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Creators/Authors contains: "Liu, Diyi"

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  1. ; ; (, Communications in Mathematical Physics)
    Free, publicly-accessible full text available June 1, 2026
  2. ; ; ; (, SIAM Journal on Applied Mathematics)
    We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer-- MacDonald PDE model, which is periodic with respect to the bilayer's moir\'e pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes--Thomas estimates. We then provide extensive numerical computations, which clarify the range of validity of the Bistritzer--MacDonald model. 
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  3. ; ; (, Physical Review Research)
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