4,551 research outputs found
Comments on M representations and geometries
We show using string dualities that Mathieu moonshine controls Gromov-Witten
invariants and periods of the holomorphic 3-form for certain
manifolds. We also discuss how the period vectors appear in flux
compactifications on these manifolds and work out the connection between
the sporadic group M and the Yukawa couplings in four dimensional
theories that arise from heterotic string theory compactifications on these
manifolds.Comment: 27 pages, v2: minor additions, published versio
Effect of intraband Coulomb repulsion on the excitonic spin-density wave
We present a study of the magnetic ground state of a two-band model with
nested electron and hole Fermi surfaces and both interband and intraband
Coulomb interactions. Our aim is to understand how the excitonic
spin-density-wave (ESDW) state induced by the interband Coulomb repulsion is
affected by the intraband interactions. We first determine the magnetic
instabilities of our model in an unbiased way by employing the random-phase
approximation (RPA) to calculate the static spin susceptibility in the
paramagnetic state. From this, we construct the mean-field phase diagram,
demonstrating the robustness of the ESDW against the intraband interaction. We
then calculate the RPA transverse spin susceptibility in the ESDW state and
show that the intraband Coulomb repulsion significantly renormalizes the
paramagnon line shape and suppresses the spin-wave velocity. We conclude with a
discussion of the relevance of this suppression for the commensurate ESDW state
of Mn-doped Cr alloys.Comment: 8 pages, 6 figure
A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems
We present a temporal decomposition scheme for solving long-horizon optimal
control problems. In the proposed scheme, the time domain is decomposed into a
set of subdomains with partially overlapping regions. Subproblems associated
with the subdomains are solved in parallel to obtain local primal-dual
trajectories that are assembled to obtain the global trajectories. We provide a
sufficient condition that guarantees convergence of the proposed scheme. This
condition states that the effect of perturbations on the boundary conditions
(i.e., initial state and terminal dual/adjoint variable) should decay
asymptotically as one moves away from the boundaries. This condition also
reveals that the scheme converges if the size of the overlap is sufficiently
large and that the convergence rate improves with the size of the overlap. We
prove that linear quadratic problems satisfy the asymptotic decay condition,
and we discuss numerical strategies to determine if the condition holds in more
general cases. We draw upon a non-convex optimal control problem to illustrate
the performance of the proposed scheme
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