Related papers: Exact Density Functionals in One Dimension

We review some of the exactly solvable one dimensional continuum fluid models of equilibrium classical statistical mechanics under the unified setting of functional integration in one dimension. We make some further developments and remarks…

We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…

We write exact equations for the thermodynamic properties of a linear polymer molecule confined to walk on a lattice of finite size. The dimension of the space in which the lattice resides can be arbitrary. We also calculate polymer…

A diffusive lattice gas is characterized by the diffusion coefficient depending only on the density. The Green-Kubo formula for diffusivity can be represented as a variational formula, but even when the equilibrium properties of a lattice…

Finite temperature density functional theory provides, in principle, an exact description of the thermodynamical equilibrium of many-electron systems. In practical applications, however, the functionals must be approximated. Efficient and…

We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…

We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a…

An approximation for the exchange-correlation energy of reduced-density-matrix-functional theory was recently derived from a study of the homogeneous electron gas (N.N. Lathiotakis, N. Helbig, E.K.U. Gross, Phys. Rev. B 75, 195120 (2007)).…

We present here exact results for a one-dimensional gas, or fluid, of hard-sphere particles with attractive boundaries. The particles, which can exchange with a bulk reservoir, mediate an interaction between the boundaries. A…

Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the…

We study both static and transport properties of model quantum dots, employing density functional theory as well as (numerically) exact methods. For the lattice model under consideration the accuracy of the local-density approximation…

We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…

We present an extension of the density-functional theory (DFT) formalism for lattice gases to systems with internal degrees of freedom. In order to test approximations commonly used in DFT approaches, we investigate the statics and dynamics…

We use the classical version of the density-functional theory in the weighted-density approximation to build up the entire phase diagram and the interface structure of a two-dimensional lattice-gas model which is known, from previous…

In this paper, we provide strong $L_2$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its…

In this work, we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation…

In the dilute limit, the properties of fermionic lattice models with short-range attractive interactions converge to those of a dilute Fermi gas in continuum space. We investigate this connection using mean-field and we show that the…

We consider the convergence of a continuous-time Markov chain approximation X^h, h>0, to an R^d-valued Levy process X. The state space of X^h is an equidistant lattice and its Q-matrix is chosen to approximate the generator of X. In…

The exact reduced density-matrix functional is derived from the Luttinger-Ward functional of the single-particle Green's function. Thereby, a formal link is provided between diagrammatic many-body approaches using Green's functions on the…

In this short review, we discuss recent advances in exact solutions of models based on a one- dimensional (1D) Coulomb gas by means of field-theoretic functional integral methods. The exact solutions can be used to assess the accuracy of…