8,245 research outputs found
On uniform convergence of Fourier series
We consider the space of all continuous functions on the
circle with uniformly convergent Fourier series. We show that if
is a continuous piecewise linear but
not linear map, then
Sequential quantum-enhanced measurement with an atomic ensemble
We propose a quantum-enhanced iterative (with steps) measurement scheme
based on an ensemble of two-level probes which asymptotically approaches
the Heisenberg limit , the number of quantum
resources. The protocol is inspired by Kitaev's phase estimation algorithm and
involves only collective manipulation and measurement of the ensemble. The
iterative procedure takes the shot-noise limited primary measurement with
precision to increasingly precise results
. A straightforward implementation of the algorithm
makes use of a two-component atomic cloud of Bosons in the precision
measurement of a magnetic field.Comment: 5 pages, 1 figur
Size-independent Young's modulus of inverted conical GaAs nanowire resonators
We explore mechanical properties of top down fabricated, singly clamped
inverted conical GaAs nanowires. Combining nanowire lengths of 2-9 m with
foot diameters of 36-935 nm yields fundamental flexural eigenmodes spanning two
orders of magnitude from 200 kHz to 42 MHz. We extract a size-independent value
of Young's modulus of (453) GPa. With foot diameters down to a few tens of
nanometers, the investigated nanowires are promising candidates for
ultra-flexible and ultra-sensitive nanomechanical devices
Estimates in Beurling--Helson type theorems. Multidimensional case
We consider the spaces of functions on the
-dimensional torus such that the sequence of the Fourier
coefficients belongs to
. The norm on is defined by
. We study the rate of
growth of the norms as
for -smooth real
functions on (the one-dimensional case was investigated
by the author earlier). The lower estimates that we obtain have direct
analogues for the spaces
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