By considering the specialisation $s_{lambda}(1,q,q^2,...,q^{n-1})$ of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape $lambda$ in terms of two properties of the boxes in the diagram f
or $lambda$. Using specialisations of symplectic and orthogonal Schur functions, we derive corresponding formulae, first given by El Samra and King, for the number of semistandard symplectic and orthogonal $lambda$-tableaux.
We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the mo
mentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations.
The PHENIX MPC-EX detector is a Si-W preshower extension to the existing PHENIX Muon Piston Calorimeters (MPC). The MPC-EX will consist of eight layers of alternating W absorber and Si mini-pad sensors and will be installed in time for RHIC Run-15. C
overing a large pseudorapidity range, 3.1 < eta < 3.8, the MPC-EX and MPC access high-x partons in the projectile nucleon (and low-x partons in the target nucleon) in p+A and transversely polarized proton-proton collisions at 200 GeV. With the addition of the MPC-EX, the neutral pion reconstruction range extends to energies > 80 GeV, a factor of four improvement over current capabilities. Not only will the MPC-EX strengthen PHENIXs existing forward neutral pion and jet measurements, it also provides the necessary neutral pion rejection to make a prompt photon measurement feasible in both p+A and p+p collisions. With this neutral pion rejection, prompt (direct + fragmentation) photon yields at high p_T, p_T > 3 GeV, can be statistically extracted using a double ratio method. In p+A collisions direct photons at forward rapidities are optimally sensitive to the gluon distribution because, unlike pions, direct photons are only produced by processes that are directly sensitive to the gluon distribution at leading order. A measurement of the forward prompt photon R_pA will cleanly access and greatly expand our understanding of the gluon nuclear parton distribution functions and provide important information about the initial state in heavy ion collisions. In transversely polarized p+p collisions the MPC-EX will make possible a measurement of the prompt photon single spin asymmetry A_N, and will help elucidate the correlation of valence partons in the proton with the proton spin.
We study state engineering through bilinear interactions between two remote qubits and two-mode Gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode
Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.
