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In this work, we prove that linear bounded operators $T$ on a Banach space $X$ allowing spectral cuts along rectifiable Jordan curves meeting their spectrum are related to classes of operators admitting an unconventional functional…

We prove and apply two theorems: First, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schr\"odinger operator on a bounded or unbounded domain, second, a perturbation and lifting estimate…

We establish $\frac{1}{2}$-H\"older continuity, or even the Lipschitz property, for the spectral measures of half-line discrete Schr\"odinger operators under suitable boundary conditions and exponentially decaying small potentials. These…

The Bandwidth Theorem of B\"ottcher, Schacht and Taraz [Mathematische Annalen 343 (1), 175-205] gives minimum degree conditions for the containment of spanning graphs H with small bandwidth and bounded maximum degree. We generalise this…

We characterize the potential V (x) that minimizes the fundamental spectral gap of weighted Schr\"odinger operators on the interval [0,{\pi}] subject to Dirichlet boundary conditions, under the constraint that the potential V (x) is convex…

For certain one-dimensional Schroedinger-type difference operators with a complex potential, a "complete" set of exponentially decaying eigenvectors is shown to exist. "Completeness" entails that the parameters involved are obtained through…

In this work, we investigate conditions which ensure the existence of an exponentially localized Wannier basis for a given periodic hamiltonian. We extend previous results in [Pan07] to include periodic zero flux magnetic fields which is…

'Magic'-angle twisted bilayer graphene has received a lot of interest due to its flat bands with potentially non-trivial topology that lead to intricate correlated phases. A spectrum with flat bands, however, does not require a twist…

By a theorem of Greene and Wu, a noncompact connected Riemannian manifold admits a smooth strictly subharmonic exhaustion function. Demailly provided an elementary proof of this fact. A further simplification of Demailly's proof and some…

For a large class of physically relevant operators on a manifold with discrete group action, we prove general results on the (non-)existence of a basis of smooth well-localised Wannier functions for their spectral subspaces. This turns out…

We prove a new criterion of weak hypercyclicity of a bounded linear operator on a Banach space. Applying this criterion, we solve few open questions. Namely, we show that if $G$ is a region of $\C$ bounded by a smooth Jordan curve $\Gamma$…

We consider perturbations of Hamiltonians whose Fourier symbol attains its minimum along a hypersurface. Such operators arise in several domains, like spintronics, theory of supercondictivity, or theory of superfluidity. Variational…

We establish a broad notion of admissible tilings of frequency space which admit associated wave packet frames with elements which are smooth and compactly supported. The framework is designed to allow for tile geometries which are…

We revisit the electronic structure and band topology of monolayer 1H-NbSe$_2$, which hosts both superconductivity and charge density wave, and its related compounds 1H-MoS$_2$, NbS$_2$, TaS$_2$, TaSe$_2$ and WS$_2$. We construct a 6-band,…

We investigate the localization properties of independent electrons in a periodic background, possibly including a periodic magnetic field, as e.g. in Chern insulators and in Quantum Hall systems. Since, generically, the spectrum of the…

In the semiclassical limit h to 0, we analyze a class of self-adjoint Schr\"odinger operators H_h = h^2 L + h W + V id_E acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is…

In this paper we discuss extensions of the canonical quantization procedure in quantum field theories. We focus specifically on S-matrix representation as a T-exponent. This extension involves flat bundles on certain infinite dimensional…

We investigate an interesting interplay of destructive interference due to lattice geometry and band folding due to enlargement of the Brillouin zone in generating and subsequently modifying the band topology in a twisted bilayer…

In this paper we consider the two-dimensional Schr\"odinger operator with an attractive potential which is a multiple of the characteristic function of an unbounded strip-shaped region, whose thickness is varying and is determined by the…

We prove that a bounded operator $T$ on a separable Banach space $X$ satisfying a strong form of the Frequent Hypercyclicity Criterion (which implies in particular that the operator is universal in the sense of Glasner and Weiss) admits…