14,221 research outputs found
A note on entanglement entropy for topological interfaces in RCFTs
In this paper we calculate the entanglement entropy for topological
interfaces in rational conformal field theories for the case where the
interface lies at the boundary of the entangling interval and for the case
where it is located in the center of the entangling interval. We compare the
results to each other and also to the recently calculated left/right entropy of
a related BCFT. We also comment of the entanglement entropies for topological
interfaces for a free compactified boson and Liouville theory.Comment: 17 pages, pdflatex, 2 figures, v2: references added, typos corrected
and figure 2 improved, v3: minor correctio
Essential countability of treeable equivalence relations
We establish a dichotomy theorem characterizing the circumstances under which
a treeable Borel equivalence relation E is essentially countable. Under
additional topological assumptions on the treeing, we in fact show that E is
essentially countable if and only if there is no continuous embedding of E1
into E. Our techniques also yield the first classical proof of the analogous
result for hypersmooth equivalence relations, and allow us to show that up to
continuous Kakutani embeddability, there is a minimum Borel function which is
not essentially countable-to-one
Quantitative Determination of the Adiabatic Condition Using Force-Detected Nuclear Magnetic Resonance
The adiabatic condition governing cyclic adiabatic inversion of proton spins
in a micron-sized ammonium chloride crystal was studied using room temperature
nuclear magnetic resonance force microscopy. A systematic degradation of
signal-to-noise was observed as the adiabatic condition became violated. A
theory of adiabatic following applicable to cyclic adiabatic inversion is
reviewed and implemented to quantitatively determine an adiabaticity threshold
from our experimental results.Comment: 5 pages, 3 fig
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