Probing neutrino mass hierarchies and ϕ13\phi_{13} with supernova neutrinos

We investigate the feasibility of probing the neutrino mass hierarchy and the mixing angle $\phi_{13}$ with the neutrino burst from a future supernova. An inverse power-law density $\rho \sim r^{n}$ with varying $n$ is adopted in the analysis as the density profile of a typical core-collapse supernova. The survival probabilities of $\nu_{e}$ and $\bar{\nu}_{e}$ are shown to reduce to two-dimensional functions of $n$ and $\phi_{13}$. It is found that in the $n-\sin^{2} \phi_{13}$ parameter space, the 3D plots of the probability functions exhibit highly non-trivial structures that are sensitive to the mass hierarchy, the mixing angle $\phi_{13}$, and the value of $n$. The conditions that lead to observable differences in the 3D plots are established. With the uncertainty of $n$ considered, a qualitative analysis of the Earth matter effect is also included.Comment: 16 pages, 3 figures. Ref [11] added, and some typos correcte

Spectral properties and magneto-optical excitations in semiconductor double-rings under Rashba spin-orbit interaction

We have numerically solved the Hamiltonian of an electron in a semiconductor double ring subjected to the magnetic flux and Rashba spin-orbit interaction. It is found that the Aharonov-Bohm energy spectrum reveals multi-zigzag periodic structures. The investigations of spin-dependent electron dynamics via Rabi oscillations in two-level and three-level systems demonstrate the possibility of manipulating quantum states. Our results show that the optimal control of photon-assisted inter-ring transitions can be achieved by employing cascade-type and $\Lambda$-type transition mechanisms. Under chirped pulse impulsions, a robust and complete transfer of an electron to the final state is shown to coincide with the estimation of the Landau-Zener formula.Comment: RevTex, 9 pages, 5 figure

Fokker-Planck equation approach to optical bistability in the bad-cavity limit

In the general framework of the system size expansion of Van Kampen and Kubo, we consider the Fokker-Planck equation for a model of absorptive bistability in the bad-cavity limit. The physical system is described by the reduced atomic density operators after adiabatic elimination of the cavity field variables. Mapping of the master equation into c-number form according to the normal-ordering mapping scheme yields known results for the atomic fluctuations and correlation functions; however, it also leads to a Fokker-Planck equation with a non-positive-definite diffusion matrix. The symmetrical-order-mapping scheme eliminates this difficulty. The leading contribution to the system size expansion yields a Fokker-Planck equation for the symmetrical-ordered density function having a positive-definite diffusion matrix. The atomic expectation values and fluctuations previously derived from the quantum Langevin equations emerge naturally from this Fokker-Planck equation

Quantum analysis of optical bistability and spectrum of fluctuations

We discuss the approach to equilibrium and the fluctuations of a bistable system under dynamical conditions such that the field variables can be eliminated adiabatically. The atomic system evolves under the action of the coherent pumping of an external field and of collective and incoherent relaxation processes. The competition between pumping and relaxation effects causes the atomic steady-state configurations to depend discontinuously on the strength of the driving field. We derive an explicit expression for the spectrum of the forward-scattered light, which exhibits hysteresis and a discontinuous dependence on the driving-field amplitude

Optical bistability: a self-consistent analysis of fluctuations and the spectrum of scattered light

The main purpose of this paper is to study the behavior of the atomic fluctuations and the spectrum of the light transmitted by an absorptive bistable device. To this end we develop an approximation scheme based on the so-called system-size expansion and apply it to the quantum-mechanical Langevin equations for the atomic fluctuation operators. The Bonifacio-Lugiato mean-field equations for bistability are derived from the lowest-order approximation to the system-size expansion, while the atomic correlation functions result from the next-higher-order expansion. The calculated spectrum of the transmitted light exhibits line narrowing near the bistable thresholds, discontinuous formation of sidebands along the high-transmission branch of the device, and hysteresis effects

Enabling Factor Analysis on Thousand-Subject Neuroimaging Datasets

The scale of functional magnetic resonance image data is rapidly increasing as large multi-subject datasets are becoming widely available and high-resolution scanners are adopted. The inherent low-dimensionality of the information in this data has led neuroscientists to consider factor analysis methods to extract and analyze the underlying brain activity. In this work, we consider two recent multi-subject factor analysis methods: the Shared Response Model and Hierarchical Topographic Factor Analysis. We perform analytical, algorithmic, and code optimization to enable multi-node parallel implementations to scale. Single-node improvements result in 99x and 1812x speedups on these two methods, and enables the processing of larger datasets. Our distributed implementations show strong scaling of 3.3x and 5.5x respectively with 20 nodes on real datasets. We also demonstrate weak scaling on a synthetic dataset with 1024 subjects, on up to 1024 nodes and 32,768 cores

Lorentz transformation and vector field flows

The parameter changes resulting from a combination of Lorentz transformation are shown to form vector field flows. The exact, finite Thomas rotation angle is determined and interpreted intuitively. Using phase portraits, the parameters evolution can be clearly visualized. In addition to identifying the fixed points, we obtain an analytic invariant, which correlates the evolution of parameters.Comment: 11 pages, 3 figures. Section IV revised and title change

Specifying angular momentum and center of mass for vacuum initial data sets

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisymmetric situation where a bound on the angular momentum by the mass has been shown to hold for black hole solutions. Our construction involves changing the solution at the linear level in a shell near infinity, and perturbing to impose the vacuum constraint equations. The procedure involves the perturbation correction of an approximate solution which is given explicitly.Comment: (v2) a minor change in the introduction and a remark added after Theorem 2.1; (v3) final version, appeared in Comm. Math. Phy

Singlet Charge 2/32/3 Quark hiding the Top: Tevatron and LEP Implications

If $c$ and $t$ quarks are strongly mixed with a weak singlet charge $2/3$ quark, $BR(t\to \ell\nu + X)$ could be suppressed via the $t\to cH^0$ mode, thereby the top quark could still hide below $M_W$, whereas the heavy quark signal observed at the Tevatron is due to the dominantly singlet quark $Q$. This may occur without affecting the small $m_c$ value. Demanding $m_Q \simeq 175$ GeV and m_t \ltap M_W, we find that $BR(t\to \ell\nu + X)$ cannot be too suppressed. The heavy quark $Q$ decays via $W,\ H$, and $Z$ bosons. The latter can lead to $b$-tagged $Z + 4$ jet events, while the strong $c$--$Q$ mixing is reflected in sizable $Q\to sW$ fraction. $Z\to t\bar c$ decay occurs at tree level and may be at the $10^{-3}$ order, leading to the signature of $Z\to \ell\nu b\bar c$, all isolated and with large $p_T$, at $10^{-5}$ order.Comment: 10 pages + 3 Figures (not included), ReVTeX, NTUTH-94-1

Lifetime Measurements in 120Xe

Lifetimes for the lowest three transitions in the nucleus $^{120}$Xe have been measured using the Recoil Distance Technique. Our data indicate that the lifetime for the $2_{1}^{+} \to 0_{1}^{+}$ transition is more than a factor of two lower than the previously adopted value and is in keeping with more recent measurements performed on this nucleus. The theoretical implications of this discrepancy and the possible reason for the erroneous earlier results are discussed. All measured lifetimes in $^{120}$Xe, as well as the systematics of the lifetimes of the 2$_{1}^{+}$ states in Xe isotopes, are compared with predictions of various models. The available data are best described by the Fermion Dynamic Symmetry Model (FDSM).Comment: 9 pages, RevTeX, 3 figures with Postscript file available on request at [email protected], [email protected]. Submitted to Phys. Rev.