This paper deals with Hamiltonians of the form H=p^2/2m+v(r), with v(r) periodic along the z direction, v(x,y,z+b)=v(x,y,z), and x, y confined in a finite domain. The wave functions of H are the well-known Bloch functions phi_{n,lambda}(r), with the fundamental property phi_{n,lambda}(x,y,z+b)=lambda phi_{n,lambda}(x,y,z) and similar for the derivative. We give the generic analytic structure (i.e., the Riemann surface) of phi_{n,lambda}(r) and their

The concept of nearsightedeness of electronic matter (NEM) was introduced by Kohn in 1996 as the physical principle underlining Yang's electronic structure algorithm of divide and conquer. It describes the fact that, for fixed chemical potential, local electronic properties at a point r, like the density n(r), depend significantly on the external potential v only at nearby points. Beyond a distance R, changes Δv of that potential, no matter how

In an earlier paper, W. Kohn had qualitatively introduced the concept of ``nearsightedness" of electrons in many-atom systems. It can be viewed as underlying such important ideas as Pauling's ``chemical bond," ``transferability" and Yang's computational principle of ``divide and conquer." It describes the fact that, for fixed chemical potential, local electronic properties, like the density $n(r)$, depend significantly on the effective external potential

The Kohn-Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high temperatures and that this solution is a uniform particle density. We prove that, at zero temperature, there are stable solutions that are not uniform. We provide the general principles behind this phenomenon, namely

We apply the recently developed plasmon hybridization method to a solid nanosphere interacting with a metallic surface. We show that the plasmon energies of the nanoparticle exhibit strong shifts with nanoparticle-surface separation. Depending on the energy of the surface plasmon, nanoparticle plasmons can either red shift or blue shift with decreasing nanoparticle-surface separation. The shifts can be explained as resulting from image-like interactions

We apply the recently developed plasmon hybridization method to nanoparticle dimers, providing a simple and intuitive description of how the energy and excitation cross sections of dimer plasmons depend on nanoparticle separation. We show that the dimer plasmons can be viewed as bonding and antibonding combinations, i.e., hybridization of the individual nanoparticle plasmons. The calculated plasmon energies are compared with results from FDTD simulations.

We show that the plasmon resonances in single metallic nanoshells and multiple concentric metallic shell particles can be understood in terms of interaction between the bare plasmon modes of the individual surfaces of the metallic shells. The interaction of these elementary plasmons results in hybridized plasmons whose energy can be tuned over a wide range of optical and infrared wavelengths. The approach can easily be generalized to more complex

We present a simple and intuitive picture, an electromagnetic analog of molecular orbital theory, that describes the plasmon response of complex nanostructures of arbitrary shape. Our model can be understood as the interaction or "hybridization" of elementary plasmons supported by nanostructures of elementary geometries. As an example, the approach is applied to the important case of a four-layer concentric nanoshell, where the hybridization of the

Using the TDLDA method, we investigate how the polarizability of the d electrons of the gold atoms influences the electronic and optical properties of metallic nanoshells. It is shown that a polarizable jellium background can introduce a significant shift of the plasmon resonances. The results of the study show that the theoretically calculated optical absorption spectra for gold nanoshells with a gold sulfide core are in excellent agreement with

We study the question of existence and uniqueness for the finite temperature Kohn-Sham equations. For finite volumes, a unique soluion is shown to exists if the effective potential satisfies a set of general conditions and the coupling constant is smaller than a certain value. For periodic background potentials, this value is proven to be volume independent. In this case, the finite volume solutions are shown to converge as the thermodynamic limit