Related papers: Peierls substitution for magnetic Bloch bands

We provide an abstract framework for singular one-dimensional Schroedinger operators with purely discrete spectra to show when the spectrum plus norming constants determine such an operator completely. As an example we apply our findings to…

We consider decaying oscillatory perturbations of periodic Schr\"odinger operators on the half line. More precisely, the perturbations we study satisfy a generalized bounded variation condition at infinity and an $L^p$ decay condition. We…

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the…

We construct multidimensional Schr\"odinger operators with a spectrum that has no gaps at high energies and that is nowhere dense at low energies. This gives the first example for which this widely expected topological structure of the…

The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on $\mathbb{R}^{n}\oplus\mathbb{R}^{n}$. In this paper we will show that the replacement of this structure by an arbitrary symplectic…

Using maximally localized Wannier functions obtained from DFT calculations, we derive an effective Hubbard Hamiltonian for a bilayer of Sr$_3$Cr$_2$O$_7$, the $n=2$ member of the Ruddlesden-Popper Sr$_{n+1}$Cr$_n$O$_{3n+1}$ system. The…

A fundamental result in pseudodifferential theory is the Calder\'on-Vaillancourt theorem, which states that a pseudodifferential operator defined from a H\"ormander symbol of order $0$ defines a bounded operator on $L^2(\mathbb{R}^d)$. In…

This paper is concerned with discrete, one-dimensional Schr\"odinger operators with real analytic potentials and one Diophantine frequency. Using localization and duality we show that almost every point in the spectrum admits a…

We study the stability properties of periodic solutions to the Nonlinear Schr\"odinger (NLS) equation with a periodic potential. We exploit the symmetries of the problem, in particular the Hamiltonian structure and the $\U(1)$ symmetry. We…

We theoretically investigate Bloch oscillations in a one-dimensional Bose-Hubbard chain, with single-particle losses from the odd lattice sites described by the Lindblad equation. For a single particle the time evolution of the state is…

Let $(\mathbb{X},d,\mu)$ be a doubling metric measure space, $L$ a non-negative self-adjoint operator on $L^2(\mathbb{X})$ satisfying the Davies-Gaffney estimate, and $X(\mathbb{X})$ a ball quasi-Banach function space on $\mathbb{X}$…

We study the transition of $\nu=1/3$ and $2/5$ fractional quantum Hall states of the honeycomb Hofstadter model as we tune to a two-orbital moir\'e superlattice Hamiltonian, motivated by the flat bands of twisted bilayer graphene in a…

For the the Schr\"odinger operator $H=-\Delta+ V(x)\cdot$, acting in the space L_2(\R^d)\,(d\ge 3), with V(x)\ge 0 and V(\cdot)\in L_{1,loc}(\R^d), we obtain some constructive conditions for discreteness of its spectrum. Basing on the…

We consider a periodic magnetic Schr\"odinger operator on a noncompact Riemannian manifold $M$ such that $H^1(M, \RR)=0$ endowed with a properly discontinuous cocompact isometric action of a discrete group. We assume that there is no…

The main mathematical manifestation of the Stark effect in quantum mechanics is the shift and the formation of clusters of eigenvalues when a spherical Hamiltonian is perturbed by lower order terms. Understanding this mechanism turned out…

We consider kernel operators defined by a dynamical system. The Hausdorff distance of spectra is estimated by the Hausdorff distance of subsystems. We prove that the spectrum map is $ \frac{1}{2} $-H\"older continuous provided the group…

For differential operators which are invariant under the action of an abelian group Bloch theory is the preferred tool to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a…

Hofstadter's butterfly, the predicted energy spectrum for non-interacting electrons confined to a two-dimensional lattice in a magnetic field, is one of the most remarkable fractal structures in nature. At rational ratios of magnetic flux…

We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schr\"odinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value $b_0$ of the intensity of the magnetic field is strictly…

We study ergodic Schr\"odinger operators defined over product dynamical systems in which one factor is periodic and the other factor is either a subshift over a finite alphabet or an irrational rotation of the circle. In the case in which…