3,038 research outputs found
Density functional theory for strongly interacting electrons
We present an alternative to the Kohn-Sham formulation of density functional
theory for the ground-state properties of strongly interacting electronic
systems. The idea is to start from the limit of zero kinetic energy and
systematically expand the universal energy functional of the density in powers
of a "coupling constant" that controls the magnitude of the kinetic energy. The
problem of minimizing the energy is reduced to the solution of a strictly
correlated electron problem in the presence of an effective potential, which
plays in our theory the same role that the Kohn-Sham potential plays in the
traditional formulation. We discuss several schemes for approximating the
energy functional, and report preliminary results for low-density quantum dots.Comment: Revised version, to appear in Phys. Rev. Let
Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints
The monadic shallow linear Horn fragment is well-known to be decidable and
has many application, e.g., in security protocol analysis, tree automata, or
abstraction refinement. It was a long standing open problem how to extend the
fragment to the non-Horn case, preserving decidability, that would, e.g.,
enable to express non-determinism in protocols. We prove decidability of the
non-Horn monadic shallow linear fragment via ordered resolution further
extended with dismatching constraints and discuss some applications of the new
decidable fragment.Comment: 29 pages, long version of CADE-26 pape
Adiabatic connection at negative coupling strengths
The adiabatic connection of density functional theory (DFT) for electronic
systems is generalized here to negative values of the coupling strength
(with {\em attractive} electrons). In the extreme limit
a simple physical solution is presented and its implications
for DFT (as well as its limitations) are discussed. For two-electron systems (a
case in which the present solution can be calculated exactly), we find that an
interpolation between the limit and the opposite limit of
infinitely strong repulsion () yields a rather accurate
estimate of the second-order correlation energy E\cor\glt[\rho] for several
different densities , without using virtual orbitals. The same procedure
is also applied to the Be isoelectronic series, analyzing the effects of
near-degeneracy.Comment: 9 pages, submitted to PR
The Fermionic Density-functional at Feshbach Resonance
We consider a dilute gas of neutral unpolarized fermionic atoms at zero
temperature.The atoms interact via a short range (tunable) attractive
interaction. We demonstrate analytically a curious property of the gas at
unitarity. Namely, the correlation energy of the gas, evaluated by second order
perturbation theory, has the same density dependence as the first order
exchange energy, and the two almost exactly cancel each other at Feshbach
resonance irrespective of the shape of the potential, provided . Here is the range of the two-body potential, and is
defined through the number density . The implications of this
result for universality is discussed.Comment: Five pages, one table. accepted for publication in PR
Leydig cells express neural cell adhesion molecules in vivo and in vitro
The neural cell adhesion molecule (NCAM) polypeptides are expressed by numerous tissues during embryonic development, where they are involved in cell-cell interactions. In the adult, NCAM expression is confined to a few cell types, including neurons and peptide-hormone-producing cells. Here we demonstrate that the Leydig cells of the adult rat, mouse, and hamster testes express NCAM as well. Western blotting showed that an NCAM of approximately 120 kDa was present in the adult testes of all three species investigated. This form was also found in freshly isolated mouse Leydig cells and in Leydig cells after 2 days in culture. After 4 days in culture, mouse Leydig cells expressed additional NCAM isoforms of approximately 140 and 180 kDa, indicating changes in alternative splicing of NCAM primary transcripts. Also, NCAM mRNA of all isoforms, as detected by S1-nuclease protection assays, increased with time in culture. The expression of the cell adhesion molecule NCAM by adult Leydig cells may explain the aggregation of Leydig cells in clusters in rodent testes, which could be a prerequisite for functional coordination of groups of Leydig cells. Furthermore, the presence of this neural and endocrine marker may indicate a closer relationship between Leydig cells and neural and peptide-hormone-producing cells than is considered to exist at the present time
Strictly correlated uniform electron droplets
We study the energetic properties of finite but internally homogeneous
D-dimensional electron droplets in the strict-correlation limit. The indirect
Coulomb interaction is found to increase as a function of the electron number,
approaching the tighter forms of the Lieb-Oxford bound recently proposed by
Rasanen et al. [Phys. Rev. Lett. 102, 206406 (2009)]. The bound is satisfied in
three-, two-, and one-dimensional droplets, and in the latter case it is
reached exactly - regardless of the type of interaction considered. Our results
provide useful reference data for delocalized strongly correlated systems, and
they can be used in the development and testing of exchange-correlation density
functionals in the framework of density-functional theory
On Functionality of Visibly Pushdown Transducers
Visibly pushdown transducers form a subclass of pushdown transducers that
(strictly) extends finite state transducers with a stack. Like visibly pushdown
automata, the input symbols determine the stack operations. In this paper, we
prove that functionality is decidable in PSpace for visibly pushdown
transducers. The proof is done via a pumping argument: if a word with two
outputs has a sufficiently large nesting depth, there exists a nested word with
two outputs whose nesting depth is strictly smaller. The proof uses technics of
word combinatorics. As a consequence of decidability of functionality, we also
show that equivalence of functional visibly pushdown transducers is
Exptime-Complete.Comment: 20 page
Optimal language policy for the preservation of a minority language
We develop a dynamic language competition model with dynamic state intervention. Parents choose the language(s) to raise their children based on the communicational value of each language as well as on their emotional attachment to the languages at hand. Languages are thus conceptualized as tools for communication as well as carriers of cultural identity. The model includes a high and a low status language, and children can be brought up as monolinguals or bilinguals. Through investment into language policies, the status of the minority language can be increased. The aim of the intervention is to preserve the minority language in a bilingual subpopulation at low costs. We investigate the dynamic structure of the optimally controlled system as well as the optimal policy, identify stable equilibria and provide numerical case studies
On the Matthew effect in research careers: Abnormality on the boundary
The observation that a socioeconomic agent with a high reputation gets a disproportionately higher recognition for the same work than an agent with lower reputation is typical in career development and wealth. This phenomenon, which is known as Matthew effect in the literature, leads to an increasing inequality over time. The present paper employs an optimal control model to study the implications of the Matthew effect on the optimal efforts of a scientist into reputation.
The solution of the model exhibits, for suffiently low effort costs, a new type of unstable equilibrium at which effort is at its upper bound. This equilibrium, which we denote as Stalling Equilibrium, serves as a threshold level separating success and failure in academia. In addition we show that at the Stalling Equilibrium the solution can be abnormal. We provide a clear economic interpretation for this solution characteristic
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