Theory and Applications of Generalized Pipek–Mezey Wannier Functions

Generalized Wannier Functions

We consider single particle Schrodinger operators with a gap in the energy spectrum. We construct a countable set of exponentially decaying functions, which form a complete, orthonormal basis set for the states below the spectral gap. Each such function is localized near a closed surface. Estimates on the exponential decay rate and a discussion of the geometry of these surfaces is included.

Partly occupied Wannier functions: Construction and applications

Applications of subordination theory to starlike functions

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

applications of subordination theory to starlike functions

let $p$ be an analytic function defined on the open unit disc $mathbb{d}$ with $p(0)=1.$ the conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{c}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of bernoulli $|w^{2}-1...

Maximally localized generalized Wannier functions for composite energy bands

We discuss a method for determining the optimally localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ‘‘generalized Wannier functions’’ we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread (n^r &n2^r&n 2 of the Wann...