8,576 research outputs found
Higher-Power Coherent and Squeezed States
A closed form expression for the higher-power coherent states (eigenstates of
) is given. The cases j=3,4 are discussed in detail, including the
time-evolution of the probability densities. These are compared to the case
j=2, the even- and odd-coherent states. We give the extensions to the
"effective" displacement-operator, higher-power squeezed states and to the
ladder-operator/minimum-uncertainty, higher-power squeezed states. The
properties of all these states are discussed.Comment: 23 pages including 9 figures. To be published in Optics
Communication
Time-dependent Schr\"odinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states
Using the transformations from paper I, we show that the Schr\"odinger
equations for: (1)systems described by quadratic Hamiltonians, (2) systems with
time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie
space-time symmetry algebras. The generators of the symmetry algebras are
obtained explicitly for each case and sets of number-operator states are
constructed. The algebras and the states are used to compute
displacement-operator coherent and squeezed states. Some properties of the
coherent and squeezed states are calculated. The classical motion of these
states is deomonstrated.Comment: LaTeX, 22 pages, new format, edited, with added discussion of the
classical motio
The exotic fraction among unassociated Fermi sources
Revealing the nature of unassociated high-energy (> 100 MeV) gamma-ray
sources remains a challenge 35 years after their discovery. Of the 934
gamma-ray sources at high Galactic latitude (|b| > 15 degrees) in the First
Fermi-LAT catalogue (1FGL), 316 have no obvious associations at other
wavelengths. In this paper, we apply the K-means unsupervised classification
algorithm to isolate potential counterparts for 18 unassociated Fermi sources
contained within a 3000 square degree `overlap region' of the sky intensively
covered in radio and optical wavelengths. Combining our results with previous
works, we reach potential associations for 119 out of the 128 Fermi sources
within said region. If these associations are correct, we estimate that less
than 20% of all remaining unassociated 1FGL sources at high Galactic latitude
(|b| > 15 degrees) might host `exotic' counterparts distinct from known classes
of gamma-ray emitters. Potentially even these outliers could be explained by
high-redshift/dust-obscured analogues of the associated sample or by
intrinsically faint radio objects. Although such estimate leaves some room for
novel discoveries, it severely restricts the possibility of detecting dark
matter subhaloes and other unconventional types of gamma-ray emitters in the
1FGL. In closing, we argue that the identification of Fermi sources at the low
end of the flux density distribution will be a complex process that might only
be achieved through a clever combination of refined classification algorithms,
multi-wavelength efforts, and dedicated optical spectroscopy.Comment: 7 pages, 5 figures, 2 table
Seeking a solution of the Pioneer Anomaly
The 1972 and 1973 launched Pioneer 10 and 11 were the first missions to
explore the outer solar system. They achieved stunning breakthroughs in
deep-space exploration. But around 1980 an unmodeled force of \sim 8 \times
10^{-8} cm/s^2, directed approximately towards the Sun, appeared in the
tracking data. It later was unambiguously verified as not being an artifact.
The origin remains unknown (although radiant heat remains a likely cause).
Increasing effort has gone into understanding this anomaly. We review the
situation and describe programs to resolve the issue.Comment: 7 pages, 1 figure, invited talk at the Fourth Meeting on CPT and
Lorentz Symmetry, 8-11 Aug. 2007, held at Indiana Universit
Earth Flyby Anomalies
In a reference frame fixed to the solar system's center of mass, a
satellite's energy will change as it is deflected by a planet. But a number of
satellites flying by Earth have also experienced energy changes in the
Earth-centered frame -- and that's a mystery.Comment: 5 pagea 3 figure
Displacement-Operator Squeezed States. I. Time-Dependent Systems Having Isomorphic Symmetry Algebras
In this paper we use the Lie algebra of space-time symmetries to construct
states which are solutions to the time-dependent Schr\"odinger equation for
systems with potentials . We describe a set of number-operator eigenstates states,
, that form a complete set of states but which, however,
are usually not energy eigenstates. From the extremal state,
, and a displacement squeeze operator derived using the Lie
symmetries, we construct squeezed states and compute expectation values for
position and momentum as a function of time, . We prove a general
expression for the uncertainty relation for position and momentum in terms of
the squeezing parameters. Specific examples, all corresponding to choices of
and having isomorphic Lie algebras, will be dealt with in the
following paper (II).Comment: 23 pages, LaTe
Lessons Learned from the Pioneers 10/11 for a Mission to Test the Pioneer Anomaly
Analysis of the radio-metric tracking data from the Pioneer 10/11 spacecraft
at distances between 20--70 astronomical units (AU) from the Sun has
consistently indicated the presence of an anomalous, small, constant Doppler
frequency drift. The drift is a blue-shift, uniformly changing with rate a_t =
(2.92 +/- 0.44) x 10^(-18) s/s^2. It can also be interpreted as a constant
acceleration of a_P = (8.74 +/- 1.33) x 10^(-8) cm/s^2 directed towards the
Sun. Although it is suspected that there is a systematic origin to the effect,
none has been found. As a result, the nature of this anomaly has become of
growing interest. Here we discuss the details of our recent investigation
focusing on the effects both external to and internal to the spacecraft, as
well as those due to modeling and computational techniques. We review some of
the mechanisms proposed to explain the anomaly and show their inability to
account for the observed behavior of the anomaly. We also present lessons
learned from this investigation for a potential deep-space experiment that will
reveal the origin of the discovered anomaly and also will characterize its
properties with an accuracy of at least two orders of magnitude below the
anomaly's size. A number of critical requirements and design considerations for
such a mission are outlined and addressed.Comment: 11 pages, invited talk given at ``35th COSPAR Scientific Assebly,''
July 18-24, 2004, Paris, Franc
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