14,880 research outputs found
Distribution of periodic points of polynomial diffeomorphisms of C^2
This paper deals with the dynamics of a simple family of holomorphic
diffeomorphisms of \C^2: the polynomial automorphisms. This family of maps
has been studied by a number of authors. We refer to [BLS] for a general
introduction to this class of dynamical systems. An interesting object from the
point of view of potential theory is the equilibrium measure of the set
of points with bounded orbits. In [BLS] is also characterized
dynamically as the unique measure of maximal entropy. Thus is also an
equilibrium measure from the point of view of the thermodynamical formalism. In
the present paper we give another dynamical interpretation of as the
limit distribution of the periodic points of
A study of preferences from nineteen selections in current children's literature.
Thesis (Ed.M.)--Boston Universit
Non-linear optomechanical measurement of mechanical motion
Precision measurement of non-linear observables is an important goal in all
facets of quantum optics. This allows measurement-based non-classical state
preparation, which has been applied to great success in various physical
systems, and provides a route for quantum information processing with otherwise
linear interactions. In cavity optomechanics much progress has been made using
linear interactions and measurement, but observation of non-linear mechanical
degrees-of-freedom remains outstanding. Here we report the observation of
displacement-squared thermal motion of a micro-mechanical resonator by
exploiting the intrinsic non-linearity of the radiation pressure interaction.
Using this measurement we generate bimodal mechanical states of motion with
separations and feature sizes well below 100~pm. Future improvements to this
approach will allow the preparation of quantum superposition states, which can
be used to experimentally explore collapse models of the wavefunction and the
potential for mechanical-resonator-based quantum information and metrology
applications.Comment: 8 pages, 4 figures, extensive supplementary material available with
published versio
Dephasing representation of quantum fidelity for general pure and mixed states
General semiclassical expression for quantum fidelity (Loschmidt echo) of
arbitrary pure and mixed states is derived. It expresses fidelity as an
interference sum of dephasing trajectories weighed by the Wigner function of
the initial state, and does not require that the initial state be localized in
position or momentum. This general dephasing representation is special in that,
counterintuitively, all of fidelity decay is due to dephasing and none due to
the decay of classical overlaps. Surprising accuracy of the approximation is
justified by invoking the shadowing theorem: twice--both for physical
perturbations and for numerical errors. It is shown how the general expression
reduces to the special forms for position and momentum states and for wave
packets localized in position or momentum. The superiority of the general over
the specialized forms is explained and supported by numerical tests for wave
packets, non-local pure states, and for simple and random mixed states. The
tests are done in non-universal regimes in mixed phase space where detailed
features of fidelity are important. Although semiclassically motivated, present
approach is valid for abstract systems with a finite Hilbert basis provided
that the discrete Wigner transform is used. This makes the method applicable,
via a phase space approach, e. g., to problems of quantum computation.Comment: 11 pages, 4 figure
Spin-polarized tunneling spectroscopy in tunnel junctions with half-metallic electrodes
We have studied the magnetoresistance (TMR) of tunnel junctions with
electrodes of La2/3Sr1/3MnO3 and we show how the variation of the conductance
and TMR with the bias voltage can be exploited to obtain a precise information
on the spin and energy dependence of the density of states. Our analysis leads
to a quantitative description of the band structure of La2/3Sr1/3MnO3 and
allows the determination of the gap delta between the Fermi level and the
bottom of the t2g minority spin band, in good agreement with data from
spin-polarized inverse photoemission experiments. This shows the potential of
magnetic tunnel junctions with half-metallic electrodes for spin-resolved
spectroscopic studies.Comment: To appear in Physical Review Letter
Crystal truncation rods in kinematical and dynamical x-ray diffraction theories
Crystal truncation rods calculated in the kinematical approximation are shown
to quantitatively agree with the sum of the diffracted waves obtained in the
two-beam dynamical calculations for different reflections along the rod. The
choice and the number of these reflections are specified. The agreement extends
down to at least of the peak intensity. For lower intensities,
the accuracy of dynamical calculations is limited by truncation of the electron
density at a mathematically planar surface, arising from the Fourier series
expansion of the crystal polarizability
Primary osteoblast-like cells from patients with end-stage kidney disease reflect gene expression, proliferation, and mineralization characteristics ex vivo.
Osteocytes regulate bone turnover and mineralization in chronic kidney disease. As osteocytes are derived from osteoblasts, alterations in osteoblast function may regulate osteoblast maturation, osteocytic transition, bone turnover, and skeletal mineralization. Thus, primary osteoblast-like cells were cultured from bone chips obtained from 24 pediatric ESKD patients. RNA expression in cultured cells was compared with RNA expression in cells from healthy individuals, to RNA expression in the bone core itself, and to parameters of bone histomorphometry. Proliferation and mineralization rates of patient cells were compared with rates in healthy control cells. Associations were observed between bone osteoid accumulation, as assessed by bone histomorphometry, and bone core RNA expression of osterix, matrix gla protein, parathyroid hormone receptor 1, and RANKL. Gene expression of osteoblast markers was increased in cells from ESKD patients and signaling genes including Cyp24A1, Cyp27B1, VDR, and NHERF1 correlated between cells and bone cores. Cells from patients with high turnover renal osteodystrophy proliferated more rapidly and mineralized more slowly than did cells from healthy controls. Thus, primary osteoblasts obtained from patients with ESKD retain changes in gene expression ex vivo that are also observed in bone core specimens. Evaluation of these cells in vitro may provide further insights into the abnormal bone biology that persists, despite current therapies, in patients with ESKD
Finite type approximations of Gibbs measures on sofic subshifts
Consider a H\"older continuous potential defined on the full shift
A^\nn, where is a finite alphabet. Let X\subset A^\nn be a specified
sofic subshift. It is well-known that there is a unique Gibbs measure
on associated to . Besides, there is a natural nested
sequence of subshifts of finite type converging to the sofic subshift
. To this sequence we can associate a sequence of Gibbs measures
. In this paper, we prove that these measures weakly converge
at exponential speed to (in the classical distance metrizing weak
topology). We also establish a strong mixing property (ensuring weak
Bernoullicity) of . Finally, we prove that the measure-theoretic
entropy of converges to the one of exponentially fast.
We indicate how to extend our results to more general subshifts and potentials.
We stress that we use basic algebraic tools (contractive properties of iterated
matrices) and symbolic dynamics.Comment: 18 pages, no figure
Thermodynamic phase transitions for Pomeau-Manneville maps
We study phase transitions in the thermodynamic description of
Pomeau-Manneville intermittent maps from the point of view of infinite ergodic
theory, which deals with diverging measure dynamical systems. For such systems,
we use a distributional limit theorem to provide both a powerful tool for
calculating thermodynamic potentials as also an understanding of the dynamic
characteristics at each instability phase. In particular, topological pressure
and Renyi entropy are calculated exactly for such systems. Finally, we show the
connection of the distributional limit theorem with non-Gaussian fluctuations
of the algorithmic complexity proposed by Gaspard and Wang [Proc. Natl. Acad.
Sci. USA 85, 4591 (1988)].Comment: 5 page
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