9,287 research outputs found
Transmission eigenvalues and thermoacoustic tomography
The spectrum of the interior transmission problem is related to the unique
determination of the acoustic properties of a body in thermoacoustic imaging.
Under a non-trapping hypothesis, we show that sparsity of the interior
transmission spectrum implies a range separation condition for the
thermoacoustic operator. In odd dimension greater than or equal to three, we
prove that the transmission spectrum for a pair of radially symmetric
non-trapping sound speeds is countable, and conclude that the ranges of the
associated thermoacoustic maps have only trivial intersection
Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions
We give explicit numerical values with 100 decimal digits for the Mertens
constant involved in the asymptotic formula for and, as a by-product, for the Meissel-Mertens constant
defined as , for , ...,
and .Comment: 12 pages, 6 table
The longest excursion of stochastic processes in nonequilibrium systems
We consider the excursions, i.e. the intervals between consecutive zeros, of
stochastic processes that arise in a variety of nonequilibrium systems and
study the temporal growth of the longest one l_{\max}(t) up to time t. For
smooth processes, we find a universal linear growth \simeq
Q_{\infty} t with a model dependent amplitude Q_\infty. In contrast, for
non-smooth processes with a persistence exponent \theta, we show that <
l_{\max}(t) > has a linear growth if \theta
\sim t^{1-\psi} if \theta > \theta_c. The amplitude Q_{\infty} and the exponent
\psi are novel quantities associated to nonequilibrium dynamics. These
behaviors are obtained by exact analytical calculations for renewal and
multiplicative processes and numerical simulations for other systems such as
the coarsening dynamics in Ising model as well as the diffusion equation with
random initial conditions.Comment: 4 pages,2 figure
Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
The representation theory of the Drinfeld doubles of dihedral groups is used
to solve the Yang-Baxter equation. Use of the 2-dimensional representations
recovers the six-vertex model solution. Solutions in arbitrary dimensions,
which are viewed as descendants of the six-vertex model case, are then obtained
using tensor product graph methods which were originally formulated for quantum
algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure
Grothendieck's constant and local models for noisy entangled quantum states
We relate the nonlocal properties of noisy entangled states to Grothendieck's
constant, a mathematical constant appearing in Banach space theory. For
two-qubit Werner states \rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}, we show
that there is a local model for projective measurements if and only if , where is Grothendieck's constant of order 3. Known bounds
on prove the existence of this model at least for ,
quite close to the current region of Bell violation, . We
generalize this result to arbitrary quantum states.Comment: 6 pages, 1 figur
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