51 research outputs found
Nonlinear collective nuclear motion
For each real number a Lie algebra of nonlinear vector fields on
three dimensional Euclidean space is reported. Although each algebra is
mathematically isomorphic to , only the vector
fields correspond to the usual generators of the general linear group. The
vector fields integrate to a nonstandard action of the general
linear group; the case integrates to a local Lie semigroup. For
each , a family of surfaces is identified that is invariant with
respect to the group or semigroup action. For positive the surfaces
describe fissioning nuclei with a neck, while negative surfaces
correspond to exotic bubble nuclei. Collective models for neck and bubble
nuclei are given by irreducible unitary representations of a fifteen
dimensional semidirect sum spectrum generating algebra spanned by its
nonlinear subalgebra plus an abelian nonlinear inertia tensor
subalgebra.Comment: 13 pages plus two figures(available by fax from authors by request
Algebraic nonlinear collective motion
Finite-dimensional Lie algebras of vector fields determine geometrical
collective models in quantum and classical physics. Every set of vector fields
on Euclidean space that generates the Lie algebra sl(3, R) and contains the
angular momentum algebra so(3) is determined. The subset of divergence-free
sl(3, R) vector fields is proven to be indexed by a real number . The
solution is the linear representation that corresponds to the
Riemann ellipsoidal model. The nonlinear group action on Euclidean space
transforms a certain family of deformed droplets among themselves. For positive
, the droplets have a neck that becomes more pronounced as
increases; for negative , the droplets contain a spherical bubble of
radius . The nonlinear vector field algebra is extended to
the nonlinear general collective motion algebra gcm(3) which includes the
inertia tensor. The quantum algebraic models of nonlinear nuclear collective
motion are given by irreducible unitary representations of the nonlinear gcm(3)
Lie algebra. These representations model fissioning isotopes () and
bubble and two-fluid nuclei ().Comment: 32pages, 4 figures not include
Global Time Distribution via Satellite-Based Sources of Entangled Photons
We propose a satellite-based scheme to perform clock synchronization between
ground stations spread across the globe using quantum resources. We refer to
this as a quantum clock synchronization (QCS) network. Through detailed
numerical simulations, we assess the feasibility and capabilities of a
near-term implementation of this scheme. We consider a small constellation of
nanosatellites equipped only with modest resources. These include quantum
devices such as spontaneous parametric down conversion (SPDC) sources,
avalanche photo-detectors (APDs), and moderately stable on-board clocks such as
chip scale atomic clocks (CSACs). In our simulations, the various performance
parameters describing the hardware have been chosen such that they are either
already commercially available, or require only moderate advances. We conclude
that with such a scheme establishing a global network of ground based clocks
synchronized to sub-nanosecond level (up to a few picoseconds) of precision,
would be feasible. Such QCS satellite constellations would form the
infrastructure for a future quantum network, able to serve as a globally
accessible entanglement resource. At the same time, our clock synchronization
protocol, provides the sub-nanosecond level synchronization required for many
quantum networking protocols, and thus, can be seen as adding an extra layer of
utility to quantum technologies in the space domain designed for other
purposes.Comment: 20 pages, 12 figures and 6 tables. Comments are welcom
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