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Findings of the wetland survey of the David Witherspoon, Inc., 1630 Site, South Knoxville, Knox County, Tennessee
In accordance with Department of Energy (DOE) Regulations surveys for wetland presence or absence were conducted in September 1996 on the DWI-1630 site (Witherspoon Landfill) located in South Knoxville, Knox County, Tennessee. The DWI-1630 site includes a closed, capped landfill area, areas of past disturbance adjacent to the capped area, and patches of hardwood forest. Wetlands were identified on the landfill cap and in a small bottomland that was formerly used for a retention pond in the southwest corner of the DWI-1630 site. The wetlands identified on the cap are man-induced, atypical situation wetlands. These areas have hydrophytic vegetation and wetland hydrology, but the soils do not have hydric characteristics. Wetland development appears to be due to a combination of the grading or subsidence of the clay landfill cap, the low permeability of the clay fill soil, and the absence of surface drainage outlets from the depressions. These atypical situation wetland areas may not be considered by the US Army Corps of Engineers or the State of Tennessee to be jurisdictional wetlands. The wetland in the former retention pond area has hydrophytic vegetation, wetland hydrology, and hydric soils and is a jurisdictional wetland
Riemann's theorem for quantum tilted rotors
The angular momentum, angular velocity, Kelvin circulation, and vortex
velocity vectors of a quantum Riemann rotor are proven to be either (1) aligned
with a principal axis or (2) lie in a principal plane of the inertia ellipsoid.
In the second case, the ratios of the components of the Kelvin circulation to
the corresponding components of the angular momentum, and the ratios of the
components of the angular velocity to those of the vortex velocity are analytic
functions of the axes lengths.Comment: 8 pages, Phys. Rev.
Toroidal quadrupole transitions associated to collective rotational-vibrational motions of the nucleus
In the frame of the algebraic Riemann Rotational Model one computes the
longitudinal, transverse and toroidal multipoles corresponding to the
excitations of low-lying levels in the ground state band of several even-even
nuclei by inelastic electron scattering (e,e'). Related to these transitions a
new quantity, which accounts for the deviations from the Siegert theorem, is
introduced. The intimate connection between the nuclear vorticity and the
dynamic toroidal quadrupole moment is underlined. Inelastic differential
cross-sections calculated at backscattering angles shows the dominancy of
toroidal form-factors over a broad range of momentum transfer.Comment: 11 pages in LaTex, 3 figures available by fax or mail, accepted for
publication in J.Phys.
Vector coherent state representations, induced representations, and geometric quantization: II. Vector coherent state representations
It is shown here and in the preceeding paper (quant-ph/0201129) that vector
coherent state theory, the theory of induced representations, and geometric
quantization provide alternative but equivalent quantizations of an algebraic
model. The relationships are useful because some constructions are simpler and
more natural from one perspective than another. More importantly, each approach
suggests ways of generalizing its counterparts. In this paper, we focus on the
construction of quantum models for algebraic systems with intrinsic degrees of
freedom. Semi-classical partial quantizations, for which only the intrinsic
degrees of freedom are quantized, arise naturally out of this construction. The
quantization of the SU(3) and rigid rotor models are considered as examples.Comment: 31 pages, part 2 of two papers, published versio
Commensurate anisotropic oscillator, SU(2) coherent states and the classical limit
We demonstrate a formally exact quantum-classical correspondence between the
stationary coherent states associated with the commensurate anisotropic
two-dimensional harmonic oscillator and the classical Lissajous orbits. Our
derivation draws upon earlier work of Louck et al [1973 \textit {J. Math.
Phys.} \textbf {14} 692] wherein they have provided a non-bijective canonical
transformation that maps, within a degenerate eigenspace, the commensurate
anisotropic oscillator on to the isotropic oscillator. This mapping leads, in a
natural manner, to a Schwinger realization of SU(2) in terms of the canonically
transformed creation and annihilation operators. Through the corresponding
coherent states built over a degenerate eigenspace, we directly effect the
classical limit via the expectation values of the underlying generators. Our
work completely accounts for the fact that the SU(2) coherent state in general
corresponds to an ensemble of Lissajous orbits.Comment: 11 pages, Latex2e, iopart.cls, replaced with published versio
Non-semisimple Lie algebras with Levi factor \frak{so}(3), \frak{sl}(2,R) and their invariants
We analyze the number N of functionally independent generalized Casimir
invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{%
oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and
\frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a
representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that
for any dimension n >= 6 there exist Lie algebras
\frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition
such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0.Comment: 16 page
An exactly solvable model of a superconducting to rotational phase transition
We consider a many-fermion model which exhibits a transition from a
superconducting to a rotational phase with variation of a parameter in its
Hamiltonian. The model has analytical solutions in its two limits due to the
presence of dynamical symmetries. However, the symmetries are basically
incompatible with one another; no simple solution exists in intermediate
situations. Exact (numerical) solutions are possible and enable one to study
the behavior of competing but incompatible symmetries and the phase transitions
that result in a semirealistic situation. The results are remarkably simple and
shed light on the nature of phase transitions.Comment: 11 pages including 1 figur
A mixed-mode shell-model theory for nuclear structure studies
We introduce a shell-model theory that combines traditional spherical states,
which yield a diagonal representation of the usual single-particle interaction,
with collective configurations that track deformations, and test the validity
of this mixed-mode, oblique basis shell-model scheme on Mg. The correct
binding energy (within 2% of the full-space result) as well as low-energy
configurations that have greater than 90% overlap with full-space results are
obtained in a space that spans less than 10% of the full space. The results
suggest that a mixed-mode shell-model theory may be useful in situations where
competing degrees of freedom dominate the dynamics and full-space calculations
are not feasible.Comment: 20 pages, 8 figures, revtex 12p
On the equivalence of pairing correlations and intrinsic vortical currents in rotating nuclei
The present paper establishes a link between pairing correlations in rotating
nuclei and collective vortical modes in the intrinsic frame. We show that the
latter can be embodied by a simple S-type coupling a la Chandrasekhar between
rotational and intrinsic vortical collective modes. This results from a
comparison between the solutions of microscopic calculations within the HFB and
the HF Routhian formalisms. The HF Routhian solutions are constrained to have
the same Kelvin circulation expectation value as the HFB ones. It is shown in
several mass regions, pairing regimes, and for various spin values that this
procedure yields moments of inertia, angular velocities, and current
distributions which are very similar within both formalisms. We finally present
perspectives for further studies.Comment: 8 pages, 4 figures, submitted to Phys. Rev.
Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations
Coherent state theory is shown to reproduce three categories of
representations of the spectrum generating algebra for an algebraic model: (i)
classical realizations which are the starting point for geometric quantization;
(ii) induced unitary representations corresponding to prequantization; and
(iii) irreducible unitary representations obtained in geometric quantization by
choice of a polarization. These representations establish an intimate relation
between coherent state theory and geometric quantization in the context of
induced representations.Comment: 29 pages, part 1 of two papers, published versio