Publications (57)
Computing the free energy of quantum Coulomb gases and molecules via quantum Gibbs sampling
Simon Becker, Cambyse Rouzé, Robert Salzmann
We develop a quantum algorithm for estimating the free energy as well as the total Gibbs state of interacting quantum Coulomb gases and molecular systems in dimensions $d \in \{2,3…
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…
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…
Benchmarking for Practice: Few-Shot Time-Series Crop-Type Classification on the EuroCropsML Dataset
Joana Reuss, Jan Macdonald, Simon Becker +4
Accurate crop-type classification from satellite time series is essential for agricultural monitoring. While various machine learning algorithms have been developed to enhance perf…
Magic angle (in)stability and mobility edges in disordered Chern insulators
Simon Becker, Izak Oltman, Martin Vogel
Why do experiments only observe one magic angle in twisted bilayer graphene, despite standard models like the chiral limit of the Bistritzer-MacDonald Hamiltonian predicting an inf…
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 magnet…
Discrete vs. continuous in the semiclassical limit
Simon Becker, Jens Wittsten, Maciej Zworski
We compare the bottom of the spectrum of discrete and continuous Schrödinger operators with periodic potentials with barriers at the boundaries of their fundamental domains. Our r…
Symmetric Tops Subject to Combined Electric Fields: Conditional Quasi-Solvability via the Quantum Hamilton-Jacobi Theory
Konrad Schatz, Bretislav Friedrich, Simon Becker +1
We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasi-solvability of the quantum symmetric top subject to combined electric fields (symmetric top…
Certifying the intrinsic character of a constitutive law for semi-crystalline polymers: a probation test
Stéphane André, Simon Becker, Camille Noûs +2
A study of methodological nature demonstrates the efficiency of a probation test allowing for the intrinsic character of a rheological constitutive law to be assessed. Such a law i…
Magnetic slowdown of topological edge states
Guillaume Bal, Simon Becker, Alexis Drouot
We study the propagation of wavepackets along curved interfaces between topological, magnetic materials. Our Hamiltonian is a massive Dirac operator with a magnetic potential. We c…
Hofstadter butterflies and metal/insulator transitions for moiré heterostructures
Simon Becker, Lingrui Ge, Jens Wittsten
We consider a tight-binding model recently introduced by Timmel and Mele for strained moiré heterostructures. We consider two honeycomb lattices to which layer antisymmetric shear…
EuroCropsML: A Time Series Benchmark Dataset For Few-Shot Crop Type Classification
Joana Reuss, Jan Macdonald, Simon Becker +2
We introduce EuroCropsML, an analysis-ready remote sensing machine learning dataset for time series crop type classification of agricultural parcels in Europe. It is the first data…
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,…
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…
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…
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…
Wannier decay and the Thouless conjecture
Simon Becker, Zhongkai Tao, Mengxuan Yang
Non-trivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions which provide natural bases for spectral subspaces. For non-trivial Bloch…
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,…
Simulating Thermal Properties of Bose-Hubbard Models on a Quantum Computer
Simon Becker, Cambyse Rouzé, Robert Salzmann
While recent advances have established efficient quantum algorithms for preparing Gibbs states of finite-dimensional systems, comparable complexity results for bosonic and other in…
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…
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…
Dirac points for twisted bilayer graphene with in-plane magnetic field
Simon Becker, Maciej Zworski
We study Dirac points of the chiral model of twisted bilayer graphene (TBG) with constant in-plane magnetic field. For a fixed small magnetic field, we show that as the angle of tw…
Honeycomb structures in magnetic fields
Simon Becker, Rui Han, Svetlana Jitomirskaya +1
We consider reduced-dimensionality models of honeycomb lattices in magnetic fields and report results about the spectrum, the density of states, self-similarity, and metal/insulato…
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…
Absence of small magic angles for disordered tunneling potentials in twisted bilayer graphene
Simon Becker, Izak Oltman, Martin Vogel
We consider small random perturbations of the standard high-symmetry tunneling potentials in the Bistritzer-MacDonald Hamiltonian describing twisted bilayer graphene. Using methods…
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…
Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart
Simon Becker, Marjan Mirahmadi, Burkhard Schmidt +2
We have subjected the planar pendulum eigenproblem to a symmetry analysis with the goal of explaining the relationship between its conditional quasi-exact solvability (C-QES) and t…
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 equat…
Twisted TMDs in the small-angle limit: exponentially flat and trivial bands
Simon Becker, Mengxuan Yang
Recent experiments discovered fractional Chern insulator states at zero magnetic field in twisted bilayer MoTe [C23,Z23] and WSe [MD23]. In this article, we study the MacDo…
Spectral Instability of Random Fredholm Operators
Simon Becker, Izak Oltman, Martin Vogel
If is an unbounded Fredholm operator of index on a Hilbert space with a dense domain , then its spectrum…
On the Hartree-Fock Ground State Manifold in Magic Angle Twisted Graphene Systems
Kevin D. Stubbs, Simon Becker, Lin Lin
Recent experiments have shown that magic angle twisted bilayer graphene (MATBG) can exhibit correlated insulator behavior at half-filling. Seminal theoretical results towards under…
Cantor spectrum of graphene in magnetic fields
Simon Becker, Rui Han, Svetlana Jitomirskaya
We consider a quantum graph as a model of graphene in magnetic fields and give a complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the redu…
Spectral analysis of the 2+1 fermionic trimer with contact interactions
Simon Becker, Alessandro Michelangeli, Andrea Ottolini
We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical…
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…
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…
Model Order Reduction for (Stochastic-) Delay Equations With Error Bounds
Simon Becker, Lorenz Richter
We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic in…
Magnetic response of twisted bilayer graphene
Simon Becker, Jihoi Kim, Xiaowen Zhu
In this article, we analyse the Bistritzer--MacDonald (BM) model (also known as the continuum model) of twisted bilayer graphene (TBG) with an additional external magnetic field. W…
Bohr--Sommerfeld rules for systems
Simon Becker, Setsuro Fujiié, Jens Wittsten
We present a complete, self-contained formulation of the Bohr--Sommerfeld quantization rule for a semiclassical self-adjoint system on the real line, arising from a si…
Quantum Gibbs Sampling in Infinite Dimensions: Generation, Mixing Times and Circuit Implementation
Simon Becker, Cambyse Rouzé, Robert Salzmann
We develop a rigorous and implementable framework for Gibbs sampling of infinite-dimensional quantum systems governed by unbounded Hamiltonians. Extending dissipative Gibbs sampler…
Convergence Rates for the Trotter Splitting for Unbounded Operators
Simon Becker, Niklas Galke, Robert Salzmann +1
We study convergence rates of the Trotter splitting in the strong operator topology. In the first part, we use complex interpola…
Spectral theory of twisted bilayer graphene in a magnetic field
Simon Becker, Xiaowen Zhu
In this article we study the Bistritzer-MacDonald (BM) model with external magnetic field. We study the spectral properties of the Hamiltonian in an external magnetic field with a…
Quantitative Assessment of PINN Inference on Experimental Data for Gravity Currents Flows
Mickaël Delcey, Yoann Cheny, Jean Schneider +2
In this paper, we apply Physics Informed Neural Networks (PINNs) to infer velocity and pressure field from Light Attenuation Technique (LAT) measurements for gravity current induce…
Exact ground state of interacting electrons in magic angle graphene
Simon Becker, Lin Lin, Kevin D. Stubbs
One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the i…
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…
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…
Magnetic oscillations in a model of graphene
Simon Becker, Maciej Zworski
We consider a quantum graph as a model of graphene in constant magnetic field and describe the density of states in terms of relativistic Landau levels satisfying a Bohr--Sommerfel…
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…
Fragile topology on solid grounds: a mathematical perspective
Simon Becker, Zhongkai Tao, Mengxuan Yang
This paper provides a mathematical perspective on fragile topology phenomena in condensed matter physics. In dimension , vanishing Chern classes of bundles of Bloch eigen…
Spectral analysis and phase transitions for long-range interactions in harmonic chains of oscillators
Simon Becker, Angeliki Menegaki, Jiming Yu
We consider chains of harmonic oscillators in two dimensions coupled to two Langevin heat reservoirs at different temperatures - a classical model for heat conduction introduce…
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…
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…
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…
Chiral limit of twisted trilayer graphene
Simon Becker, Tristan Humbert, Jens Wittsten +1
We initiate the mathematical study of the Bistritzer-MacDonald Hamiltonian for twisted trilayer graphene in the chiral limit (and beyond). We develop a spectral theoretic approach…
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…
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,…
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…
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…