7,966 research outputs found
Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2
Transformations involving only local operations assisted with classical
communication are investigated for multipartite entangled pure states having
tensor rank 2. All necessary and sufficient conditions for the possibility of
deterministically converting truly multipartite, rank-2 states into each other
are given. Furthermore, a chain of local operations that successfully achieves
the transformation has been identified for all allowed transformations. The
identified chains have two nice features: (1) each party needs to carry out at
most one local operation and (2) all of these local operations are also
deterministic transformations by themselves. Finally, it is found that there
are disjoint classes of states, all of which can be identified by a single real
parameter, which remain invariant under deterministic transformations.Comment: 27 pages, 1 figure; added new references and improved the
presentatio
Elastic wave cloaking via symmetrized transformation media
Transformation media theory, which steers waves in solids via an effective
geometry induced by a refractive material (Fermat's principle of least action),
provides a means of controlling vibrations and elastic waves beyond the
traditional dissipative structures regime. In particular, it could be used to
create an elastic wave cloak, shielding an interior region against elastic
waves while simultaneously preventing scattering in the outside domain.
However, as a true elastic wave cloak would generally require nonphysical
materials with stiffness tensors lacking the minor symmetry (implying
asymmetric stress), the utility of such an elastic wave cloak has thus far been
limited. Here we develop a means of overcoming this limitation via the
development of a symmetrized elastic cloak, sacrificing some of the performance
of the perfect cloak for the sake of restoring the minor symmetry. We test the
performance of the symmetrized elastic cloak for shielding a tunnel against
seismic waves, showing that it can be used to reduce the average displacement
within the tunnel by an order of magnitude (and reduce energy by two orders of
magnitude) for waves above a critical frequency of the cloak. This critical
frequency, which corresponds to the generation of surface waves at the
cloak-interior interface, can be used to develop a simple heuristic model of
the symmetrized elastic cloak's performance for a generic problem
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