2 citations · 5 across the 9 of their papers we have counts for
12 papers
The Spectrum of the Discrete Mathieu Operator with Nonreal Coupling
Frédéric Klopp, Izak Oltman
We study the discrete Mathieu operator with nonreal coupling in the large-period limit, using complex WKB methods for analytic finite-difference equations. We obtain quantization f…
Quantum percolation conjecture on regular trees
Simon Becker, Izak Oltman
For Bernoulli bond percolation on every regular tree of degree at least three, we prove that infinite clusters appear strictly before absolutely continuous spectrum. Throughout an…
Disorder on the hyperbolic square lattice I: Anderson delocalization and absolutely continuous spectrum
Simon Becker, Izak Oltman
We study the Anderson model on hyperbolic lattices. The graph is the Cartesian product of the Euclidean lattice with the regular hyperbolic square lattice having five squares at ea…
Spectra of Non-Self-Adjoint Almost Mathieu Matrices and the Scottish Flag Operator
Simon Becker, Izak Oltman
For and a potential phase , we study the non-self-adjoint almost Mathieu matrix obtained by multiplying the discrete Laplacian by a complex phase…
The asymptotic structure of forward scattering
Nicholas Lohr, Izak Oltman, Ethan Sussman +1
Perturbed plane waves are fundamental objects in scattering theory on Euclidean space and asymptotically Euclidean spaces. In this paper, we investigate the structure of perturbed…
A Poisson Formula for the Wave Propagator on Schwarzschild-de Sitter Backgrounds
Izak Oltman, Ben Pineau
This paper proposes a Poisson formula for the wave propagator of the Schwarzschild--de Sitter (SdS) metric. That is done by proving a Poisson formula relating wave propagators and…
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…
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…
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…
Particle Trajectories for Quantum Maps
Yonah Borns-Weil, Izak Oltman
We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements…
A probabilistic Weyl-law for perturbed Berezin-Toeplitz operators
Izak Oltman
This paper proves a probabilistic Weyl-law for the spectrum of randomly perturbed Berezin-Toeplitz operators, generalizing a result proven by Martin Vogel in 2020. This is done fol…
An exotic calculus of Berezin-Toeplitz operators
Izak Oltman
We develop a calculus of Berezin-Toeplitz operators quantizing exotic classes of smooth functions on compact Kähler manifolds and acting on holomorphic sections of powers of positi…