46 citations · 386 across the 28 of their papers we have counts for
29 papers
From the chiral model of TBG to the Bistritzer--MacDonald model
Simon Becker, Maciej Zworski
We analyse the splitting of exact flat bands in the chiral model of the twisted bilayer graphene (TBG) when the coupling of the full Bistritzer--MacDonald model is taken…
Degenerate flat bands in twisted bilayer graphene
Simon Becker, Tristan Humbert, Maciej Zworski
We prove that in the chiral limit of the Bistritzer--MacDonald Hamiltonian, there exist magic angles at which the Hamiltonian exhibits flat bands of multiplicity four instead of tw…
Classical shadow tomography for continuous variables quantum systems
Simon Becker, Nilanjana Datta, Ludovico Lami +1
In this article we develop a continuous variable (CV) shadow tomography scheme with wide ranging applications in quantum optics. Our work is motivated by the increasing experimenta…
Fine structure of flat bands in a chiral model of magic angles
Simon Becker, Tristan Humbert, Maciej Zworski
We analyze symmetries of Bloch eigenfunctions at magic angles for the Tarnopolsky--Kruchkov--Vishwanath chiral model of the twisted bilayer graphene (TBG) following the framework i…
Integrability in the chiral model of magic angles
Simon Becker, Tristan Humbert, Maciej Zworski
Magic angles in the chiral model of twisted bilayer graphene are parameters for which the chiral version of the Bistritzer--MacDonald Hamiltonian exhibits a flat band at energy zer…
Semiclassical quantization conditions in strained moiré lattices
Simon Becker, Jens Wittsten
In this article we generalize the Bohr-Sommerfeld rule for scalar symbols at a potential well to matrix-valued symbols having eigenvalues that may coalesce precisely at the bottom…
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…
From Classical to Quantum: Uniform Continuity Bounds on Entropies in Infinite Dimensions
Simon Becker, Nilanjana Datta, Michael G. Jabbour
We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimens…
Computability of magnetic Schrödinger and Hartree equations on unbounded domains
Simon Becker, Jonathan Sewell, Euan Tebbutt
We study the computability of global solutions to linear Schrödinger equations with magnetic fields and the Hartree equation on . We show that the solution can always…
Computing solutions of Schrödinger equations on unbounded domains- On the brink of numerical algorithms
Simon Becker, Anders Hansen
We address the open problem of determining which classes of time-dependent linear Schrödinger equations and focusing and defocusing cubic and quintic non-linear Schrödinger equatio…
Spectral characterization of magic angles in twisted bilayer graphene
Simon Becker, Mark Embree, Jens Wittsten +1
Twisted bilayer graphene (TBG) has been experimentally observed to exhibit almost flat bands when the twisting occurs at certain magic angles. In this letter, we report new results…
Quantum Zeno effect for open quantum systems
Simon Becker, Nilanjana Datta, Robert Salzmann
We prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quan…
The optimal spectral gap for regular and disordered harmonic networks of oscillators
Simon Becker, Angeliki Menegaki
We consider one-dimensional chains and multi-dimensional networks of harmonic oscillators coupled to two Langevin heat reservoirs at different temperatures. Each particle interacts…
Quantum statistical learning via Quantum Wasserstein natural gradient
Simon Becker, Wuchen Li
In this article, we introduce a new approach towards the statistical learning problem to approximate a targ…
Mathematics of magic angles in a model of twisted bilayer graphene
Simon Becker, Mark Embree, Jens Wittsten +1
We provide a mathematical account of the recent Physical Reviews Letter by Tarnopolsky--Kruchkov--Vishwanath. The new contributions are a spectral characterization of magic angles,…
Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
Simon Becker, Nilanjana Datta, Ludovico Lami +1
We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results…
Density of states and Delocalization for discrete magnetic random Schrödinger operators
Simon Becker, Rui Han
We study discrete magnetic random Schrödinger operators on the square and honeycomb lattice. For the non-random magnetic operator on the hexagonal lattice with any rational magneti…
Schrödinger and polyharmonic operators on infinite graphs: Parabolic well-posedness and p-independence of spectra
Simon Becker, Federica Gregorio, Delio Mugnolo
We analyze properties of semigroups generated by Schrödinger operators or polyharmonic operators , on metric graphs both on -spaces and spaces of continuous fu…
Convergence rates for the quantum central limit theorem
Simon Becker, Nilanjana Datta, Ludovico Lami +1
Various quantum analogues of the central limit theorem, which is one of the cornerstones of probability theory, are known in the literature. One such analogue, due to Cushen and Hu…
Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces
Simon Becker, Carsten Hartmann, Martin Redmann +1
We analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear S(P)DEs with multiplicative noise based on balanced truncation. For the fi…
Spectral gap in mean-field -model
Simon Becker, Angeliki Menegaki
We study the dependence of the spectral gap for the generator of the Ginzburg-Landau dynamics for all \emph{-models} with mean-field interaction and magnetic field,…
Convergence rates for quantum evolution & entropic continuity bounds in infinite dimensions
Simon Becker, Nilanjana Datta
By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite-dimensions, which are…
Geometry of energy landscapes and the optimizability of deep neural networks
Simon Becker, Yao Zhang, Alpha A. Lee
Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empiric…
Infinite-dimensional bilinear and stochastic balanced truncation with error bounds
Simon Becker, Carsten Hartmann
Along the ideas of Curtain and Glover, we extend the balanced truncation method for infinite-dimensional linear systems to bilinear and stochastic systems. Specifically , we apply…