10,992 research outputs found
Coherent state triplets and their inner products
It is shown that if H is a Hilbert space for a representation of a group G,
then there are triplets of spaces F_H, H, F^H, in which F^H is a space of
coherent state or vector coherent state wave functions and F_H is its dual
relative to a conveniently defined measure. It is shown also that there is a
sequence of maps F_H -> H -> F^H which facilitates the construction of the
corresponding inner products. After completion if necessary, the F_H, H, and
F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H
is often easier to evaluate in F_H than F^H. Thus, we obtain integral
expressions for the inner products of coherent state and vector coherent state
representations. These expressions are equivalent to the algebraic expressions
of K-matrix theory, but they are frequently more efficient to apply. The
construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it
contained errors that are being correcte
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
Control of macrophytes by grass carp (ctenopharyngodon idella) in a Waikato drain, New Zealand
Hornwort (Ceratophyllum demersum L.) and other aquatic macrophytes have historically been mechanically removed from the Rangiriri drain and Churchill East drain to maintain drain efficiency. As an alternative control method for the high plant biomass that accumulates at the end of summer, the effect of stocking diploid grass carp (Ctenopharyngodon idella L.) on the aquatic vegetation was evaluated in these Waikato drainage systems. At the start of the trial, both drains had a low diversity of aquatic macrophytes, and of the nine species (including the emergents), seven were exotic. Two months after grass carp were released to Churchill East drain (the treated drain) the four submerged and floating macrophyte species became scarce in the main drain. Over the same period, these species increased in biomass in Rangiriri drain (the untreated drain), where hornwort became dense and surface-reaching and remained so for the duration of the trial. However, grass carp did not control submerged vegetation in smaller side drains or the shallow, upper parts of the main drain, or the marginal sprawling species and emergent species. The cost of leasing the grass carp was similar to the cost of clearing the drains mechanically, but grass carp provided continuous weed control. However, subsequent to this trial, 62 dead grass carp were found in Churchill East drain in February 2001, and weed cover subsequently increased. This illustrates that grass carp management in New Zealand agricultural drains can be problematic due to periodic fish kills
Determination of the wind response of Saturn 5 by statistical methods, volume 1
Statistical analysis of Saturn 5 launch vehicle wind response - Vol.
Schools Respond to Risk Management Programs for Asbestos, Lead in Drinking Water and Radon
Based on a study of the three EPA-initiated, public school risk management programs noted in the title, the authors find that state agency involvement is an important factor in the success of such programs. They also find, e.g., that school districts are justifiably reluctant to comply with tentative program
Representations of the Weyl group and Wigner functions for SU(3)
Bases for SU(3) irreps are constructed on a space of three-particle tensor
products of two-dimensional harmonic oscillator wave functions. The Weyl group
is represented as the symmetric group of permutations of the particle
coordinates of these space. Wigner functions for SU(3) are expressed as
products of SU(2) Wigner functions and matrix elements of Weyl transformations.
The constructions make explicit use of dual reductive pairs which are shown to
be particularly relevant to problems in optics and quantum interferometry.Comment: : RevTex file, 11 pages with 2 figure
Spin and recombination dynamics of excitons and free electrons in p-type GaAs : effect of carrier density
Carrier and spin recombination are investigated in p-type GaAs of acceptor
concentration NA = 1.5 x 10^(17) cm^(-3) using time-resolved photoluminescence
spectroscopy at 15 K. At low pho- tocarrier concentration, acceptors are mostly
neutral and photoelectrons can either recombine with holes bound to acceptors
(e-A0 line) or form excitons which are mostly trapped on neutral acceptors
forming the (A0X) complex. It is found that the spin lifetime is shorter for
electrons that recombine through the e-A0 transition due to spin relaxation
generated by the exchange scattering of free electrons with either trapped or
free holes, whereas spin flip processes are less likely to occur once the
electron forms with a free hole an exciton bound to a neutral acceptor. An
increase of exci- tation power induces a cross-over to a regime where the
bimolecular band-to-band (b-b) emission becomes more favorable due to screening
of the electron-hole Coulomb interaction and ionization of excitonic complexes
and free excitons. Then, the formation of excitons is no longer possible, the
carrier recombination lifetime increases and the spin lifetime is found to
decrease dramatically with concentration due to fast spin relaxation with free
photoholes. In this high density regime, both the electrons that recombine
through the e-A0 transition and through the b-b transition have the same spin
relaxation time.Comment: 4 pages, 5 figure
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
Effect of the Pauli principle on photoelectron spin transport in GaAs
In p+ GaAs thin films, the effect of photoelectron degeneracy on spin
transport is investigated theoretically and experimentally by imaging the spin
polarization profile as a function of distance from a tightly-focussed light
excitation spot. Under degeneracy of the electron gas (high concentration, low
temperature), a dip at the center of the polarization profile appears with a
polarization maximum at a distance of about from the center. This
counterintuitive result reveals that photoelectron diffusion depends on spin,
as a direct consequence of the Pauli principle. This causes a concentration
dependence of the spin stiffness while the spin dependence of the mobility is
found to be weak in doped material. The various effects which can modify spin
transport in a degenerate electron gas under local laser excitation are
considered. A comparison of the data with a numerical solution of the coupled
diffusion equations reveals that ambipolar coupling with holes increases the
steady-state photo-electron density at the excitation spot and therefore the
amplitude of the degeneracy-induced polarization dip. Thermoelectric currrents
are predicted to depend on spin under degeneracy (spin Soret currents), but
these currents are negligible except at very high excitation power where they
play a relatively small role. Coulomb spin drag and bandgap renormalization are
negligible due to electrostatic screening by the hole gas
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