10,483 research outputs found
Construction of SU(3) irreps in canonical SO(3)-coupled bases
Alternative canonical methods for defining canonical SO(3)-coupled bases for
SU(3) irreps are considered and compared. It is shown that a basis that
diagonalizes a particular linear combination of SO(3) invariants in the SU(3)
universal enveloping algebra gives basis states that have good quantum
numbers in the asymptotic rotor-model limit.Comment: no figure
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construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it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
The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing
A connection is made between the exact eigen states of the BCS Hamiltonian
and the predictions made by the Tamm-Dancoff Approximation. This connection is
made by means of a parametrised algebra, which gives the exact quasi-spin
algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the
other. Using this algebra to construct the Bethe Ansatz solution of the BCS
Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the
secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An
example is discussed in depth.Comment: Submitted to the proceedings of the Group28 conference
(Newcastle-upon-Tyne, UK). Journal of Physics: Conference Serie
Weak Gravitational Flexion
Flexion is the significant third-order weak gravitational lensing effect
responsible for the weakly skewed and arc-like appearance of lensed galaxies.
Here we demonstrate how flexion measurements can be used to measure galaxy halo
density profiles and large-scale structure on non-linear scales, via
galaxy-galaxy lensing, dark matter mapping and cosmic flexion correlation
functions. We describe the origin of gravitational flexion, and discuss its
four components, two of which are first described here. We also introduce an
efficient complex formalism for all orders of lensing distortion. We proceed to
examine the flexion predictions for galaxy-galaxy lensing, examining isothermal
sphere and Navarro, Frenk & White (NFW) profiles and both circularly symmetric
and elliptical cases. We show that in combination with shear we can precisely
measure galaxy masses and NFW halo concentrations. We also show how flexion
measurements can be used to reconstruct mass maps in 2-D projection on the sky,
and in 3-D in combination with redshift data. Finally, we examine the
predictions for cosmic flexion, including convergence-flexion
cross-correlations, and find that the signal is an effective probe of structure
on non-linear scales.Comment: 17 pages, including 12 figures, submitted to MNRA
Thermoelectric and Seebeck coefficients of granular metals
In this work we present a detailed study and derivation of the thermopower
and thermoelectric coefficient of nano-granular metals at large tunneling
conductance between the grains, g_T>> 1. An important criterion for the
performance of a thermoelectric device is the thermodynamic figure of merit
which is derived using the kinetic coefficients of granular metals. All results
are valid at intermediate temperatures, E_c>>T/g_T>\delta, where \delta is the
mean energy level spacing for a single grain and E_c its charging energy. We
show that the electron-electron interaction leads to an increase of the
thermopower with decreasing grain size and discuss our results in the light of
future generation thermoelectric materials for low temperature applications.
The behavior of the figure of merit depending on system parameters like grain
size, tunneling conductance, and temperature is presented.Comment: 27 pages, 10 figures, revtex
Preparation of Dicke States in an Ion Chain
We have investigated theoretically and experimentally a method for preparing
Dicke states in trapped atomic ions. We consider a linear chain of ion
qubits that is prepared in a particular Fock state of motion, . The
phonons are removed by applying a laser pulse globally to the qubits, and
converting the motional excitation to flipped spins. The global nature of
this pulse ensures that the flipped spins are shared by all the target ions
in a state that is a close approximation to the Dicke state \D{N}{m}. We
calculate numerically the fidelity limits of the protocol and find small
deviations from the ideal state for and . We have demonstrated
the basic features of this protocol by preparing the state \D{2}{1} in two
Mg target ions trapped simultaneously with an Al
ancillary ion.Comment: 5 pages, 2 figure
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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