394 research outputs found
On the Strong Homotopy Lie-Rinehart Algebra of a Foliation
It is well known that a foliation F of a smooth manifold M gives rise to a
rich cohomological theory, its characteristic (i.e., leafwise) cohomology.
Characteristic cohomologies of F may be interpreted, to some extent, as
functions on the space P of integral manifolds (of any dimension) of the
characteristic distribution C of F. Similarly, characteristic cohomologies with
local coefficients in the normal bundle TM/C of F may be interpreted as vector
fields on P. In particular, they possess a (graded) Lie bracket and act on
characteristic cohomology H. In this paper, I discuss how both the Lie bracket
and the action on H come from a strong homotopy structure at the level of
cochains. Finally, I show that such a strong homotopy structure is canonical up
to isomorphisms.Comment: 41 pages, v2: almost completely rewritten, title changed; v3:
presentation partly changed after numerous suggestions by Jim Stasheff,
mathematical content unchanged; v4: minor revisions, references added. v5:
(hopefully) final versio
Domain modeling and grid generation for multi-block structured grids with application to aerodynamic and hydrodynamic configurations
About five years ago, a joint development was started of a flow simulation system for engine-airframe integration studies on propeller as well as jet aircraft. The initial system was based on the Euler equations and made operational for industrial aerodynamic design work. The system consists of three major components: a domain modeller, for the graphical interactive subdivision of flow domains into an unstructured collection of blocks; a grid generator, for the graphical interactive computation of structured grids in blocks; and a flow solver, for the computation of flows on multi-block grids. The industrial partners of the collaboration and NLR have demonstrated that the domain modeller, grid generator and flow solver can be applied to simulate Euler flows around complete aircraft, including propulsion system simulation. Extension to Navier-Stokes flows is in progress. Delft Hydraulics has shown that both the domain modeller and grid generator can also be applied successfully for hydrodynamic configurations. An overview is given about the main aspects of both domain modelling and grid generation
Quantum non-demolition measurement enables macroscopic Leggett-Garg tests
We show how a test of macroscopic realism based on Leggett-Garg inequalities
(LGIs) can be performed in a macroscopic system. Using a continuous-variable
approach, we consider quantum non-demolition (QND) measurements applied to
atomic ensembles undergoing magnetically-driven coherent oscillation. We
identify measurement schemes requiring only Gaussian states as inputs and
giving a significant LGI violation with realistic experimental parameters and
imperfections. The predicted violation is shown to be due to true quantum
effects rather than to a classical invasivity of the measurement. Using QND
measurements to tighten the "clumsiness loophole" forces the stubborn
macrorealist to re-create quantum back action in his or her account of
measurement
The cosmological constant and the relaxed universe
We study the role of the cosmological constant (CC) as a component of dark
energy (DE). It is argued that the cosmological term is in general unavoidable
and it should not be ignored even when dynamical DE sources are considered.
From the theoretical point of view quantum zero-point energy and phase
transitions suggest a CC of large magnitude in contrast to its tiny observed
value. Simply relieving this disaccord with a counterterm requires extreme
fine-tuning which is referred to as the old CC problem. To avoid it, we discuss
some recent approaches for neutralising a large CC dynamically without adding a
fine-tuned counterterm. This can be realised by an effective DE component which
relaxes the cosmic expansion by counteracting the effect of the large CC.
Alternatively, a CC filter is constructed by modifying gravity to make it
insensitive to vacuum energy.Comment: 6 pages, no figures, based on a talk presented at PASCOS 201
Revisiting longitudinal plasmon-axion conversion in external magnetic fields
In the presence of an external magnetic field the axion and the photon mix.
In particular, the dispersion relation of a longitudinal plasmon always crosses
the dispersion relation of the axion (for small axion masses), thus leading to
a resonant conversion. Using thermal field theory we concisely derive the axion
emission rate, applying it to astrophysical and laboratory scenarios. For the
Sun, depending on the magnetic field profile plasmon-axion conversion can
dominate over Primakoff production at low energies (eV). This
both provides a new axion source for future helioscopes and, in the event of
discovery, would probe the magnetic field structure of the Sun. In the case of
white dwarfs (WDs), plasmon-axion conversion provides a pure photon coupling
probe of the axion, which may contribute significantly for low-mass WDs.
Finally we rederive and confirm the axion absorption rate of the recently
proposed plasma haloscopes.Comment: Matches published version. 14 pages, 8 figure
Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
Entanglement entropy obeys area law scaling for typical physical quantum
systems. This may naively be argued to follow from locality of interactions. We
show that this is not the case by constructing an explicit simple spin chain
Hamiltonian with nearest neighbor interactions that presents an entanglement
volume scaling law. This non-translational model is contrived to have couplings
that force the accumulation of singlet bonds across the half chain. Our result
is complementary to the known relation between non-translational invariant,
nearest neighbor interacting Hamiltonians and QMA complete problems.Comment: 9 pages, 4 figure
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