2,519 research outputs found
Scalable ultra-sensitive detection of heterogeneity via coupled bistable dynamics
We demonstrate how the collective response of globally coupled bistable
elements can strongly reflect the presence of very few non-identical elements
in a large array of otherwise identical elements. Counter-intuitively, when
there are a small number of elements with natural stable state different from
the bulk of the elements, {\em all} the elements of the system evolve to the
stable state of the minority due to strong coupling. The critical fraction of
distinct elements needed to produce this swing shows a sharp transition with
increasing , scaling as . Furthermore, one can find a global
bias that allows robust {\em one bit} sensitivity to heterogeneity.
Importantly, the time needed to reach the attracting state does not increase
with the system size. We indicate the relevance of this ultra-sensitive generic
phenomenon for massively parallelized search applications.Comment: 4 Pages, 4 Figure
Alternative Canonical Formalism for the Wess-Zumino-Witten Model
We study a canonical quantization of the Wess--Zumino--Witten (WZW) model
which depends on two integer parameters rather than one. The usual theory can
be obtained as a contraction, in which our two parameters go to infinity
keeping the difference fixed. The quantum theory is equivalent to a generalized
Thirring model, with left and right handed fermions transforming under
different representations of the symmetry group. We also point out that the
classical WZW model with a compact target space has a canonical formalism in
which the current algebra is an affine Lie algebra of non--compact type.
Also, there are some non--unitary quantizations of the WZW model in which
there is invariance only under half the conformal algebra (one copy of the
Virasoro algebra).Comment: 22 pages; UR-133
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