Related papers: Wannier decay and the Thouless conjecture

The equation $- \Delta u + V u = 0$ in the cylinder $\mathbb{R} \times (0,2\pi)^d$ with periodic boundary conditions is considered. The potential $V$ is assumed to be bounded, and both functions $u$ and $V$ are assumed to be real-valued. It…

For functions $f$ in Dirichlet-type spaces we study how to determine constructively optimal polynomials $p_n$ that minimize $\|p f-1\|_\alpha$ among all polynomials $p$ of degree at most $n$. Then we give upper and lower bounds for the rate…

Let ${\mathbb F}_0$ be an algebraically closed field, with $char({\mathbb F}_0)=0$. In this article, for prime numbers $p\geq 2$, we construct smooth affine algebras $B$ over ${\mathbb F}_0$, with $\dim B=p+2$. Further, we construct…

Localized Wannier functions provide an efficient and intuitive means by which to compute dielectric properties from first principles. They are most commonly constructed in a post-processing step, following total-energy minimization.…

We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.

Given scheme-theoretic equations for a nonsingular subvariety, we prove that the higher cohomology groups for suitable twists of the corresponding ideal sheaf vanish. From this result, we obtain linear bounds on the multigraded…

We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic…

Orbital magnetic susceptibility involves rich physics such as interband effects despite of its conceptual simplicity. In order to appreciate the rich physics related to the orbital magnetic susceptibility, it is essential to derive a…

A detailed study of complex-space singularities of the two-dimensional incompressible Euler equation is performed in the short-time asymptotic r\'egime when such singularities are very far from the real domain; this allows an exact…

We consider a periodic Schroedinger operator and the composite Wannier functions corresponding to a relevant family of its Bloch bands, separated by a gap from the rest of the spectrum. We study the associated localization functional…

In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials…

We investigate the electronic structure of over-coordinated defects in amorphous silicon via density-functional total-energy calculations, with the aim of understanding the relationship between topological and electronic properties on a…

Bent functions are Boolean functions that are maximally nonlinear. They can be represented as bent squares, i.e., square matrices for which each row and each column is the Walsh spectrum of a Boolean function. Using this representation, it…

We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…

We show that the Chern character of a variation of polarized Hodge structures of weight one with nilpotent residues at $\infty$ dies up to torsion in the Chow ring, except in codimension 0.

Functionals that strive to correct for such self-interaction errors, such as those obtained by imposing the Perdew-Zunger self-interaction correction or the generalized Koopmans' condition, become orbital dependent or orbital-density…

We present an alternative formalism for calculating the maximally localized Wannier functions in crystalline solids, obtaining an expression which is extremely simple and general. In particular, our scheme is exactly invariant under…

We consider weak solutions to the incompressible Euler equations. It is shown that energy conservation holds in any Onsager critical class in which smooth functions are dense. The argument is independent of the specific critical regularity…

This paper investigates the global existence and the decay rate in time of a solution to the Cauchy problem for an incompressible Oldroyd model with a deformation tensor damping term. There are three major results. The first is the global…

The decay of an unstable D-brane via closed string emission and open string pair production is considered in subcritical string theory with a spacelike linear dilaton. The decay rate is given by the imaginary part of the annulus, which has…