2,071 research outputs found
Determinants of Hankel Matrices
The purpose of this paper is to compute asymptotically Hankel determinants
for weights that are supported in a semi-infinite interval.The main idea is to
reduce the problem to determinants of other operators whose determinant
asymptotics are well known.Comment: 18 pages, LaTeX fil
Landau Fermi Liquid Picture of Spin Density Functional Theory: Strutinsky Approach to Quantum Dots
We analyze the ground state energy and spin of quantum dots obtained from
spin density functional theory (SDFT) calculations. First, we introduce a
Strutinsky-type approximation, in which quantum interference is treated as a
correction to a smooth Thomas-Fermi description. For large irregular dots, we
find that the second-order Strutinsky expressions have an accuracy of about 5
percent compared to the full SDFT and capture all the qualitative features.
Second, we perform a random matrix theory/random plane wave analysis of the
Strutinsky SDFT expressions. The results are statistically similar to the SDFT
quantum dot statistics. Finally, we note that the second-order Strutinsky
approximation provides, in essence, a Landau Fermi liquid picture of spin
density functional theory. For instance, the leading term in the spin channel
is simply the familiar exchange constant. A direct comparison between SDFT and
the perturbation theory derived ``universal Hamiltonian'' is thus made
possible.Comment: Submitted to Physical Review
Electron-Electron Interactions in Isolated and Realistic Quantum Dots: A Density Functional Theory Study
We use Kohn-Sham spin-density-functional theory to study the statistics of
ground-state spin and the spacing between conductance peaks in the Coulomb
blockade regime for both 2D isolated and realistic quantum dots. We make a
systematic investigation of the effects of electron-electron interaction
strength and electron number on both the peak spacing and spin distributions. A
direct comparison between the distributions from isolated and realistic dots
shows that, despite the difference in the boundary conditions and confining
potential, the statistical properties are qualitatively the same. Strong
even/odd pairing in the peak spacing distribution is observed only in the weak
e-e interaction regime and vanishes for moderate interactions. The probability
of high spin ground states increases for stronger e-e interaction and seems to
saturate around . The saturated value is larger than previous
theoretical predictions. Both spin and conductance peak spacing distributions
show substantial variation as the electron number increases, not saturating
until . To interpret our numerical results, we analyze the spin
distribution in the even case using a simple two-level model.Comment: 10 pages, 12 figures, submitted to Phys. Rev.
Time-Dependent Transport Through Molecular Junctions
We investigate transport properties of molecular junctions under two types of
bias--a short time pulse or an AC bias--by combining a solution for the Green
functions in the time domain with electronic structure information coming from
ab initio density functional calculations. We find that the short time response
depends on lead structure, bias voltage, and barrier heights both at the
molecule-lead contacts and within molecules. Under a low frequency AC bias, the
electron flow either tracks or leads the bias signal (capacitive or resistive
response) depending on whether the junction is perfectly conducting or not. For
high frequency, the current lags the bias signal due to the kinetic inductance.
The transition frequency is an intrinsic property of the junctions.Comment: 5 pages, 9 figure
The Role of the Exchange-Correlation Potential in ab initio Electron Transport Calculations
The effect of the exchange-correlation potential in ab initio electron
transport calculations is investigated by constructing optimized effective
potentials (OEP) using different energy functionals or the electron density
from second-order perturbation theory. We calculate electron transmission
through two atomic chain systems, one with charge transfer and one without.
Dramatic effects are caused by two factors: changes in the energy gap and the
self-interaction error. The error in conductance caused by the former is about
one order of magnitude while that caused by the latter ranges from several
times to two orders of magnitude, depending on the coupling strength and charge
transfer. The implications for accurate quantum transport calculations are
discussed.Comment: 4 pages, published version, substantially revised discussion and
revisions for clarit
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