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E. Prodan

Publications and source records attributed to E. Prodan.

15 recordsLinked to original sources
arXiv2007

DC Conductance of Molecular Wires

Inspired by the work of Kamenev and Kohn, we present a general discussion of the two-terminal dc conductance of molecular devices within the framework of Time Dependent Current-Density Functional Theory. We derive a formally exact expression for the adiabatic conductance and we discuss the dynamical corrections. For junctions made of long molecular chains that can be either metallic or insulating, we derive the exact asymptotic behavior of the adiabatic conductance as a function of the chain's length. Our results follow from the analytic structure of the bands of a periodic molecular chain and a compact expression for the Green's functions. In the case of an insulating chain, not only do we obtain the exponentially decaying factors, but also the corresponding amplitudes, which depend very sensitively on the electronic properties of the contacts. We illustrate the theory by a numerical study of a simple insulating structure connected to two metallic jellium leads.

cond-mat.mtrl-sci↗
arXiv2006

Analytic structure of Bloch functions for linear molecular chains

This paper deals with Hamiltonians of the form $H=-{\bf \nabla}^2+v(\rr)$, with $v(\rr)$ periodic along the $z$ direction, $v(x,y,z+b)=v(x,y,z)$. The wavefunctions of $H$ are the well known Bloch functions $ψ_{n,λ}(\rr)$, with the fundamental property $ψ_{n,λ}(x,y,z+b)=λψ_{n,λ}(x,y,z)$ and $\partial_zψ_{n,λ}(x,y,z+b)=λ\partial_zψ_{n,λ}(x,y,z)$. We give the generic analytic structure (i.e. the Riemann surface) of $ψ_{n,λ}(\rr)$ and their corresponding energy, $E_n(λ)$, as functions of $λ$. We show that $E_n(λ)$ and $ψ_{n,λ}(x,y,z)$ are different branches of two multi-valued analytic functions, $E(λ)$ and $ψ_λ(x,y,z)$, with an essential singularity at $λ=0$ and additional branch points, which are generically of order 1 and 3, respectively. We show where these branch points come from, how they move when we change the potential and how to estimate their location. Based on these results, we give two applications: a compact expression of the Green's function and a discussion of the asymptotic behavior of the density matrix for insulating molecular chains.

cond-mat.other↗
arXiv2005

Nearsightedness of Electronic Matter in One Dimension

The concept of nearsightedeness of electronic matter (NEM) was introduced by W. Kohn in 1996 as the physical principal underlining Yang's electronic structure alghoritm 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. Changes $Δv$ of that potential, {\it no matter how large}, beyond a distance $\textsf{R}$, have {\it limited} effects on local electronic properties, which tend to zero as function of $\textsf{R}$. This remains true even if the changes in the external potential completely surrounds the point $r$. NEM can be quantitatively characterized by the nearsightedness range, $\textsf{\textsf{R}}(r,Δn)$, defined as the smallest distance from $r$, beyond which {\it any} change of the external potential produces a density change, at $r$, smaller than a given $Δn$. The present paper gives a detailed analysis of NEM for periodic metals and insulators in 1D and includes sharp, explicit estimates of the nearsightedness range. Since NEM involves arbitrary changes of the external potential, strong, even qualitative changes can occur in the system, such as the discretization of energy bands or the complete filling of the insulating gap of an insulator with continuum spectrum. In spite of such drastic changes, we show that $Δv$ has only a limited effect on the density, which can be quantified in terms of simple parameters of the unperturbed system.

cond-mat.stat-mech↗
arXiv2005

Nearsightedness of Electronic Matter

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 only at nearby points. Changes of that potential, {\it no matter how large}, beyond a distance $\textsf{R}$ have {\it limited} effects on local electronic properties, which rapidly tend to zero as function of $\textsf{R}$. In the present paper, the concept is first sharpened for representative models of uncharged fermions moving in external potentials, followed by a discussion of the effects of electron-electron interactions and of perturbing external charges.

cond-mat.mtrl-sci↗
arXiv2005

Symmetry breaking in the self-consistent Kohn-Sham equations

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 this solution is a uniform particle density. We show that, at zero temperature, there are stable solutions that are not uniform. We provide the general principles behind this phenomenon, namely the conditions when it can be observed and how to construct these non-uniform solutions. Two concrete examples are provided, including fermions on the sphere which are shown to crystallize in a structure that resembles the C$_{60}$ molecule.

cond-mat.stat-mech↗
arXiv2003

Electronic structure and optical properties of metallic nanoshells

The electronic structure and optical properties of metallic nanoshells are investigated using a jellium model and the Time Dependent Local Density Approximation (TDLDA). An efficient numerical implementation enables applications to nanoshells of realistic size with up to a million electrons. We demonstrate how a frequency dependent background polarizability of the jellium shell can be included in the TDLDA formalism. The energies of the plasmon resonances are calculated for nanoshells of different sizes and with different dielectric cores, dielectric embedding media, and dielectric shell backgrounds. The plasmon energies are found to be in good agreement with the results from classical Mie scattering theory using a Drude dielectric function. A comparison with experimental data shows excellent agreement between theory and the measured frequency dependent absorption spectra.

cond-mat.mtrl-sci↗
arXiv2003

On the Kohn-Sham equations with periodic background potentials

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 is considered. The local density approximation is shown to satisfy the general conditions mentioned above.

cond-mat.mtrl-sci↗
arXiv2002

The phase diagram for the $(λϕ^{4}+σϕ^{2})_{2}$ model

The two parameter model is reduced to a one parameter model by using simple transformations. Because the separation between different phase regions for a one parameter model is just a point, the equivalence between the two models leads to the exact equation of the line that separates the broken and un-broken phases in the $(λ,σ)$ plane. Also, we obtain nontrivial estimates on the stability region for this model.

hep-th↗
arXiv1999

Gaussian, Mean Field and Variational Approximation: the Equivalence

We show the equivalence between the three approximation schemes for self-interacting (1+1)-D scalar field theories. Based on rigorous results of [1, 2], we are able to prove that the Gaussian approximation is very precise for certain limits of coupling constants. The $λϕ^{4}+σϕ^{2}$ model will be used as a concrete application.

quant-ph↗
arXiv1999

Spontaneous Transitions in Quantum Mechanics

The problem of spontaneous pair creation in static external fields is reconsidered. A weak version of the conjecture proposed by G Nenciu (1980) is seated and proved. The method reduces the proof of the general conjecture to the study of the evolution, associated with a time dependent Hamiltonian, of a vector which is eigenvector of this Hamiltonian at some given time. Possible ways of proving the general conjecture are discussed.

math-ph↗
arXiv1999

Transport properties of fermionic systems

We extend the method discovered by A Y Alekseev et al to the case of fermions in external fields. A general formula for conductance G is proved. In the (1+1)-D case with symmetry at time reflection, it is shown that: G=e^2/h+o(a^), where a is the strength of the external field. In (3+1)-D free case, it is checked that G=n*e^2/h, where n is the number of the filled energetic bands of the transversal quantization.

quant-ph↗
arXiv1999

Transfer matrices for scalar fields on curved spaces

We apply Nelson's technique of constructing Euclidean fields to the case of classical scalar fields on curved spaces. It is shown how to construct a transfer matrix and, for a class of metrics, the basic spectral properties of its generator are investigated. An application concerning decoupling of non-convex disjoint region is given.

math-ph↗
arXiv1998

The dielectric behavior of the living cell suspensions

In the limit of small concentrations and weak applied electric fields, the dielectric permittivity of suspensions of arbitrarily shaped, shelled and charged particles is calculated. It is proved that the dielectric behavior at low frequencies is dominated by the effects of the diffusion of the free charges on the shell surfaces. Our theoretical formula is valid in the low range of frequencies (alpha dispersion) as well as in the high range of frequencies (beta dispersion). Will result that one can measure the membrane electrical potential by a simple investigation of the living cell suspension dielectric properties.

physics.bio-ph↗
arXiv1998

Quantum Field Theory of the Pinned Density Wave

A model is discussed in which an electric field induces quantum nucleation of soliton-antisoliton pairs in a pinned charge or spin density wave. Coulomb blockade prevents pair creation until the electric field exceeds a sharp threshold value, which can be much smaller than the classical depinning field. We calculate the vacuum state energy and expectation value of the phase, which is treated as a quantum scalar field. We find that the phase can also be much smaller, below threshold, than predicted by classical ``sliding'' density wave models.

cond-mat.supr-con↗