17,093 research outputs found
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
An averaging method is applied to derive effective approximation to the
following singularly perturbed nonlinear stochastic damped wave equation \nu
u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain
\,, \,. Here is a small parameter
characterising the singular perturbation, and \,, \,, parametrises the strength of the noise. Some scaling transformations
and the martingale representation theorem yield the following effective
approximation for small , u_t=\D u+f(u)+\nu^\alpha\dot{W} to an error of
\ord{\nu^\alpha}\,.Comment: 16 pages. Submitte
Implementing optimal control pulse shaping for improved single-qubit gates
We employ pulse shaping to abate single-qubit gate errors arising from the
weak anharmonicity of transmon superconducting qubits. By applying shaped
pulses to both quadratures of rotation, a phase error induced by the presence
of higher levels is corrected. Using a derivative of the control on the
quadrature channel, we are able to remove the effect of the anharmonic levels
for multiple qubits coupled to a microwave resonator. Randomized benchmarking
is used to quantify the average error per gate, achieving a minimum of
0.007+/-0.005 using 4 ns-wide pulse.Comment: 4 pages, 4 figure
Robust Dropping Criteria for F-norm Minimization Based Sparse Approximate Inverse Preconditioning
Dropping tolerance criteria play a central role in Sparse Approximate Inverse
preconditioning. Such criteria have received, however, little attention and
have been treated heuristically in the following manner: If the size of an
entry is below some empirically small positive quantity, then it is set to
zero. The meaning of "small" is vague and has not been considered rigorously.
It has not been clear how dropping tolerances affect the quality and
effectiveness of a preconditioner . In this paper, we focus on the adaptive
Power Sparse Approximate Inverse algorithm and establish a mathematical theory
on robust selection criteria for dropping tolerances. Using the theory, we
derive an adaptive dropping criterion that is used to drop entries of small
magnitude dynamically during the setup process of . The proposed criterion
enables us to make both as sparse as possible as well as to be of
comparable quality to the potentially denser matrix which is obtained without
dropping. As a byproduct, the theory applies to static F-norm minimization
based preconditioning procedures, and a similar dropping criterion is given
that can be used to sparsify a matrix after it has been computed by a static
sparse approximate inverse procedure. In contrast to the adaptive procedure,
dropping in the static procedure does not reduce the setup time of the matrix
but makes the application of the sparser for Krylov iterations cheaper.
Numerical experiments reported confirm the theory and illustrate the robustness
and effectiveness of the dropping criteria.Comment: 27 pages, 2 figure
Muonium as a shallow center in GaN
A paramagnetic muonium (Mu) state with an extremely small hyperfine parameter
was observed for the first time in single-crystalline GaN below 25 K. It has a
highly anisotropic hyperfine structure with axial symmetry along the [0001]
direction, suggesting that it is located either at a nitrogen-antibonding or a
bond-centered site oriented parallel to the c-axis. Its small ionization energy
(=< 14 meV) and small hyperfine parameter (--10^{-4} times the vacuum value)
indicate that muonium in one of its possible sites produces a shallow state,
raising the possibility that the analogous hydrogen center could be a source of
n-type conductivity in as-grown GaN.Comment: 4 figures, to be published in Phys. Rev. Letter
Ricci flows with unbounded curvature
We show that any noncompact Riemann surface admits a complete Ricci flow
g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference
Non-local nuclear spin quieting in quantum dot molecules: Optically-induced extended two-electron spin coherence time
We demonstrate the extension of coherence between all four two-electron spin
ground states of an InAs quantum dot molecule (QDM) via non-local suppression
of nuclear spin fluctuations in both constituent quantum dots (QDs), while
optically addressing only the upper QD transitions. Long coherence times are
revealed through dark-state spectroscopy as resulting from nuclear spin locking
mediated by the exchange interaction between the QDs. Lineshape analysis
provides the first measurement of the quieting of the Overhauser field
distribution correlating with reduced nuclear spin fluctuations.Comment: Supplementary materials can be found on the publication page of our
website. http://research.physics.lsa.umich.edu/dst/Publications.htm
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