4,439 research outputs found
Energy Expectation Values and the Integral HellmannâFeynman Theorem: H2+ Molecule
It is by now well known that the integral HellmannâFeynman (IHF) theorem has little quantitative utility for chemically interesting problems, although the formalism potentially affords a ready physical interpretation of changes in molecular conformation. In this paper, the IHF theorem is applied to variational and simple LCAO wavefunctions for the H2+ ground state, which range in quality from crude to essentially exact. The IHF results improve quite dramatically with the quality of the wavefunctions. This suggests that errors in the IHF formula may be of the same order as those in the wavefunction. (In contrast, errors in variationally determined energies are of second order.) Our results suggest a convenient test which can be applied to any revised IHF formalism developed in the future.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70096/2/JCPSA6-49-3-1284-1.pd
Effective field theory approach to Casimir interactions on soft matter surfaces
We utilize an effective field theory approach to calculate Casimir
interactions between objects bound to thermally fluctuating fluid surfaces or
interfaces. This approach circumvents the complicated constraints imposed by
such objects on the functional integration measure by reverting to a point
particle representation. To capture the finite size effects, we perturb the
Hamiltonian by DH that encapsulates the particles' response to external fields.
DH is systematically expanded in a series of terms, each of which scales
homogeneously in the two power counting parameters: \lambda \equiv R/r, the
ratio of the typical object size (R) to the typical distance between them (r),
and delta=kB T/k, where k is the modulus characterizing the surface energy. The
coefficients of the terms in DH correspond to generalized polarizabilities and
thus the formalism applies to rigid as well as deformable objects.
Singularities induced by the point particle description can be dealt with using
standard renormalization techniques. We first illustrate and verify our
approach by re-deriving known pair forces between circular objects bound to
films or membranes. To demonstrate its efficiency and versatility, we then
derive a number of new results: The triplet interactions present in these
systems, a higher order correction to the film interaction, and general scaling
laws for the leading order interaction valid for objects of arbitrary shape and
internal flexibility.Comment: 4 pages, 1 figur
The Annual Cycle of SST in the Eastern Tropical Pacific, Diagnosed in an Ocean GCM
The annual onset of the east Pacific cold tongue is diagnosed in an ocean GCM simulation of the tropical Pacific. The model uses a mixed-layer scheme that explicitly simulates the processes of vertical exchange of heat and momentum with the deeper layers of the ocean; comparison with observations of temperature and currents shows that many important aspects of the model fields are realistic. As previous studies have found, the heat balance in the eastern tropical Pacific is notoriously complicated, and virtually every term in the balance plays a significant role at one time or another. However, despite many complications, the three-dimensional ocean advection terms in the cold tongue region tend to cancel each other in the annual cycle and, to first order, the variation of SST can be described as simply following the variation of net solar radiation at the sea surface (sun minus clouds). The cancellation is primarily between cooling due to equatorial upwelling and warming due to tropical instability waves, both of which are strongest in the second half of the year (when the winds are stronger). Even near the equator, where the ocean advection is relatively intense, the terms associated with cloudiness variations are among the largest contributions to the SST balance. The annual cycle of cloudiness transforms the semiannual solar cycle at the top of the atmosphere into a largely 1 cycle yrâ1 variation of insolation at the sea surface. However, the annual cycle of cloudiness appears closely tied to SST in coupled feedbacks (positive for low stratus decks and negative for deep cumulus convection), so the annual cycle of SST cannot be fully diagnosed in an ocean-only modeling context as in the present study. Zonal advection was found to be a relatively small influence on annual equatorial cold tongue variations; in particular, there was little direct (oceanic) connection between the Peru coastal upwelling and equatorial annual cycles. Meridional advection driven by cross-equatorial winds has been conjectured as a key factor leading to the onset of the cold tongue. The results suggest that the SST changes due to this mechanism are modest, and if meridional advection is in fact a major influence, then it must be through interaction with another process (such as a coupled feedback with stratus cloudiness). At present, it is not possible to evaluate this feedback quantitatively
Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints
We propose a general method for deformation quantization of any second-class
constrained system on a symplectic manifold. The constraints determining an
arbitrary constraint surface are in general defined only locally and can be
components of a section of a non-trivial vector bundle over the phase-space
manifold. The covariance of the construction with respect to the change of the
constraint basis is provided by introducing a connection in the ``constraint
bundle'', which becomes a key ingredient of the conversion procedure for the
non-scalar constraints. Unlike in the case of scalar second-class constraints,
no Abelian conversion is possible in general. Within the BRST framework, a
systematic procedure is worked out for converting non-scalar second-class
constraints into non-Abelian first-class ones. The BRST-extended system is
quantized, yielding an explicitly covariant quantization of the original
system. An important feature of second-class systems with non-scalar
constraints is that the appropriately generalized Dirac bracket satisfies the
Jacobi identity only on the constraint surface. At the quantum level, this
results in a weakly associative star-product on the phase space.Comment: LaTeX, 21 page
Does Low Frequency X-ray QPO Behavior in GRS 1915+105 Influence Subsequent X-ray and Infrared Evolution?
Using observations with the Rossi X-ray Timing Explorer, we examine the
behavior of 2-10 Hz quasi-periodic oscillations (QPOs) during spectrally-hard
dips in the x-ray light curve of GRS 1915+105 that are accompanied by infrared
flares. Of the twelve light-curves examined, nine are beta-class and three are
alpha-class following the scheme of Belloni et al. (2000). In most cases, the
QPO frequency is most strongly correlated to the power law flux, which
partially contradicts some earlier claims that the strongest correlation is
between QPO frequency and blackbody flux. Seven beta-class curves are highly
correlated to blackbody features. In several cases, the QPO evolution appears
to decouple from the spectral evolution. We find that beta-class light-curves
with strong correlations can be distinguished from those without by their
``trigger spike'' morphology. We also show that the origin and strength of the
subsequent infrared flare may be causally linked to the variations in QPO
frequency evolution and not solely tied to the onset of soft x-ray flaring
behavior. We divide the twelve alpha- and beta-class light-curves into three
groups based on the evolution of the QPO, the morphology of the trigger spike,
and the infrared flare strength. An apparent crossover case leads us to
conclude that these groups are not unique modes but represent part of a
continuum of accretion behaviors. We believe the QPO behavior at the initiation
of the hard dip can ultimately be used to determine the terminating x-ray
behavior, and the following infrared flaring behavior.Comment: 29 pages, 9 figures, to be published in Ap
CMB Signals of Neutrino Mass Generation
We propose signals in the cosmic microwave background to probe the type and
spectrum of neutrino masses. In theories that have spontaneous breaking of
approximate lepton flavor symmetries at or below the weak scale, light
pseudo-Goldstone bosons recouple to the cosmic neutrinos after nucleosynthesis
and affect the acoustic oscillations of the electron-photon fluid during the eV
era. Deviations from the Standard Model are predicted for both the total energy
density in radiation during this epoch, \Delta N_nu, and for the multipole of
the n'th CMB peak at large n, \Delta l_n. The latter signal is difficult to
reproduce other than by scattering of the known neutrinos, and is therefore an
ideal test of our class of theories. In many models, the large shift, \Delta
l_n \approx 8 n_S, depends on the number of neutrino species that scatter via
the pseudo-Goldstone boson interaction. This interaction is proportional to the
neutrino masses, so that the signal reflects the neutrino spectrum. The
prediction for \Delta N_nu is highly model dependent, but can be accurately
computed within any given model. It is very sensitive to the number of
pseudo-Goldstone bosons, and therefore to the underlying symmetries of the
leptons, and is typically in the region of 0.03 < \Delta N_nu < 1. This signal
is significantly larger for Majorana neutrinos than for Dirac neutrinos, and,
like the scattering signal, varies as the spectrum of neutrinos is changed from
hierarchical to inverse hierarchical to degenerate.Comment: 40 pages, 4 figure
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