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 $C_l$, 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 $C_l$'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 $l=7$ and $l=8$. 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 $H_{S}=c mathbf{S}^{2}$ 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 $\alpha = 2(\hbar S)^2/(I\Delta)$ determines the ground state of the molecule. Here $\hbar S$ is the spin, $I$ is the moment of inertia, and $\Delta$ is the tunnel splitting. The magnetic moment of the molecule is zero at $\alpha \alpha_c$. At $\alpha \to \infty$ the spin of the molecule localizes in one of the directions along the anisotropy axis.Comment: 4 pages, 3 figure

Virtual Resonant States in Two-Photon Decay Processes: Lower-Order Terms, Subtractions, and Physical Interpretations

We investigate the two-photon decay rate of a highly excited atomic state which can decay to bound states of lower energy via cascade processes. We show that a naive treatment of the process, based on the introduction of phenomenological decay rates for the intermediate, resonant states, leads to lower-order terms which need to be subtracted in order to obtain the coherent two-photon correction to the decay rate. The sum of the lower-order terms is exactly equal to the one-photon decay rate of the initial state, provided the naive two-photon decay rates are summed over all available two-photon channels. A quantum electrodynamics (QED) treatment of the problem leads to an "automatic" subtraction of the lower-order terms.Comment: 8 pages, RevTe