536 research outputs found
Angular versus radial correlation effects on momentum distributions of light two-electron ions
We investigate different correlation mechanisms for two-electron systems and
compare their respective effects on various electron distributions. The
simplicity of the wave functions used allows for the derivation of closed-form
analytical expressions for all electron distributions. Among other features, it
is shown that angular and radial correlation mechanisms have opposite effects
on Compton profiles at small momenta.Comment: 22 pages, 5 figures, 3 tabl
Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
A countable set of asymptotic space -- localized solutions is constructed by
the complex germ method in the adiabatic approximation for the nonstationary
Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic
potential. The asymptotic parameter is 1/T, where is the adiabatic
evolution time.
A generalization of the Berry phase of the linear Schr\"odinger equation is
formulated for the Gross-Pitaevskii equation. For the solutions constructed,
the Berry phases are found in explicit form.Comment: 13 pages, no figure
Non-Linear Vibrations in Nuclei
We have perfomed Time Dependant Hartree-Fock (TDHF) calculations on the non
linear response of nuclei. We have shown that quadrupole (and dipole) motion
produces monopole (and quadrupole) oscillations in all atomic nuclei. We have
shown that these findings can be interpreted as a large coupling between one
and two phonon states leading to large anharmonicities.Comment: 4 pages, 3 figure
Alfv\'en Reflection and Reverberation in the Solar Atmosphere
Magneto-atmospheres with Alfv\'en speed [a] that increases monotonically with
height are often used to model the solar atmosphere, at least out to several
solar radii. A common example involves uniform vertical or inclined magnetic
field in an isothermal atmosphere, for which the Alfv\'en speed is exponential.
We address the issue of internal reflection in such atmospheres, both for
time-harmonic and for transient waves. It is found that a mathematical boundary
condition may be devised that corresponds to perfect absorption at infinity,
and, using this, that many atmospheres where a(x) is analytic and unbounded
present no internal reflection of harmonic Alfv\'en waves. However, except for
certain special cases, such solutions are accompanied by a wake, which may be
thought of as a kind of reflection. For the initial-value problem where a
harmonic source is suddenly switched on (and optionally off), there is also an
associated transient that normally decays with time as O(t-1) or O(t-1 ln t),
depending on the phase of the driver. Unlike the steady-state harmonic
solutions, the transient does reflect weakly. Alfv\'en waves in the solar
corona driven by a finite-duration train of p-modes are expected to leave such
transients.Comment: Accepted by Solar Physic
Electronic Structure Calculation by First Principles for Strongly Correlated Electron Systems
Recent trends of ab initio studies and progress in methodologies for
electronic structure calculations of strongly correlated electron systems are
discussed. The interest for developing efficient methods is motivated by recent
discoveries and characterizations of strongly correlated electron materials and
by requirements for understanding mechanisms of intriguing phenomena beyond a
single-particle picture. A three-stage scheme is developed as renormalized
multi-scale solvers (RMS) utilizing the hierarchical electronic structure in
the energy space. It provides us with an ab initio downfolding of the global
band structure into low-energy effective models followed by low-energy solvers
for the models. The RMS method is illustrated with examples of several
materials. In particular, we overview cases such as dynamics of semiconductors,
transition metals and its compounds including iron-based superconductors and
perovskite oxides, as well as organic conductors of kappa-ET type.Comment: 44 pages including 38 figures, to appear in J. Phys. Soc. Jpn. as an
invited review pape
Uniform electron gases
We show that the traditional concept of the uniform electron gas (UEG) --- a
homogeneous system of finite density, consisting of an infinite number of
electrons in an infinite volume --- is inadequate to model the UEGs that arise
in finite systems. We argue that, in general, a UEG is characterized by at
least two parameters, \textit{viz.} the usual one-electron density parameter
and a new two-electron parameter . We outline a systematic
strategy to determine a new density functional across the
spectrum of possible and values.Comment: 8 pages, 2 figures, 5 table
A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry
We present here a review of the fundamental topics of Hartree-Fock theory in
Quantum Chemistry. From the molecular Hamiltonian, using and discussing the
Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock
equations for the electronic problem. Special emphasis is placed in the most
relevant mathematical aspects of the theoretical derivation of the final
equations, as well as in the results regarding the existence and uniqueness of
their solutions. All Hartree-Fock versions with different spin restrictions are
systematically extracted from the general case, thus providing a unifying
framework. Then, the discretization of the one-electron orbitals space is
reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition
of the basic underlying concepts related to the construction and selection of
Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we
close the review with a section in which the most relevant modern developments
(specially those related to the design of linear-scaling methods) are commented
and linked to the issues discussed. The whole work is intentionally
introductory and rather self-contained, so that it may be useful for non
experts that aim to use quantum chemical methods in interdisciplinary
applications. Moreover, much material that is found scattered in the literature
has been put together here to facilitate comprehension and to serve as a handy
reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and
subeqn package
Kinetic energy bounds for particles confined in spherically-symmetric traps with non-standard dimensions
The kinetic energy of non-relativistic single-particle systems with arbitrary D-dimensional central potentials is found to be bounded from below by means of the orbital hyperangular quantum number, the dimensionality and some radial and logarithmic expectation values of the form langrkrang and langrk (ln r)mrang. Beyond the intrinsic physico-mathematical interest of this problem, we want to contribute to the current development of the theory of independent particles confined in spherically symmetric traps with non-standard dimensions. The latter has been motivated by the recent experimental achievements of the evaporative cooling of dilute (i.e. almost non-interacting) fermions in magnetic traps.We are very grateful for partial support from Junta de Andalucía (under the grants
FQM-0207 and FQM-481), Ministerio de Educación y Ciencia (under the project FIS2005-00973), and the European Research Network NeCCA (under the project INTAS-03-51-6637).
RGF acknowledges the support of Junta de Andalucía under the program of Retorno de
Investigadores a Centros de Investigación Andaluces, and PSM the support of Ministerio de Educación y Ciencia under the program FPU
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