2,006 research outputs found
Congruences for Taylor expansions of quantum modular forms
Recently, a beautiful paper of Andrews and Sellers has established linear
congruences for the Fishburn numbers modulo an infinite set of primes. Since
then, a number of authors have proven refined results, for example, extending
all of these congruences to arbitrary powers of the primes involved. Here, we
take a different perspective and explain the general theory of such congruences
in the context of an important class of quantum modular forms. As one example,
we obtain an infinite series of combinatorial sequences connected to the
"half-derivatives" of the Andrews-Gordon functions and with Kashaev's invariant
on torus knots, and we prove conditions under which the sequences
satisfy linear congruences modulo at least of primes of primes
Dynamics of Holographic Entanglement Entropy Following a Local Quench
We discuss the behaviour of holographic entanglement entropy following a
local quench in 2+1 dimensional strongly coupled CFTs. The entanglement
generated by the quench propagates along an emergent light-cone, reminiscent of
the Lieb-Robinson light-cone propagation of correlations in non-relativistic
systems. We find the speed of propagation is bounded from below by the
entanglement tsunami velocity obtained earlier for global quenches in
holographic systems, and from above by the speed of light. The former is
realized for sufficiently broad quenches, while the latter pertains for well
localized quenches. The non-universal behavior in the intermediate regime
appears to stem from finite-size effects. We also note that the entanglement
entropy of subsystems reverts to the equilibrium value exponentially fast, in
contrast to a much slower equilibration seen in certain spin models.Comment: 27 pages, 12 figures. v2: added refs and fixed typos. v3: added
clarifications, published versio
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