8,197 research outputs found

### Non-cyclic Geometric Phase due to Spatial Evolution in a Neutron Interferometer

We present a split-beam neutron interferometric experiment to test the
non-cyclic geometric phase tied to the spatial evolution of the system: the
subjacent two-dimensional Hilbert space is spanned by the two possible paths in
the interferometer and the evolution of the state is controlled by phase
shifters and absorbers. A related experiment was reported previously by
Hasegawa et al. [Phys. Rev. A 53, 2486 (1996)] to verify the cyclic spatial
geometric phase. The interpretation of this experiment, namely to ascribe a
geometric phase to this particular state evolution, has met severe criticism
from Wagh [Phys. Rev. A 59, 1715 (1999)]. The extension to a non-cyclic
evolution manifests the correctness of the interpretation of the previous
experiment by means of an explicit calculation of the non-cyclic geometric
phase in terms of paths on the Bloch-sphere.Comment: 4 pages, revtex

### Adaptive Filtering for Large Space Structures: A Closed-Form Solution

In a previous paper Schaechter proposes using an extended Kalman filter to estimate adaptively the (slowly varying) frequencies and damping ratios of a large space structure. The time varying gains for estimating the frequencies and damping ratios can be determined in closed form so it is not necessary to integrate the matrix Riccati equations. After certain approximations, the time varying adaptive gain can be written as the product of a constant matrix times a matrix derived from the components of the estimated state vector. This is an important savings of computer resources and allows the adaptive filter to be implemented with approximately the same effort as the nonadaptive filter. The success of this new approach for adaptive filtering was demonstrated using synthetic data from a two mode system

### Phase Dynamics of Two Entangled Qubits

We make a geometric study of the phases acquired by a general pure bipartite
two level system after a cyclic unitary evolution. The geometric representation
of the two particle Hilbert space makes use of Hopf fibrations. It allows for a
simple description of the dynamics of the entangled state's phase during the
whole evolution. The global phase after a cyclic evolution is always an entire
multiple of $\pi$ for all bipartite states, a result that does not depend on
the degree of entanglement. There are three different types of phases combining
themselves so as to result in the $n \pi$ global phase. They can be identified
as dynamical, geometrical and topological. Each one of them can be easily
identified using the presented geometric description. The interplay between
them depends on the initial state and on its trajectory and the results
obtained are shown to be in connection to those on mixed states phases.Comment: 9 figures, slightly different version from the accepted on

### Flow Equations for Uplifting Half-Flat to Spin(7) Manifolds

In this short supplement to [1], we discuss the uplift of half-flat six-folds
to Spin(7) eight-folds by fibration of the former over a product of two
intervals. We show that the same can be done in two ways - one, such that the
required Spin(7) eight-fold is a double G_2 seven-fold fibration over an
interval, the G_2 seven-fold itself being the half-flat six-fold fibered over
the other interval, and second, by simply considering the fibration of the
half-flat six-fold over a product of two intervals. The flow equations one gets
are an obvious generalization of the Hitchin's flow equations (to obtain
seven-folds of G_2 holonomy from half-flat six-folds [2]). We explicitly show
the uplift of the Iwasawa using both methods, thereby proposing the form of the
new Spin(7) metrics. We give a plausibility argument ruling out the uplift of
the Iwasawa manifold to a Spin(7) eight fold at the "edge", using the second
method. For $Spin(7)$ eight-folds of the type $X_7\times S^1$, $X_7$ being a
seven-fold of SU(3) structure, we motivate the possibility of including
elliptic functions into the "shape deformation" functions of seven-folds of
SU(3) structure of [1] via some connections between elliptic functions, the
Heisenberg group, theta functions, the already known $D7$-brane metric [3] and
hyper-K\"{a}hler metrics obtained in twistor spaces by deformations of
Atiyah-Hitchin manifolds by a Legendre transform in [4].Comment: 12 pages, LaTeX; v3: (JMP) journal version which includes clarifying
remarks related to connection between Spin(7)-folds and SU(3)structur

### Minimal Uncertainty in Momentum: The Effects of IR Gravity on Quantum Mechanics

The effects of the IR aspects of gravity on quantum mechanics is
investigated. At large distances where due to gravity the space-time is curved,
there appears nonzero minimal uncertainty $\Delta p_{0}$ in the momentum of a
quantum mechanical particle. We apply the minimal uncertainty momentum to some
quantum mechanical interferometry examples and show that the phase shift
depends on the area surrounded by the path of the test particle . We also put
some limits on the related parameters. This prediction may be tested through
future experiments. The assumption of minimal uncertainty in momentum can also
explain the anomalous excess of the mass of the Cooper pair in a rotating thin
superconductor ring.Comment: 8 pages, revised version accepted by PR

### Transformation toughened ceramics for the heavy duty diesel engine technology program

The objective of this program is to develop an advanced high temperature oxide structural ceramic for application to the heavy duty diesel engine. The approach is to employ transformation toughening by additions of ZrO.5HfO.5O2 solid solution to the oxide ceramics, mullite (2Al2O3S2SiO2) and alumina (Al2O3). The study is planned for three phases, each 12 months in duration. This report covers Phase 1. During this period, processing techniques were developed to incorporate the ZrO.5HfO.5O2 solid solution in the matrices while retaining the necessary metastable tetragonal phase. Modulus of rupture and of elasticity, coefficient of thermal expansion, fracture toughness by indent technique and thermal diffusivity of representative specimens were measured. In Phase 2, the process will be improved to provide higher mechanical strength and to define the techniques for scale up to component size. In Phase 3, full scale component prototypes will be fabri-]cated

### Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations

We study the relationship between numerical solutions for inverting Tippe Top
and the structure of the dynamical equations. The numerical solutions confirm
oscillatory behaviour of the inclination angle $\theta(t)$ for the symmetry
axis of the Tippe Top. They also reveal further fine features of the dynamics
of inverting solutions defining the time of inversion. These features are
partially understood on the basis of the underlying dynamical equations

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