100 research outputs found
Gravitational duality near de Sitter space
Gravitational instantons ''Lambda-instantons'' are defined here for any given
value Lambda of the cosmological constant. A multiple of the Euler
characteristic appears as an upper bound for the de Sitter action and as a
lower bound for a family of quadratic actions. The de Sitter action itself is
found to be equivalent to a simple and natural quadratic action. In this paper
we also describe explicitly the reparameterization and duality invariances of
gravity (in 4 dimensions) linearized about de Sitter space. A noncovariant
doubling of the fields using the Hamiltonian formalism leads to first order
time evolution with manifest duality symmetry. As a special case we recover the
linear flat space result of Henneaux and Teitelboim by a smooth limiting
process.Comment: 13 pages, no figure - v2 contains only small redactional changes (one
reference added) and is essentially the published versio
The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature
The harmonic oscillator as a distinguished dynamical system can be defined
not only on the Euclidean plane but also on the sphere and on the hyperbolic
plane, and more generally on any configuration space with constant curvature
and with a metric of any signature, either Riemannian (definite positive) or
Lorentzian (indefinite). In this paper we study the main properties of these
`curved' harmonic oscillators simultaneously on any such configuration space,
using a Cayley-Klein (CK) type approach, with two free parameters \ki, \kii
which altogether correspond to the possible values for curvature and signature
type: the generic Riemannian and Lorentzian spaces of constant curvature
(sphere , hyperbolic plane , AntiDeSitter sphere {\bf
AdS}^{\unomasuno} and DeSitter sphere {\bf dS}^{\unomasuno}) appear in this
family, with the Euclidean and Minkowski spaces as flat limits.
We solve the equations of motion for the `curved' harmonic oscillator and
obtain explicit expressions for the orbits by using three different methods:
first by direct integration, second by obtaining the general CK version of the
Binet's equation and third, as a consequence of its superintegrable character.
The orbits are conics with centre at the potential origin in any CK space,
thereby extending this well known Euclidean property to any constant curvature
configuration space. The final part of the article, that has a more geometric
character, presents those results of the theory of conics on spaces of constant
curvature which are pertinent.Comment: 29 pages, 6 figure
Entangling macroscopic oscillators exploiting radiation pressure
It is shown that radiation pressure can be profitably used to entangle {\it
macroscopic} oscillators like movable mirrors, using present technology. We
prove a new sufficient criterion for entanglement and show that the achievable
entanglement is robust against thermal noise. Its signature can be revealed
using common optomechanical readout apparatus.Comment: 4 pages, 2 eps figures, new separability criterion added, new figure
2, authors list change
Evolution of Anisotropies in Eddington-Born-Infeld Cosmology
Recently a Born-Infeld action for dark energy and dark matter that uses
additional affine connections was proposed. At background level, it was shown
that the new proposal can mimic the standard cosmological evolution. In Bianchi
cosmologies, contrary to the scalar field approach (e.g., Chaplygin gas), the
new approach leads to anisotropic pressure, raising the issues of stability of
the isotropic solution under anisotropic perturbations and, being it stable,
how the anisotropies evolve. In this work, the Eddington-Born-Infeld proposal
is extended to a Bianchi type I scenario and residual post-inflationary
anisotropies are shown to decay in time. Moreover, it is shown that the shears
decay following a damped oscillatory pattern, instead of the standard
exponential-like decay. Allowing for some fine tuning on the initial
conditions, standard theoretical bounds on the shears can be avoided.Comment: 10 pages, 7 figures. v2: ref. added, v3: figs. improved, new
paragraph in the Conclusions. Accepted in PR
Uncertainty relations in curved spaces
Uncertainty relations for particle motion in curved spaces are discussed. The
relations are shown to be topologically invariant. New coordinate system on a
sphere appropriate to the problem is proposed. The case of a sphere is
considered in details. The investigation can be of interest for string and
brane theory, solid state physics (quantum wires) and quantum optics.Comment: published version; phase space structure discussion adde
Zitterbewegung (trembling motion) of electrons in narrow gap semiconductors
Theory of trembling motion [Zitterbewegung (ZB)] of charge carriers in
various narrow-gap materials is reviewed. Nearly free electrons in a periodic
potential, InSb-type semiconductors, bilayer graphene, monolayer graphene and
carbon nanotubes are considered. General features of ZB are emphasized. It is
shown that, when the charge carriers are prepared in the form of Gaussian wave
packets, the ZB has a transient character with the decay time of femtoseconds
in graphene and picoseconds in nanotubes. Zitterbewegung of electrons in
graphene in the presence of an external magnetic field is mentioned. A
similarity of ZB in semiconductors to that of relativistic electrons in a
vacuum is stressed. Possible ways of observing the trembling motion in solids
are mentioned.Comment: 8 pages, 5 figure
Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aert's machine-models
From the beginning of his research, the Belgian physicist Diederik Aerts has
shown great creativity in inventing a number of concrete machine-models that
have played an important role in the development of general mathematical and
conceptual formalisms for the description of the physical reality. These models
can also be used to demystify much of the strangeness in the behavior of
quantum entities, by allowing to have a peek at what's going on - in structural
terms - behind the "quantum scenes," during a measurement. In this author's
view, the importance of these machine-models, and of the approaches they have
originated, have been so far seriously underappreciated by the physics
community, despite their success in clarifying many challenges of quantum
physics. To fill this gap, and encourage a greater number of researchers to
take cognizance of the important work of so-called Geneva-Brussels school, we
describe and analyze in this paper two of Aerts' historical machine-models,
whose operations are based on simple breakable elastic bands. The first one,
called the spin quantum-machine, is able to replicate the quantum probabilities
associated with the spin measurement of a spin-1/2 entity. The second one,
called the \emph{connected vessels of water model} (of which we shall present
here an alternative version based on elastics) is able to violate Bell's
inequality, as coincidence measurements on entangled states can do.Comment: 15 pages, 5 figure
Classical and quantum integrability in 3D systems
In this contribution, we discuss three situations in which complete
integrability of a three dimensional classical system and its quantum version
can be achieved under some conditions. The former is a system with axial
symmetry. In the second, we discuss a three dimensional system without spatial
symmetry which admits separation of variables if we use ellipsoidal
coordinates. In both cases, and as a condition for integrability, certain
conditions arise in the integrals of motion. Finally, we study integrability in
the three dimensional sphere and a particular case associated with the Kepler
problem in .Comment: plenary talk on the Conference QTS-5, July 2007, Valladolid, Spai
Magnetism, FeS colloids, and Origins of Life
A number of features of living systems: reversible interactions and weak
bonds underlying motor-dynamics; gel-sol transitions; cellular connected
fractal organization; asymmetry in interactions and organization; quantum
coherent phenomena; to name some, can have a natural accounting via
interactions, which we therefore seek to incorporate by expanding the horizons
of `chemistry-only' approaches to the origins of life. It is suggested that the
magnetic 'face' of the minerals from the inorganic world, recognized to have
played a pivotal role in initiating Life, may throw light on some of these
issues. A magnetic environment in the form of rocks in the Hadean Ocean could
have enabled the accretion and therefore an ordered confinement of
super-paramagnetic colloids within a structured phase. A moderate H-field can
help magnetic nano-particles to not only overcome thermal fluctuations but also
harness them. Such controlled dynamics brings in the possibility of accessing
quantum effects, which together with frustrations in magnetic ordering and
hysteresis (a natural mechanism for a primitive memory) could throw light on
the birth of biological information which, as Abel argues, requires a
combination of order and complexity. This scenario gains strength from
observations of scale-free framboidal forms of the greigite mineral, with a
magnetic basis of assembly. And greigite's metabolic potential plays a key role
in the mound scenario of Russell and coworkers-an expansion of which is
suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed
Krishnaswami Alladi, Springer 201
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