9,061 research outputs found
Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory
We derive an explicit expression for the functional derivative of the
subleading term in the strong interaction limit expansion of the generalized
Levy--Lieb functional for the special case of two electrons in one dimension.
The expression is derived from the zero point energy (ZPE) functional, which is
valid if the quantum state reduces to strongly correlated electrons in the
strong coupling limit. The explicit expression is confirmed numerically and
respects the relevant sum-rule. We also show that the ZPE potential is able to
generate a bond mid-point peak for homo-nuclear dissociation and is properly of
purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems,
whereas the exact peaks should be finite.Comment: 12 pages, 7 figure
Decoherence-assisted transport and quantum criticalities
We study the dynamics of a two-level quantum system interacting with an
external environment that takes the form of an XY spin chain in the presence of
an external magnetic field. While the presence of the bath itself can enhance
the transition probability from the lower level to the upper level of the
system, we show that this noise-assisted phenomenon is sensitive to a change of
the quantum phase of the environment. The derivative of the transition
probability displays a maximum in correspondence with the critical value of the
applied field both in the case of isotropic and anisotropic chains
Power calculation for gravitational radiation: oversimplification and the importance of time scale
A simplified formula for gravitational-radiation power is examined. It is
shown to give completely erroneous answers in three situations, making it
useless even for rough estimates. It is emphasized that short timescales, as
well as fast speeds, make classical approximations to relativistic calculations
untenable.Comment: Three pages, no figures, accepted for publication in Astronomische
Nachrichte
Exchange-correlation functionals from the strongly-interacting limit of DFT: Applications to model chemical systems
We study model one-dimensional chemical systems (representative of their
three-dimensional counterparts) using the strictly-correlated electrons (SCE)
functional, which, by construction, becomes asymptotically exact in the limit
of infinite coupling strength. The SCE functional has a highly non-local
dependence on the density and is able to capture strong correlation within
Kohn- Sham theory without introducing any symmetry breaking. Chemical systems,
however, are not close enough to the strong-interaction limit so that, while
ionization energies and the stretched H2 molecule are accurately described,
total energies are in general way too low. A correction based on the exact next
leading order in the expansion at infinite coupling strength of the
Hohenberg-Kohn functional largely improves the results.Comment: 9 pages, 6 figures. Submitted to PCCP's Themed Collection on Density
Functional Theory and its Application
Radiative emission of solar features in Ca II K
We investigated the radiative emission of different types of solar features
in the spectral range of the Ca II K line.
We analyzed full-disk 2k x 2k observations from the PSPT Precision Solar
Photometric Telescope. The data were obtained by using three narrow-band
interference filters that sample the Ca II K line with different pass bands.
Two filters are centered in the line core, the other in the red wing of the
line. We measured the intensity and contrast of various solar features,
specifically quiet Sun (inter-network), network, enhanced network, plage, and
bright plage (facula) regions. Moreover, we compared the results obtained with
those derived from the numerical synthesis performed for the three PSPT filters
with a widely used radiative code on a set of reference semi-empirical
atmosphere models.Comment: In Proceedings of the 25th NSO Workshop: Chromospheric Structure and
Dynamic
Robustness of different indicators of quantumness in the presence of dissipation
The dynamics of a pair of coupled harmonic oscillators in separate or common
thermal environments is studied, focusing on different indicators of
quantumness, such as entanglement, twin oscillators correlations and quantum
discord. We compare their decay under the effect of dissipation and show,
through a phase diagram, that entanglement is more likely to survive
asymptotically than twin oscillators correlations
Spin Resolution of the Electron-Gas Correlation Energy: Positive same-spin contribution
The negative correlation energy per particle of a uniform electron gas of
density parameter and spin polarization is well known, but its
spin resolution into up-down, up-up, and down-down contributions is not.
Widely-used estimates are incorrect, and hamper the development of reliable
density functionals and pair distribution functions. For the spin resolution,
we present interpolations between high- and low-density limits that agree with
available Quantum Monte Carlo data. In the low-density limit for ,
we find that the same-spin correlation energy is unexpectedly positive, and we
explain why. We also estimate the up and down contributions to the kinetic
energy of correlation.Comment: new version, to appear in PRB Rapid Communicatio
Droplet minimizers for the Gates-Lebowitz-Penrose free energy functional
We study the structure of the constrained minimizers of the
Gates-Lebowitz-Penrose free-energy functional ,
non-local functional of a density field , , a
-dimensional torus of side length . At low temperatures, is not convex, and has two distinct global minimizers,
corresponding to two equilibrium states. Here we constrain the average density
L^{-d}\int_{{\cal T}_L}m(x)\dd x to be a fixed value between the
densities in the two equilibrium states, but close to the low density
equilibrium value. In this case, a "droplet" of the high density phase may or
may not form in a background of the low density phase, depending on the values
and . We determine the critical density for droplet formation, and the
nature of the droplet, as a function of and . The relation between the
free energy and the large deviations functional for a particle model with
long-range Kac potentials, proven in some cases, and expected to be true in
general, then provides information on the structure of typical microscopic
configurations of the Gibbs measure when the range of the Kac potential is
large enough
Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence
The combination of density functional theory with other approaches to the
many-electron problem through the separation of the electron-electron
interaction into a short-range and a long-range contribution is a promising
method, which is raising more and more interest in recent years. In this work
some properties of the corresponding correlation energy functionals are derived
by studying the electron-electron coalescence condition for a modified
(long-range-only) interaction. A general relation for the on-top (zero
electron-electron distance) pair density is derived, and its usefulness is
discussed with some examples. For the special case of the uniform electron gas,
a simple parameterization of the on-top pair density for a long-range only
interaction is presented and supported by calculations within the ``extended
Overhauser model''. The results of this work can be used to build
self-interaction corrected short-range correlation energy functionals.Comment: revised version, to appear in Phys. Rev.
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