing a quantum
particle moving in a geometrically open billiard that consists of a number of
fixed hard-disk or hard-sphere scatterers. Using the technique of multiple
collision expansions we provide a first-principle analytical calculation of the
time-dependent autocorrelation function for the wave packet in the high-energy
diffraction regime, in which the particle's de Broglie wave length, while being
small compared to the size of the scatterers, is large enough to prevent the
formation of geometric shadow over distances of the order of the particle's
free flight path. The hard-disk or hard-sphere scattering system must be
sufficiently dilute in order for this high-energy diffraction regime to be
achievable. Apart from the overall exponential decay, the autocorrelation
function exhibits a generally complicated sequence of relatively strong peaks
corresponding to partial revivals of the wave packet. Both the exponential
decay (or escape) rate and the revival peak structure are predominantly
determined by the underlying classical dynamics. A relation between the escape
rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the
counterpart classical system, previously known for hard-disk billiards, is
strengthened by generalization to three spatial dimensions. The results of the
quantum mechanical calculation of the time-dependent autocorrelation function
agree with predictions of the semiclassical periodic orbit theory.Comment: 24 pages, 13 figure
Dzyaloshinskii-Moriya domain walls in magnetic nanotubes
We present an analytic study of domain-wall statics and dynamics in
ferromagnetic nanotubes with spin-orbit-induced Dzyaloshinskii-Moriya
interaction (DMI). Even at the level of statics, dramatic effects arise from
the interplay of space curvature and DMI: the domains become chirally twisted
leading to more compact domain walls. The dynamics of these chiral structures
exhibits several interesting features. Under weak applied currents, they
propagate without distortion. The dynamical response is further enriched by the
application of an external magnetic field: the domain wall velocity becomes
chirality-dependent and can be significantly increased by varying the DMI.
These characteristics allow for enhanced control of domain wall motion in
nanotubes with DMI, increasing their potential as information carriers in
future logic and storage devices.Comment: 7 pages, 7 figure
- …