32,806 research outputs found
Detecting topology change via correlations and entanglement from gauge/gravity correspondence
We compute a momentum space version of the entanglement spectrum and
entanglement entropy of general Young tableau states, and one-point functions
on Young tableau states. These physical quantities are used to measure the
topology of the dual spacetime geometries in the context of gauge/gravity
correspondence. The idea that Young tableau states can be obtained by
superposing coherent states is explicitly verified. In this quantum
superposition, a topologically distinct geometry is produced by superposing
states dual to geometries with a trivial topology. Furthermore we have a
refined bound for the overlap between coherent states and the rectangular Young
tableau state, by using the techniques of symmetric groups and representations.
This bound is exponentially suppressed by the total edge length of the Young
tableau. It is also found that the norm squared of the overlaps is bounded
above by inverse powers of the exponential of the entanglement entropies. We
also compute the overlaps between Young tableau states and other states
including squeezed states and multi-mode entangled states which have
similarities with those appeared in quantum information theory.Comment: 48 pages. version in Journal of Mathematical Physic
Positivity properties of Jacobi-Stirling numbers and generalized Ramanujan polynomials
Generalizing recent results of Egge and Mongelli, we show that each diagonal
sequence of the Jacobi-Stirling numbers \js(n,k;z) and \JS(n,k;z) is a
P\'olya frequency sequence if and only if and study the
-total positivity properties of these numbers. Moreover, the polynomial
sequences \biggl\{\sum_{k=0}^n\JS(n,k;z)y^k\biggr\}_{n\geq 0}\quad \text{and}
\quad \biggl\{\sum_{k=0}^n\js(n,k;z)y^k\biggr\}_{n\geq 0} are proved to be
strongly -log-convex. In the same vein, we extend a recent result of
Chen et al. about the Ramanujan polynomials to Chapoton's generalized Ramanujan
polynomials. Finally, bridging the Ramanujan polynomials and a sequence arising
from the Lambert function, we obtain a neat proof of the unimodality of the
latter sequence, which was proved previously by Kalugin and Jeffrey.Comment: 17 pages, 2 tables, the proof of Lemma 3.3 is corrected, final
version to appear in Advances in Applied Mathematic
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