10,675 research outputs found
A strong operator topology adiabatic theorem
We prove an adiabatic theorem for the evolution of spectral data under a weak
additive perturbation in the context of a system without an intrinsic time
scale. For continuous functions of the unperturbed Hamiltonian the convergence
is in norm while for a larger class functions, including the spectral
projections associated to embedded eigenvalues, the convergence is in the
strong operator topology.Comment: 15 pages, no figure
Integrable RCS as a proposed replacement for Fermilab Booster
Integrable optics is an innovation in particle accelerator design that
potentially enables a greater betatron tune spread and damps collective
instabilities. An integrable rapid-cycling synchrotron (RCS) would be an
effective replacement for the Fermilab Booster, as part of a plan to reach
multi-MW beam power at 120 GeV for the Fermilab high-energy neutrino program.
We provide an example integrable lattice with features of a modern RCS -
dispersion-free drifts, low momentum compaction factor, superperiodicity,
chromaticity correction, bounded beta functions, and separate-function magnets.Comment: arXiv admin note: substantial text overlap with arXiv:1703.0095
Bridge trisections of knotted surfaces in 4--manifolds
We prove that every smoothly embedded surface in a 4--manifold can be
isotoped to be in bridge position with respect to a given trisection of the
ambient 4--manifold; that is, after isotopy, the surface meets components of
the trisection in trivial disks or arcs. Such a decomposition, which we call a
\emph{generalized bridge trisection}, extends the authors' definition of bridge
trisections for surfaces in . Using this new construction, we give
diagrammatic representations called \emph{shadow diagrams} for knotted surfaces
in 4--manifolds. We also provide a low-complexity classification for these
structures and describe several examples, including the important case of
complex curves inside . Using these examples, we prove that
there exist exotic 4--manifolds with --trisections for certain values of
. We conclude by sketching a conjectural uniqueness result that would
provide a complete diagrammatic calculus for studying knotted surfaces through
their shadow diagrams.Comment: 17 pages, 5 figures. Comments welcom
Characterizing Dehn surgeries on links via trisections
We summarize and expand known connections between the study of Dehn surgery
on links and the study of trisections of closed, smooth 4-manifolds. In
addition, we describe how the potential counterexamples to the Generalized
Property R Conjecture given by Gompf, Scharlemann, and Thompson yield genus
four trisections of the standard four-sphere that are unlikely to be standard.
Finally, we give an analog of the Casson- Gordon Rectangle Condition for
trisections that can be used to obstruct reducibility of a given trisection.Comment: 15 pages, 4 color figures. Comments welcome
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