Higher-Power Coherent and Squeezed States

A closed form expression for the higher-power coherent states (eigenstates of $a^{j}$) 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 $V(x,\tau)=g^{(2)}(\tau)x^2+g^{(1)}(\tau)x +g^{(0)}(\tau)$. We describe a set of number-operator eigenstates states, $\{\Psi_n(x,\tau)\}$, that form a complete set of states but which, however, are usually not energy eigenstates. From the extremal state, $\Psi_0$, 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, $\tau$. 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 $V(x,\tau)$ 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