Flow in a slowly-tapering channel with oscillating walls

The flow of a fluid in a channel with walls inclined at an angle to each other is investigated at arbitrary Reynolds number. The flow is driven by an oscillatory motion of the wall incorporating a time-periodic displacement perpendicular to the channel centreline. The gap between the walls varies linearly with distance along the channel and is a prescribed periodic function of time. An approximate solution is constructed assuming that the angle of inclination of the walls is small. At leading order the flow corresponds to that in a channel with parallel, vertically oscillating walls examined by Hall and Papageorgiou \cite{HP}. A careful study of the governing partial differential system for the first order approximation controlling the tapering flow due to the wall inclination is conducted. It is found that as the Reynolds number is increased from zero the tapering flow loses symmetry and undergoes exponential growth in time. The loss of symmetry occurs at a lower Reynolds number than the symmetry-breaking for the parallel-wall flow. A window of asymmetric, time-periodic solutions is found at higher Reynolds number, and these are reached via a quasiperiodic transient from a given set of initial conditions. Beyond this window stability is again lost to exponentially growing solutions as the Reynolds number is increased

Testing Broken U(1) Symmetry in a Two-Component Atomic Bose-Einstein Condensate

We present a scheme for determining if the quantum state of a small trapped Bose-Einstein condensate is a state with well defined number of atoms, a Fock state, or a state with a broken U(1) gauge symmetry, a coherent state. The proposal is based on the observation of Ramsey fringes. The population difference observed in a Ramsey fringe experiment will exhibit collapse and revivals due to the mean-field interactions. The collapse and revival times depend on the relative strength of the mean-field interactions for the two components and the initial quantum state of the condensate.Comment: 20 Pages RevTex, 3 Figure

Flavor Alignment Solutions to the Strong CP Problem in Supersymmetry

An approach to solving the Strong CP Problem in supersymmetric theories is discussed which uses abelian family symmetries to align the mass matrices of the quarks and squarks. In this way both the Strong CP Problem and the characteristic flavor and CP problems of supersymmetry can be solved in a single way.Comment: 13 pages, LaTe

Gravitational Smearing of Minimal Supersymmetric Unification Predictions

A short and mean paper.Comment: 10 pages total + 1 postscript figure (included), revised: all lines are TRULY < 70 characters long (try it!); LBL-32905, UCB-PTH-92/3

Family Unification in Five and Six Dimensions

In family unification models, all three families of quarks and leptons are grouped together into an irreducible representation of a simple gauge group, thus unifying the Standard Model gauge symmetries and a gauged family symmetry. Large orthogonal groups, and the exceptional groups $E_7$ and $E_8$ have been much studied for family unification. The main theoretical difficulty of family unification is the existence of mirror families at the weak scale. It is shown here that family unification without mirror families can be realized in simple five-dimensional and six-dimensional orbifold models similar to those recently proposed for SU(5) and SO(10) grand unification. It is noted that a family unification group that survived to near the weak scale and whose coupling extrapolated to high scales unified with those of the Standard model would be evidence accessible in principle at low energy of the existence of small (Planckian or GUT-scale) extra dimensions.Comment: 13 pages, 2 figures, minor corrections, references adde

Gaussian quantum marginal problem

The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of several modes. We find that this result implies a solution to the problem of sharing of entanglement in pure Gaussian states and allows for estimating the global entropy of non-Gaussian states based on local measurements. Implications to the actual preparation of multi-mode continuous-variable entangled states are discussed. We compare the findings with the marginal problem for qubits, the solution of which for pure states has a strikingly similar and in fact simple form.Comment: 18 pages, 1 figure, material added, references updated, except from figure identical with version to appear in Commun. Math. Phy

Quasi-spin Model for Macroscopic Quantum Tunnelling between Two Coupled Bose-Einstein Condensates

The macroscopic quantum tunneling between two coupled Bose-Einstein condensates (BEC) (radio-frequency coupled two-component BECs or two BECs confined in a double-well potential) is mapped onto the tunneling of an uniaxial spin with an applied magnetic field. The tunneling exponent is calculated with an imaginary-time path-integral method. In the limit of low barrier, the dependence of tunneling exponent on the system parameters is obtained, and the crossover temperature from thermal regime to quantum regime is estimated. The detailed information about the tunnelling will give help to control population conversion between coupled BECs and realize quantum computation with coupled BECs.Comment: 20 pages, 4 figures, accepted by Phys.Rev.

On the massless "just-so" solution to the solar neutrino problem

We study the effect of the non-resonant, vacuum oscillation-like neutrino flavor conversion induced by non-standard flavor changing and non-universal flavor diagonal neutrino interactions with electrons in the sun. We have found an acceptable fit for the combined analysis for the solar experiments total rates, the Super-Kamiokande (SK) energy spectrum and zenith angle dependence. Phenomenological constraints on non-standard flavor changing and non-universal flavor diagonal neutrino interactions are considered.Comment: 4 pages, Latex, uses eps

Improvements in the determination of ISS Ca II K parameters

Measurements of the ionized Ca II K line are one of the major resources for long-term studies of solar and stellar activity. They also play a critical role in many studies related to solar irradiance variability, particularly as a ground-based proxy to model the solar ultraviolet flux variation that may influence the Earth's climate. Full disk images of the Sun in Ca II K have been available from various observatories for more than 100 years and latter synoptic Sun-as-a-star observations in Ca II K began in the early 1970s. One of these instruments, the Integrated Sunlight Spectrometer (ISS) has been in operation at Kitt Peak (Arizona) since late 2006. The ISS takes daily observations of solar spectra in nine spectra bands, including the Ca II K and H line s. We describe recent improvements in data reduction of Ca II K observations, and present time variations of nine parameters derived from the profile of this spectral line