Abstract:
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it is important to take into account the spatial dependence of the permittivity of the medium. However, due to the ensuing theoretical and computational challenges, this inhomogeneous dielectric response of the medium is often ignored or excessively simplified. We develop a variational formulation of electrostatics to accurately investigate systems that exhibit this inhomogeneous dielectric response. Our formulation is based on a true energy functional of the polarization charge density. The defining characteristic of a true energy functional is that at its minimum it evaluates to the actual value of the energy; this is a feature not found in many commonly used electrostatic functionals. We explore in detail the charged systems that exhibit sharp discontinuous change in dielectric permittivity, and we show that for this case our functional reduces to a functional of only the surface polarization charge density. We apply this reduced functional to study model problems for which analytical solutions are well known. We demonstrate, in addition, that the functional has many properties that make it ideal for use in molecular dynamics simulations.

Abstract:
We present a rigorous Ewald summation formula to evaluate the electrostatic interactions in two-dimensionally periodic planar interfaces of three-dimensional systems. By rewriting the Fourier part of the summation formula of the original Ewald2D expression with an explicit order N2 complexity to a closed form Fourier integral, we find that both the previously developed electrostatic layer correction term and the boundary correction term naturally arise from the expression of a rigorous trapezoidal summation of the Fourier integral part. We derive the exact corrections to the trapezoidal summation in a form of contour integrals offering precise error bounds with given parameter sets of mesh size and system length. Numerical calculations of Madelung constants in model ionic crystals of slab geometry have been performed to support our analytical results.

Abstract:
We present justification and rigorous procedure for electron partitioning among atoms in extended systems. The method is based on wavefunction topology and the modern theory of polarization, rather than charge density partitioning or wavefunction projection, and, as such, re-formulates the concept of oxidation state without assuming real-space charge transfer between atoms. This formulation provides rigorous electrostatics of finite extent solids, including films and nanowires.

Abstract:
Canonical quantization of electromagnetic field inside the time--spatially dispersive inhomogeneous dielectrics is presented. Interacting electromagnetic and matter excitation fields create the closed system, Hamiltonian of which may be diagonalized by generalized polariton transformation. Resulting dispersion relations coincide with the classical ones obtained by the solution of wave equation, the corresponding mode decomposition is, however, orthogonal and complete in the enlarged Hilbert space.

Abstract:
Recent progress in the understanding of the effect of electrostatics in soft matter is presented. A vast amount of materials contains ions ranging from the molecular scale (e.g., electrolyte) to the meso/macroscopic one (e.g., charged colloidal particles or polyelectrolytes). Their (micro)structure and physicochemical properties are especially dictated by the famous and redoubtable long-ranged Coulomb interaction. In particular theoretical and simulational aspects, including the experimental motivations, will be discussed.

Abstract:
In this work we investigate in detail, the different regimes of the pioneering work of Chklovskii et al. (1992), which provides an analytical description to model the electrostatics at the edges of a two-dimensional electron gas. We take into account full electrostatics and calculate the charge distribution by solving the 3D Poisson equation self-consistently. The Chklovskii formalism is reintroduced and is employed to determine the widths of the incompressible edge-states also considering the spin degree of freedom. It is shown that, the odd integer filling fractions cannot exist for large magnetic field intervals if many-body effects are neglected. We explicitly show that, the incompressible strips which are narrower than the quantum mechanical length scales vanish. We numerically and analytically show that, the non-self-consistent picture becomes inadequate considering realistic Hall bar geometries, predicting large incompressible strips. The details of this picture is investigated considering device properties together with the many-body and the disorder effects. Moreover, we provide semi-empirical formulas to estimate realistic density distributions for different physical boundary conditions.

Abstract:
The standard Maxwell formulation of the problem of polarized dielectrics suffers from a number of difficulties, both conceptual and practical. These difficulties are particularly significant in the case of liquid interfaces, where the ability of the interfacial multipoles to change their orientations to minimize their free energies leads to interfacial polarization localized within a thin microscopic layer. A formalism to capture this physical reality of localized interfacial polarization is proposed and is based on the surface charge as the source of microscopic electric fields in dielectrics. The surface charge density incorporates the local structure of the interface into electrostatic calculations. The corresponding surface susceptibility and interface dielectric constant provide local closures to the electrostatic boundary value problem. A robust approach to calculate the surface susceptibility from numerical simulations is proposed. The susceptibility can alternatively be extracted from a number of solution experiments, in particular those sensitive to the overall dipole moment of a closed dielectric surface. The theory is applied to the solvent-induced spectral shift and high-frequency dielectric response of solutions.

Abstract:
We argue that acceleration induces electric polarization in usual dielectrics. Both accelerations in superfluid participate in the medium polarization. Excitations contribution to the polarization is calculated at low temperatures. Estimates of the effect show order of magnitude agreement with recent experimental results on electric effect of superflow.

Abstract:
Nano Transistor represents a unique system for exploring physical phenomena pertaining to charge transport at the nano scale and is expected to play a critical role in future evolution of electronic and optoelectronic devices. This paper summarizes some of the essential electrostatics of nano Metal Oxide Semiconductor Field effect Transistor (MOSFET) and their electrical properties. Though the general focus of this work is on surface potential yet the first part presents a brief discussion of the independence of charge at the top of the barrier in the channel of MOS Transistor on Drain voltage. The quantum capacitance is discussed at length. The superposition theorem is used, thereafter, to obtain an expression for self consistent potential in the channel. Finally the I-V characteristics of the device are explored using Landauer formalism. The simulated results for a device are observed to represent the realistic behaviour of the device.

Abstract:
Response of a single-walled carbon nanotube to external electric field, F, is calculated analytically within the classical electrostatics. Field-induced charge density distribution is approximately linear along the axis of metallic nanotube and depends rather weakly, as ln(h/r), on the nanotube length, h, (here r is the nanotube radius). In a semiconducting nanotube with a gap, E_g, charge separation occurs as F exceeds the threshold value F_{th}=E_g/eh. For F>F_{th}, positively and negatively charged regions at the ends of nanotube are separated by a neutral strip in the middle. For bent nanotubes the number of neutral strips can be one or two depending on the direction of F.