157 research outputs found
Positive Liouville theorems and asymptotic behavior for p-Laplacian type elliptic equations with a Fuchsian potential
We study positive Liouville theorems and the asymptotic behavior of positive
solutions of p-Laplacian type elliptic equations of the form Q'(u):= -
pLaplace(u) + V |u|^{p-2} u = 0 in X, where X is a domain in R^d, d > 1, and
1<p<infty. We assume that the potential V has a Fuchsian type singularity at a
point zeta, where either zeta=infty and X is a truncated C^2-cone, or zeta=0
and zeta is either an isolated point of a boundary of X or belongs to a
C^2-portion of the boundary of X.Comment: 39 pages. Stronger results in the radial case, other results and
conclusions are unchanged, considerable restructuring of the paper,
introduction is modified, typos corrected, references adde
Bayesian quantum frequency estimation in presence of collective dephasing
We advocate a Bayesian approach to optimal quantum frequency estimation - an
important issue for future quantum enhanced atomic clock operation. The
approach provides a clear insight into the interplay between decoherence and
the extent of the prior knowledge in determining the optimal interrogation
times and optimal estimation strategies. We propose a general framework capable
of describing local oscillator noise as well as additional collective atomic
dephasing effects. For a Gaussian noise the average Bayesian cost can be
expressed using the quantum Fisher information and thus we establish a direct
link between the two, often competing, approaches to quantum estimation theoryComment: 15 pages, 3 figure
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