skip to main content


Title: Boundedness of non-local operators with spatially dependent coefficients and $$L_p$$-estimates for non-local equations
Award ID(s):
2055244
NSF-PAR ID:
10416895
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Calculus of Variations and Partial Differential Equations
Volume:
62
Issue:
2
ISSN:
0944-2669
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Southern Belize has received less archaeological attention than other areas due in large part to its remote location. However, the difficulty in accessing the area in recent times does not necessarily equate to isolation for the Classic Period Maya who lived in what is now the Toledo District. This paper discusses petrographic data collected on ceramic vessels recovered from burial contexts at Uxbenká, Belize. The partial and reconstructed whole vessels from these primary contexts include locally produced vessels that are stylistically and technologically unique to the southern Belize region and vessels produced elsewhere. We use these data to evaluate how local Uxbenká potters produced ceramic vessels for local consumption and to identify long-distance interaction networks between Uxbenká and other regions of the Maya Lowlands. Our data indicate that most of the pottery at Uxbenká was produced locally. However, elite tombs often include both local and non-local vessels. The elites of Uxbenká engaged in interaction with people living much farther afield in regions like the Belize River Valley and possibly Guatemala. 
    more » « less
  2. We advance the characterization of complexity in quantum many-body systems by examiningWW-states embedded in a spin chain. Such states show an amount of non-stabilizerness or “magic”, measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into aWW-state, while in the rest of the phase to which the classical point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state’s Stabilizer Rényi Entropy is the sum of that of theWW-states plus an extensive local contribution. Our work reveals thatWW-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.

     
    more » « less