5,646 research outputs found
Collective quantum jumps of Rydberg atoms
We study an open quantum system of atoms with long-range Rydberg interaction,
laser driving, and spontaneous emission. Over time, the system occasionally
jumps between a state of low Rydberg population and a state of high Rydberg
population. The jumps are inherently collective and in fact exist only for a
large number of atoms. We explain how entanglement and quantum measurement
enable the jumps, which are otherwise classically forbidden.Comment: 4 page
A general wavelet-based profile decomposition in the critical embedding of function spaces
We characterize the lack of compactness in the critical embedding of
functions spaces having similar scaling properties in the
following terms : a sequence bounded in has a subsequence
that can be expressed as a finite sum of translations and dilations of
functions such that the remainder converges to zero in as
the number of functions in the sum and tend to . Such a
decomposition was established by G\'erard for the embedding of the homogeneous
Sobolev space into the in dimensions with
, and then generalized by Jaffard to the case where is a Riesz
potential space, using wavelet expansions. In this paper, we revisit the
wavelet-based profile decomposition, in order to treat a larger range of
examples of critical embedding in a hopefully simplified way. In particular we
identify two generic properties on the spaces and that are of key use
in building the profile decomposition. These properties may then easily be
checked for typical choices of and satisfying critical embedding
properties. These includes Sobolev, Besov, Triebel-Lizorkin, Lorentz, H\"older
and BMO spaces.Comment: 24 page
Revisiting the exercise heart rate-music tempo preference relationship
In the present study, we investigated a hypothesized quartic relationship (meaning three inflection points) between exercise heart rate (HR) and preferred music tempo. Initial theoretical predictions suggested a positive linear relationship (Iwanaga, 1995a, 1995b); however, recent experimental work has shown that as exercise HR increases, step changes and plateaus that punctuate the profile of music tempo preference may occur (Karageorghis, Jones, & Stuart, 2008). Tempi bands consisted of slow (95–100 bpm), medium
(115–120 bpm), fast (135–140 bpm), and very fast (155–160 bpm) music. Twenty-eight active undergraduate students cycled at exercise intensities representing 40, 50, 60, 70, 80, and 90% of their maximal HR reserve while their music preference was assessed using a 10-point scale. The Exercise Intensity x Music Tempo interaction was significant, F(6.16, 160.05) = 7.08, p < .001, ηp 2 =.21, as was the test for both cubic and quartic trajectories in the exercise HR–preferred-music-tempo relationship (p < .001). Whereas slow tempo music was not preferred at any exercise intensity, preference for fast tempo increased, relative to medium and very fast tempo music, as exercise intensity increased. The implications for the prescription of music in exercise and physical activity contexts are discussed
Absolute frequency measurements of 85Rb nF7/2 Rydberg states using purely optical detection
A three-step laser excitation scheme is used to make absolute frequency
measurements of highly excited nF7/2 Rydberg states in 85Rb for principal
quantum numbers n=33-100. This work demonstrates the first absolute frequency
measurements of rubidium Rydberg levels using a purely optical detection
scheme. The Rydberg states are excited in a heated Rb vapour cell and Doppler
free signals are detected via purely optical means. All of the frequency
measurements are made using a wavemeter which is calibrated against a GPS
disciplined self-referenced optical frequency comb. We find that the measured
levels have a very high frequency stability, and are especially robust to
electric fields. The apparatus has allowed measurements of the states to an
accuracy of 8.0MHz. The new measurements are analysed by extracting the
modified Rydberg-Ritz series parameters.Comment: 12 pages, 5 figures, submitted to New. J. Phy
Ionization of Rydberg atoms by blackbody radiation
We have studied an ionization of alkali-metal Rydberg atoms by blackbody
radiation (BBR). The results of the theoretical calculations of ionization
rates of Li, Na, K, Rb and Cs Rydberg atoms are presented. Calculations have
been performed for nS, nP and nD states which are commonly used in a variety of
experiments, at principal quantum numbers n=8-65 and at the three ambient
temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we
take into account the contributions of BBR-induced redistribution of population
between Rydberg states prior to photoionization and field ionization by
extraction electric field pulses. The obtained results show that these
phenomena affect both the magnitude of measured ionization rates and shapes of
their dependences on n. A Cooper minimum for BBR-induced transitions between
bound Rydberg states of Li has been found. The calculated ionization rates are
compared with our earlier measurements of BBR-induced ionization rates of Na nS
and nD Rydberg states with n=8-20 at 300 K. A good agreement for all states
except nS with n>15 is observed. Useful analytical formulas for quick
estimation of BBR ionization rates of Rydberg atoms are presented. Application
of BBR-induced ionization signal to measurements of collisional ionization
rates is demonstrated.Comment: 36 pages, 16 figures. Paper is revised following NJP referees'
comments and suggestion
The Progenitors of Dwarf Spheroidal Galaxies
Dwarf spheroidal (dSph) galaxies present an evolutionary puzzle that we
explore in 40 early- and late-type dwarfs in the Local Group and nearby field.
Although dSphs formed stars over extended periods, today all but one are free
of detectable interstellar matter (ISM), even in the Fornax dSph, where stars
still formed 100 Myr ago. Combining metallicities for red giants with HI data
from the literature, we show that the well-known offset in
luminosity-metallicity (L-Z) relations for dSphs and dwarf irregular (dIrr)
galaxies exists also when comparing only their old stellar populations: dSphs
have higher mean stellar metallicities for a fixed luminosity. Evidently
younger dSphs experienced more efficient enrichment than young dIrrs. Dwarf
galaxies, whose locus in the L-Z diagram is consistent with that of dSphs even
for baryonic luminosities, are the ``transition-type dwarfs'' Phoenix, DDO210,
LGS3, Antlia, and KKR25. They have mixed dIrr/dSph morphologies, low stellar
masses, low angular momentum, and HI contents of less than a few 10^6 solar
masses. Unlike dIrrs, many transition-type dwarfs would closely resemble dSphs
if their gas were removed; they are likely dSph progenitors. As gas removal is
key, we consider the empirical evidence for various gas removal processes. We
suggest that internal gas removal mechanisms are inadequate and favor ram
pressure stripping to make dSphs. A combination of initial conditions and
environment seems to support the formation of dSphs, which appear to form from
small galaxies with active early star formation, whose evolution halts due to
externally induced gas loss. Transition-type dwarfs then are dSphs that kept
their ISM, and therefore should replace dSphs in isolated locations where
stripping is ineffective. (Abridged)Comment: 25 pages in AASTeX two-column preprint style, 1 table, 3 figures.
Accepted for publication in the Astronomical Journal (April 2003 issue
Concentration analysis and cocompactness
Loss of compactness that occurs in may significant PDE settings can be
expressed in a well-structured form of profile decomposition for sequences.
Profile decompositions are formulated in relation to a triplet , where
and are Banach spaces, , and is, typically, a
set of surjective isometries on both and . A profile decomposition is a
representation of a bounded sequence in as a sum of elementary
concentrations of the form , , , and a remainder that
vanishes in . A necessary requirement for is, therefore, that any
sequence in that develops no -concentrations has a subsequence
convergent in the norm of . An imbedding with this
property is called -cocompact, a property weaker than, but related to,
compactness. We survey known cocompact imbeddings and their role in profile
decompositions
Interaction of vortices in viscous planar flows
We consider the inviscid limit for the two-dimensional incompressible
Navier-Stokes equation in the particular case where the initial flow is a
finite collection of point vortices. We suppose that the initial positions and
the circulations of the vortices do not depend on the viscosity parameter \nu,
and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex
system is well-posed on the interval [0,T]. Under these assumptions, we prove
that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a
superposition of Lamb-Oseen vortices whose centers evolve according to a
viscous regularization of the point vortex system. Convergence holds uniformly
in time, in a strong topology which allows to give an accurate description of
the asymptotic profile of each individual vortex. In particular, we compute to
leading order the deformations of the vortices due to mutual interactions. This
allows to estimate the self-interactions, which play an important role in the
convergence proof.Comment: 39 pages, 1 figur
On the Nature of Andromeda IV
Lying at a projected distance of 40' or 9 kpc from the centre of M31,
Andromeda IV is an enigmatic object first discovered during van den Bergh's
search for dwarf spheroidal companions to M31. Being bluer, more compact and
higher surface brightness than other known dwarf spheroidals, it has been
suggested that And IV is either a relatively old `star cloud' in the outer disk
of M31 or a background dwarf galaxy. We present deep HST WFPC2 observations of
And IV and the surrounding field which, along with ground-based long-slit
spectroscopy and Halpha imagery, are used to decipher the true nature of this
puzzling object. We find compelling evidence that And IV is a background galaxy
seen through the disk of M31. The moderate surface brightness (SB(V)~24), very
blue colour (V-I<~0.6), low current star formation rate (~0.001 solar mass/yr)
and low metallicity (~10% solar) reported here are consistent with And IV being
a small dwarf irregular galaxy, perhaps similar to Local Group dwarfs such as
IC 1613 and Sextans A. Although the distance to And IV is not tightly
constrained with the current dataset, various arguments suggest it lies in the
range 5<~D<~8 Mpc, placing it well outside the confines of the Local Group. It
may be associated with a loose group of galaxies, containing major members UGC
64, IC 1727 and NGC 784. We report an updated position and radial velocity for
And IV.Comment: 26 pages, LaTex with 9 figures (including 6 jpg plates). Accepted for
publication in A
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