Related papers: Integral representations for the Hartman--Watson d…

In this note, we investigate the density of the exponential functional of the fractional Brownian motion. Based on the techniques of Malliavin's calculus, we provide a log-normal upper bound for the density.

The effective action for the charge density and the photon field is proposed as a generalization of the density functional. A simple definition is given for the density functional, as the functional Legendre transform of the generator…

To understand sparse systems we must account for both strong local atom bonds and weak nonlocal van der Waals forces between atoms separated by empty space. A fully nonlocal functional form [H. Rydberg, B.I. Lundqvist, D.C. Langreth, and M.…

Starting from an integral representation for the eigenvalue density at finite N, it is shown by a saddle-point analysis that the known result (Durhuus and Olesen, 1981) can be recovered.

An equation proposed by Levy, Perdew and Sahni in 1984 [PRA 30, 2745 (1984)] is an orbital--free formulation of density functional theory. However, this equation describes a bosonic system. Here, we analyze on a very fundamental level, how…

We generalize Roth's theorem on three term arithmetic progressions to translation invariant quadratic forms in at least 17 variables. We use Fourier-analysis, restriction theory, uniformity norms and Roth's density increment method to show…

In practical implementations of density-functional theory, the only term where an orbital description is needed is the kinetic one. Even this term in principle depends on the density only, but its explicit form is unknown. We provide a…

The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. In this Part~II of a…

This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in…

Detailed discussion of university textbook statements (Harwit 1988) concerning the Poynting-Robertson effect (P-R effect) is presented. Discussion is concentrated on better physical understanding of the P-R effect. References to complete…

This note is an addendum to our earlier work \cite{humi}. In \cite{humi}, we studied a Hamiltonian action for a generalized Calabi-Yau manifold and showed that the Duistermaat-Heckman theorem holds. The purpose of this note is to show that…

A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg, et al., Phys. Rev. Lett. 91, 126402…

We introduce a method for computing quantum mechanical forces through surface integrals over the stress tensor within the framework of density functional theory. This approach avoids the inaccuracies of traditional force calculations using…

An integro-differential equation satisfied by an eigenvalue density defined as the logarithmic derivative of the average inverse characteristic polynomial of a Wilson loop in two dimensional pure Yang Mills theory with gauge group SU(N) is…

We derive the effective theories for heavy particles with a functional integral approach by integrating away the states with high velocity and with high virtuality. This formulation is non-perturbative and has a close connection with the…

We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…

In this paper we first prove a Clark--Ocone formula for any bounded measurable functional on Poisson space. Then using this formula, under some conditions on the intensity measure of Poisson random measure, we prove a variational…

Equations of motion of spinning density for extended objects, and corresponding deviation equations are derived. The problem of motion for a variable mass to a spinning extended object is obtained. Spinning fluids may be considered as a…

We generalize the Bergman-Milton spectral representation, originally derived for a two-component composite, to extract the spectral density function for the effective dielectric constant of a graded composite. This work has been motivated…

We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic orbital-free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a…