435 research outputs found
Exceptional Points in a Non-Hermitian Topological Pump
We investigate the effects of non-Hermiticity on topological pumping, and
uncover a connection between a topological edge invariant based on topological
pumping and the winding numbers of exceptional points. In Hermitian lattices,
it is known that the topologically nontrivial regime of the topological pump
only arises in the infinite-system limit. In finite non-Hermitian lattices,
however, topologically nontrivial behavior can also appear. We show that this
can be understood in terms of the effects of encircling a pair of exceptional
points during a pumping cycle. This phenomenon is observed experimentally, in a
non-Hermitian microwave network containing variable gain amplifiers.Comment: 7 pages, 7 figures. The first author did the experiment, and the
second author did the theoretical stud
Computing matrix inversion with optical networks
With this paper we bring about a discussion on the computing potential of
complex optical networks and provide experimental demonstration that an optical
fiber network can be used as an analog processor to calculate matrix inversion.
A 3x3 matrix is inverted as a proof-of-concept demonstration using a fiber
network containing three nodes and operating at telecomm wavelength. For an NxN
matrix, the overall solving time (including setting time of the matrix elements
and calculation time of inversion) scales as O(N^2), whereas matrix inversion
by most advanced computer algorithms requires ~O(N^2.37) computational time.
For well-conditioned matrices, the error of the inversion performed optically
is found to be less than 3%, limited by the accuracy of measurement equipment.Comment: 5 page
Measurement of a topological edge invariant in a microwave network
We report on the measurement of topological invariants in an electromagnetic
topological insulator analog formed by a microwave network, consisting of the
winding numbers of scattering matrix eigenvalues. The experiment can be
regarded as a variant of a topological pump, with non-zero winding implying the
existence of topological edge states. In microwave networks, unlike most other
systems exhibiting topological insulator physics, the winding can be directly
observed. The effects of loss on the experimental results, and on the
topological edge states, is discussed.Comment: 10 pages, 10 figure
On radicals of module coalgebras
We introduce the notion of an idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of B-module coalgebras, then every B-module coalgebra contains a unique maximal B-submodule coalgebra in R. Moreover, a B-module coalgebra C is a member of R if, and only if, D B is in R for every simple subcoalgebra D of C. The collection of B-cocleft coalgebras and the collection of H-projective module coalgebras over a Hopf algebra H are idempotent radical classes. As applications, we use these idempotent radical classes to give another proofs for a projectivity theorem and a normal basis theorem of Schneider without assuming a bijective antipode. © 2007 Elsevier Ltd. All rights reserved
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