4,888 research outputs found
SU(N) Wigner-Racah algebra for the matrix of second moments of embedded Gaussian unitary ensemble of random matrices
Recently Pluhar and Weidenmueller [Ann. Phys. (N.Y.) Vol 297, 344 (2002)]
showed that the eigenvectors of the matrix of second moments of embedded
Gaussian unitary ensemble of random matrices generated by k-body interactions
(EGUE(k)) for m fermions in N single particle states are SU(N) Wigner
coefficients and derived also an expression for the eigenvalues. Going beyond
this work, we will show that the eigenvalues of this matrix are square of a
SU(N) Racah coefficient and thus the matrix of second moments of EGUE(k) is
solved completely by SU(N) Wigner-Racah algebra.Comment: 16 page
Angular-planar CMB power spectrum
Gaussianity and statistical isotropy of the Universe are modern cosmology's
minimal set of hypotheses. In this work we introduce a new statistical test to
detect observational deviations from this minimal set. By defining the
temperature correlation function over the whole celestial sphere, we are able
to independently quantify both angular and planar dependence (modulations) of
the CMB temperature power spectrum over different slices of this sphere. Given
that planar dependence leads to further modulations of the usual angular power
spectrum , this test can potentially reveal richer structures in the
morphology of the primordial temperature field. We have also constructed an
unbiased estimator for this angular-planar power spectrum which naturally
generalizes the estimator for the usual 's. With the help of a chi-square
analysis, we have used this estimator to search for observational deviations of
statistical isotropy in WMAP's 5 year release data set (ILC5), where we found
only slight anomalies on the angular scales and . Since this
angular-planar statistic is model-independent, it is ideal to employ in
searches of statistical anisotropy (e.g., contaminations from the galactic
plane) and to characterize non-Gaussianities.Comment: Replaced to match the published version. Journal-ref: Phys.Rev. D80
063525 (2009
Implementation of optimal phase-covariant cloning machines
The optimal phase covariant cloning machine (PQCM) broadcasts the information
associated to an input qubit into a multi-qubit systems, exploiting a partial
a-priori knowledge of the input state. This additional a priori information
leads to a higher fidelity than for the universal cloning. The present article
first analyzes different experimental schemes to implement the 1->3 PQCM. The
method is then generalized to any 1->M machine for odd value of M by a
theoretical approach based on the general angular momentum formalism. Finally
different experimental schemes based either on linear or non-linear methods and
valid for single photon polarization encoded qubits are discussed.Comment: 7 pages, 3 figure
Polarized entangled Bose-Einstein condensation
We consider a mixture of two distinct species of atoms of pseudospin-1/2 with
both intraspecies and Interspecies spin-exchange interactions, and find all the
ground stats in a general case of the parameters in the effective Hamiltonian.
In general, corresponding to the two species and two pseudo-spin states, there
are four orbital wave functions into which the atoms condense. We find that in
certain parameter regimes, the ground state is the so-called polarized
entangled Bose-Einstein condensation, i.e. in addition to condensation of
interspecies singlet pairs, there are unpaired atoms with spins polarized in
the same direction. The interspecies entanglement and polarization
significantly affect the generalized Gross-Pitaevskii equations governing the
four orbital wave functions into which the atoms condense, as an interesting
interplay between spin and orbital degrees of freedom.Comment: 14 pages, received by PRA on 27 October 201
Surfactant-induced migration of a spherical drop in Stokes flow
In Stokes flows, symmetry considerations dictate that a neutrally-buoyant
spherical particle will not migrate laterally with respect to the local flow
direction. We show that a loss of symmetry due to flow-induced surfactant
redistribution leads to cross-stream drift of a spherical drop in Poiseuille
flow. We derive analytical expressions for the migration velocity in the limit
of small non-uniformities in the surfactant distribution, corresponding to
weak-flow conditions or a high-viscosity drop. The analysis predicts that the
direction of migration is always towards the flow centerline.Comment: Significant extension with additional text, figures, equations, et
N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature
We investigate the large N reduced model of gauge theory on a curved
spacetime through the plane wave matrix model. We formally derive the action of
the N=4 supersymmetric Yang-Mills theory on R \times S^3 from the plane wave
matrix model in the large N limit. Furthermore, we evaluate the effective
action of the plane wave matrix model up to the two-loop level at finite
temperature. We find that the effective action is consistent with the free
energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature
limit where the planar contributions dominate. We conclude that the plane wave
matrix model can be used as a large N reduced model to investigate
nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \times
S^3.Comment: 31pages: added comments and reference
Noncommuting spherical coordinates
Restricting the states of a charged particle to the lowest Landau level
introduces a noncommutativity between Cartesian coordinate operators. This idea
is extended to the motion of a charged particle on a sphere in the presence of
a magnetic monopole. Restricting the dynamics to the lowest energy level
results in noncommutativity for angular variables and to a definition of a
noncommuting spherical product. The values of the commutators of various
angular variables are not arbitrary but are restricted by the discrete
magnitude of the magnetic monopole charge. An algebra, isomorphic to angular
momentum, appears. This algebra is used to define a spherical star product.
Solutions are obtained for dynamics in the presence of additional angular
dependent potentials.Comment: 5 pages, RevTex4 fil
Spin evolution of spin-1 Bose-Einstein condensates
An analytical formula is obtained to describe the evolution of the average
populations of spin components of spin-1 atomic gases. The formula is derived
from the exact time-dependent solution of the Hamiltonian without using approximation. Therefore it goes beyond the mean
field theory and provides a general, accurate, and complete description for the
whole process of non-dissipative evolution starting from various initial
states. The numerical results directly given by the formula coincide
qualitatively well with existing experimental data, and also with other
theoretical results from solving dynamic differential equations. For some
special cases of initial state, instead of undergoing strong oscillation as
found previously, the evolution is found to go on very steadily in a very long
duration.Comment: 7 pages, 3 figures
Rotational States of Magnetic Molecules
We study a magnetic molecule that exhibits spin tunneling and is free to
rotate about its anisotropy axis. Exact low-energy eigenstates of the molecule
that are superpositions of spin and rotational states are obtained. We show
that parameter determines the ground state of
the molecule. Here is the spin, is the moment of inertia, and
is the tunnel splitting. The magnetic moment of the molecule is zero
at . At the spin of the molecule localizes in one of
the directions along the anisotropy axis.Comment: 4 pages, 3 figure
Proton emission induced by polarized photons
The proton emission induced by polarized photons is studied in the energy
range above the giant resonance region and below the pion emission threshold.
Results for the 12C, 16O and 40Ca nuclei are presented. The sensitivity of
various observables to final state interaction, meson exchange currents and
short range correlations is analyzed. We found relevant effects due to the
virtual excitation of the resonance.Comment: 12 pages, 11 figures, 1 tabl
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