29 citations · 150 across the 20 of their papers we have counts for
21 papers
Discrete-to-continuum convergence of the density of states for Mathieu's equation
Peter Hofhansel, Alexander B. Watson
The density of states of a self-adjoint operator generalizes the eigenvalue distribution of a Hermitian matrix. We prove convergence of the density of states for a tight-binding mo…
Growth-fragmentations, Brownian cone excursions and SLE(6) explorations of a quantum disc
William Da Silva, Ellen Powell, Alexander Watson
The aim of this article is to present a growth-fragmentation process naturally embedded in a Brownian excursion from boundary to apex in a cone of angle . This growth-fragmen…
Dirac cones and magic angles in the Bistritzer--MacDonald TBG Hamiltonian
Simon Becker, Solomon Quinn, Zhongkai Tao +2
We demonstrate the generic existence of Dirac cones in the full Bistritzer--MacDonald Hamiltonian for twisted bilayer graphene. Its complementary set, when Dirac cones are absent,…
Modeling of electronic dynamics in twisted bilayer graphene
Tianyu Kong, Diyi Liu, Mitchell Luskin +1
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 aper…
From incommensurate bilayer heterostructures to Allen-Cahn: An exact thermodynamic limit
Michael Hott, Alexander B. Watson, Mitchell Luskin
We give a complete and rigorous derivation of the mechanical energy for twisted 2D bilayer heterostructures without any approximation beyond the existence of an empirical many-body…
Mathematical aspects of the Kubo formula for electrical conductivity with dissipation
Alexander B. Watson, Dionisios Margetis, Mitchell Luskin
In this expository article, we present a systematic formal derivation of the Kubo formula for the linear-response current due to a time-harmonic electric field applied to non-inter…
On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform
Dionisios Margetis, Alexander B. Watson, Mitchell Luskin
We describe the low-temperature optical conductivity as a function of frequency for a quantum-mechanical system of electrons that hop along a polymer chain. To this end, we invoke…
Bistritzer-MacDonald dynamics in twisted bilayer graphene
Alexander B. Watson, Tianyu Kong, Allan H. MacDonald +1
The Bistritzer-MacDonald (BM) model, introduced in \cite{Bistritzer2011}, attempts to capture the electronic properties of twisted bilayer graphene (TBG), even at incommensurate tw…
Computing Truncated Joint Approximate Eigenbases for Model Order Reduction
Terry A. Loring, Fredy Vides
In this document, some elements of the theory and algorithmics corresponding to the existence and computability of approximate joint eigenpairs for finite collections of matrices w…
Computing spectral properties of topological insulators without artificial truncation or supercell approximation
Matthew J. Colbrook, Andrew Horning, Kyle Thicke +1
Topological insulators (TIs) are renowned for their remarkable electronic properties: quantised bulk Hall and edge conductivities, and robust edge wave-packet propagation, even in…
Edge state dynamics along curved interfaces
Guillaume Bal, Simon Becker, Alexis Drouot +3
We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omniprese…
Existence of the first magic angle for the chiral model of bilayer graphene
Alexander B. Watson, Mitchell Luskin
We consider the chiral model of twisted bilayer graphene introduced by Tarnopolsky-Kruchkov-Vishwanath (TKV). TKV have proved that for inverse twist angles such that the effect…
Locality of the windowed local density of states
Terry A. Loring, Jianfeng Lu, Alexander B. Watson
We introduce a generalization of local density of states which is "windowed" with respect to position and energy, called the windowed local density of states (wLDOS). This definiti…
The Iterated Projected Position Algorithm for Constructing Exponentially Localized Generalized Wannier Functions for Periodic and Non-Periodic Insulators in Two Dimensions and Higher
Kevin D. Stubbs, Alexander B. Watson, Jianfeng Lu
Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which de…
Defect resonances of truncated crystal structures
Jianfeng Lu, Jeremy L. Marzuola, Alexander B. Watson
Defects in the atomic structure of crystalline materials may spawn electronic bound states, known as \emph{defect states}, which decay rapidly away from the defect. Simplified mode…
Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher
Jianfeng Lu, Kevin D. Stubbs, Alexander B. Watson
Exponentially-localized Wannier functions (ELWFs) are an orthonormal basis of the Fermi projection of a material consisting of functions which decay exponentially fast away from th…
Wave-packet propagation in a finite topological insulator and the spectral localizer index
Jonathan Michala, Alexander Pierson, Terry A. Loring +1
We consider a model of electrons in a finite topological insulator. We numerically study the propagation of electronic wave-packets localized near edges of the structure in the pre…
Computing edge states without hard truncation
Kyle Thicke, Alexander B. Watson, Jianfeng Lu
We present a numerical method which accurately computes the discrete spectrum and associated bound states of Hamiltonians which model electronic "edge" states localized at boundari…
Dirac operators and domain walls
Jianfeng Lu, Alexander B. Watson, Michael I. Weinstein
We study the eigenvalue problem for a one-dimensional Dirac operator with a spatially varying ``mass'' term. It is well-known that when the mass function has the form of a kink, or…
Wavepackets in inhomogeneous periodic media: propagation through a one-dimensional band crossing
Alexander B. Watson, Michael I. Weinstein
We consider a model of an electron in a crystal moving under the influence of an external electric field: Schroedinger's equation in one spatial dimension with a potential which is…
Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature
Alexander B. Watson, Jianfeng Lu, Michael I. Weinstein
We consider a model of an electron in a crystal moving under the influence of an external electric field: Schrödinger's equation with a potential which is the sum of a periodic fun…