6,023 research outputs found
Helium 2 3S - 2 1S metrology at 1557 nm
An experiment is proposed to excite the 'forbidden' 1s2s 3S1 - 1s2s 1S0
magnetic dipole (M1) transition at 1557 nm in a collimated and slow atomic beam
of metastable helium atoms. It is demonstrated that an excitation rate of 5000
/s can be realised with the beam of a 2W narrowband telecom fiber laser
intersecting the atomic beam perpendicularly. A Doppler-limited sub-MHz
spectroscopic linewidth is anticipated. Doppler-free excitation of 2% of
trapped and cooled atoms may be realised in a one-dimensional optical lattice
geometry, using the 2W laser both for trapping and spectroscopy. The very small
(8 Hz) natural linewidth of this transition presents an opportunity for
accurate tests of atomic structure calculations of the helium atom. A
measurement of the 3He - 4He isotope shift allows for accurate determination of
the difference in nuclear charge radius of both isotopes.Comment: accepted for publication in Europhysics Letter
Total energies from variational functionals of the Green function and the renormalized four-point vertex
We derive variational expressions for the grand potential or action in terms
of the many-body Green function which describes the propagation of
particles and the renormalized four-point vertex which describes the
scattering of two particles in many-body systems. The main ingredient of the
variational functionals is a term we denote as the -functional which plays
a role analogously to the usual -functional studied by Baym (G.Baym,
Phys.Rev. 127, 1391 (1962)) in connection with the conservation laws in
many-body systems. We show that any -derivable theory is also
-derivable and therefore respects the conservation laws. We further set
up a computational scheme to obtain accurate total energies from our
variational functionals without having to solve computationally expensive sets
of self-consistent equations. The input of the functional is an approximate
Green function and an approximate four-point vertex
obtained at a relatively low computational cost. The
variational property of the functional guarantees that the error in the total
energy is only of second order in deviations of the input Green function and
vertex from the self-consistent ones that make the functional stationary. The
functionals that we will consider for practical applications correspond to
infinite order summations of ladder and exchange diagrams and are therefore
particularly suited for applications to highly correlated systems. Their
practical evaluation is discussed in detail.Comment: 21 pages, 10 figures. Physical Review B (accepted
Levels of self-consistency in the GW approximation
We perform calculations on atoms and diatomic molecules at different
levels of self-consistency and investigate the effects of self-consistency on
total energies, ionization potentials and on particle number conservation. We
further propose a partially self-consistent scheme in which we keep the
correlation part of the self-energy fixed within the self-consistency cycle.
This approximation is compared to the fully self-consistent results and to
the and the approximations. Total energies, ionization
potentials and two-electron removal energies obtained with our partially
self-consistent approximation are in excellent agreement with fully
self-consistent results while requiring only a fraction of the
computational effort. We also find that self-consistent and partially
self-consistent schemes provide ionization energies of similar quality as the
values but yield better total energies and energy differences.Comment: 11 pages, 3 figures, 3 table
Successes and Failures of Kadanoff-Baym Dynamics in Hubbard Nanoclusters
We study the non-equilibrium dynamics of small, strongly correlated clusters,
described by a Hubbard Hamiltonian, by propagating in time the Kadanoff-Baym
equations within the Hartree-Fock, 2nd Born, GW and T-matrix approximations. We
compare the results to exact numerical solutions. We find that the T-matrix is
overall superior to the other approximations, and is in good agreement with the
exact results in the low-density regime. In the long time limit, the many-body
approximations attain an unphysical steady state which we attribute to the
implicit inclusion of infinite order diagrams in a few-body system.Comment: 4 pages, 4 figure
Observation of Nonspreading Wave Packets in an Imaginary Potential
We propose and experimentally demonstrate a method to prepare a nonspreading
atomic wave packet. Our technique relies on a spatially modulated absorption
constantly chiseling away from an initially broad de Broglie wave. The
resulting contraction is balanced by dispersion due to Heisenberg's uncertainty
principle. This quantum evolution results in the formation of a nonspreading
wave packet of Gaussian form with a spatially quadratic phase. Experimentally,
we confirm these predictions by observing the evolution of the momentum
distribution. Moreover, by employing interferometric techniques, we measure the
predicted quadratic phase across the wave packet. Nonspreading wave packets of
this kind also exist in two space dimensions and we can control their amplitude
and phase using optical elements.Comment: 4 figure
Steinberg modules and Donkin pairs
We prove that in positive characteristic a module with good filtration for a
group of type E6 restricts to a module with good filtration for a subgroup of
type F4. (Recall that a filtration of a module for a semisimple algebraic group
is called good if its layers are dual Weyl modules.) Our result confirms a
conjecture of Brundan for one more case. The method relies on the canonical
Frobenius splittings of Mathieu. Next we settle the remaining cases, in
characteristic not 2, with a computer-aided variation on the old method of
Donkin.Comment: 16 pages; proof of Brundan's conjecture adde
Separation of the Exchange-Correlation Potential into Exchange plus Correlation: an Optimized Effective Potential Approach
Most approximate exchange-correlation functionals used within density
functional theory are constructed as the sum of two distinct contributions for
exchange and correlation. Separating the exchange component from the entire
functional is useful since, for exchange, exact relations exist under uniform
density scaling and spin scaling. In the past, accurate exchange-correlation
potentials have been generated from essentially exact densities constructed
using information from either quantum chemistry or quantum Monte Carlo
calculations but they have not been correctly decomposed into their separate
exchange and correlation components, except for two-electron systems. exchange
and correlation components (except for two-electron systems). Using a recently
proposed method, equivalent to the solution of an optimized effective potential
problem with the corresponding orbitals replaced by the exact Kohn-Sham
orbitals, we obtain the separation according to the density functional theory
definition. We compare the results for the Ne and Be atoms with those obtained
by the previously used approximate separation scheme
Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise
It is generally known that the orbital diamagnetism of a classical system of
charged particles in thermal equilibrium is identically zero -- the Bohr-van
Leeuwen theorem. Physically, this null result derives from the exact
cancellation of the orbital diamagnetic moment associated with the complete
cyclotron orbits of the charged particles by the paramagnetic moment subtended
by the incomplete orbits skipping the boundary in the opposite sense. Motivated
by this crucial, but subtle role of the boundary, we have simulated here the
case of a finite but \emph{unbounded} system, namely that of a charged particle
moving on the surface of a sphere in the presence of an externally applied
uniform magnetic field. Following a real space-time approach based on the
classical Langevin equation, we have computed the orbital magnetic moment which
now indeed turns out to be non-zero, and has the diamagnetic sign. To the best
of our knowledge, this is the first report of the possibility of finite
classical diamagnetism in principle, and it is due to the avoided cancellation.Comment: Accepted for publication in EP
Ages for illustrative field stars using gyrochronology: viability, limitations and errors
We here develop an improved way of using a rotating star as a clock, set it
using the Sun, and demonstrate that it keeps time well. This technique, called
gyrochronology, permits the derivation of ages for solar- and late-type main
sequence stars using only their rotation periods and colors. The technique is
clarified and developed here, and used to derive ages for illustrative groups
of nearby, late-type field stars with measured rotation periods. We first
demonstrate the reality of the interface sequence, the unifying feature of the
rotational observations of cluster and field stars that makes the technique
possible, and extends it beyond the proposal of Skumanich by specifying the
mass dependence of rotation for these stars. We delineate which stars it cannot
currently be used on. We then calibrate the age dependence using the Sun. The
errors are propagated to understand their dependence on color and period.
Representative age errors associated with the technique are estimated at ~15%
(plus possible systematic errors) for late-F, G, K, & early-M stars. Ages
derived via gyrochronology for the Mt. Wilson stars are shown to be in good
agreement with chromospheric ages for all but the bluest stars, and probably
superior. Gyro ages are then calculated for each of the active main sequence
field stars studied by Strassmeier and collaborators where other ages are not
available. These are shown to be mostly younger than 1Gyr, with a median age of
365Myr. The sample of single, late-type main sequence field stars assembled by
Pizzolato and collaborators is then assessed, and shown to have gyro ages
ranging from under 100Myr to several Gyr, and a median age of 1.2Gyr. Finally,
we demonstrate that the individual components of the three wide binaries
XiBooAB, 61CygAB, & AlphaCenAB yield substantially the same gyro ages.Comment: 58 pages, 18 color figures, accepted for publication in The
Astrophysical Journal; Age uncertainties slightly modified upon correcting an
algebraic error in Section
The Unique History of the Globular Cluster Omega Centauri
Using current observational data and simple dynamical modeling, we
demonstrate that Omega Cen is not special among the Galactic globular clusters
in its ability to produce and retain the heavy elements dispersed in the AGB
phase of stellar evolution. The multiple stellar populations observed in Omega
Cen cannot be explained if it had formed as an isolated star cluster. The
formation within a progenitor galaxy of the Milky Way is more likely, although
the unique properties of Omega Cen still remain a mystery.Comment: published version with minor change
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