2,073 research outputs found
Sub-Planck spots of Schroedinger cats and quantum decoherence
Heisenberg's principle states that the product of uncertainties of
position and momentum should be no less than Planck's constant . This is
usually taken to imply that phase space structures associated with sub-Planck
() scales do not exist, or, at the very least, that they do not
matter. I show that this deeply ingrained prejudice is false: Non-local
"Schr\"odinger cat" states of quantum systems confined to phase space volume
characterized by `the classical action' develop spotty structure
on scales corresponding to sub-Planck . Such
structures arise especially quickly in quantum versions of classically chaotic
systems (such as gases, modelled by chaotic scattering of molecules), that are
driven into nonlocal Schr\"odinger cat -- like superpositions by the quantum
manifestations of the exponential sensitivity to perturbations. Most
importantly, these sub-Planck scales are physically significant: determines
sensitivity of a quantum system (or of a quantum environment) to perturbations.
Therefore sub-Planck controls the effectiveness of decoherence and
einselection caused by the environment. It may also be relevant in
setting limits on sensitivity of Schr\"odinger cats used as detectors.Comment: Published in Nature 412, 712-717 (2001
Topological Schr\"odinger cats: Non-local quantum superpositions of topological defects
Topological defects (such as monopoles, vortex lines, or domain walls) mark
locations where disparate choices of a broken symmetry vacuum elsewhere in the
system lead to irreconcilable differences. They are energetically costly (the
energy density in their core reaches that of the prior symmetric vacuum) but
topologically stable (the whole manifold would have to be rearranged to get rid
of the defect). We show how, in a paradigmatic model of a quantum phase
transition, a topological defect can be put in a non-local superposition, so
that - in a region large compared to the size of its core - the order parameter
of the system is "undecided" by being in a quantum superposition of conflicting
choices of the broken symmetry. We demonstrate how to exhibit such a
"Schr\"odinger kink" by devising a version of a double-slit experiment suitable
for topological defects. Coherence detectable in such experiments will be
suppressed as a consequence of interaction with the environment. We analyze
environment-induced decoherence and discuss its role in symmetry breaking.Comment: 7 pages, 4 figure
Decoherence from a Chaotic Environment: An Upside Down "Oscillator" as a Model
Chaotic evolutions exhibit exponential sensitivity to initial conditions.
This suggests that even very small perturbations resulting from weak coupling
of a quantum chaotic environment to the position of a system whose state is a
non-local superposition will lead to rapid decoherence. However, it is also
known that quantum counterparts of classically chaotic systems lose exponential
sensitivity to initial conditions, so this expectation of enhanced decoherence
is by no means obvious. We analyze decoherence due to a "toy" quantum
environment that is analytically solvable, yet displays the crucial phenomenon
of exponential sensitivity to perturbations. We show that such an environment,
with a single degree of freedom, can be far more effective at destroying
quantum coherence than a heat bath with infinitely many degrees of freedom.
This also means that the standard "quantum Brownian motion" model for a
decohering environment may not be as universally applicable as it once was
conjectured to be.Comment: RevTeX, 29 pages, 5 EPS figures. Substantially rewritten analysis,
improved figures, additional references, and errors fixed. Final version (to
appear in PRA
Fragility of a class of highly entangled states of many quantum-bits
We consider a Quantum Computer with n quantum-bits (`qubits'), where each
qubit is coupled independently to an environment affecting the state in a
dephasing or depolarizing way. For mixed states we suggest a quantification for
the property of showing {\it quantum} uncertainty on the macroscopic level. We
illustrate in which sense a large parameter can be seen as an indicator for
large entanglement and give hypersurfaces enclosing the set of separable
states. Using methods of the classical theory of maximum likelihood estimation
we prove that this parameter is decreasing with 1/\sqrt{n} for all those states
which have been exposed to the environment.
Furthermore we consider a Quantum Computer with perfect 1-qubit gates and
2-qubit gates with depolarizing error and show that any state which can be
obtained from a separable initial state lies inbetween a family of pairs of
certain hypersurfaces parallel to those enclosing the separable ones.Comment: 9 Pages, RevTe
What is "system": some decoherence-theory arguments
We discuss the possibility of making the {\it initial} definitions of
mutually different (possibly interacting, or even entangled) systems in the
context of decoherence theory. We point out relativity of the concept of
elementary physical system as well as point out complementarity of the
different possible divisions of a composite system into "subsystems", thus
eventually sharpening the issue of 'what is system'.Comment: 9 pages, no figure
Quantum Chaotic Environments, The Butterfly Effect, And Decoherence
We investigate the sensitivity of quantum systems that are chaotic in a
classical limit, to small perturbations of their equations of motion. This
sensitivity, originally studied in the context of defining quantum chaos, is
relevant to decoherence in situations when the environment has a chaotic
classical counterpart.Comment: 4 pages, 3 figure
The Chandra Fornax Survey - I: The Cluster Environment
We present the first results of a deep Chandra survey of the inner 1 degree
of the Fornax cluster of galaxies. Ten 50 ksec pointings were obtained in a
mosaic centered on the giant elliptical galaxy NGC 1399 at the nominal cluster
center. Emission and temperature maps of Fornax are presented, and an initial
study of 771 detected X-ray point sources is made. Regions as small as 100pc
are resolved. The intra-cluster gas in Fornax exhibits a highly asymmetric
morphology and temperature structure, dominated by a 180 kpc extended ``plume''
of low surface brightness, cool, ~1 keV) gas to the North-East of NGC 1399 with
a sharper edge to the South West. The elliptical galaxy NGC 1404 also exhibits
a cool halo of X-ray gas within the cluster, with a highly sharpened leading
edge as it presumably falls into the cluster, and a cometary-like tail. We
estimate that some ~200-400 point sources are physically associated with
Fornax. Confirming earlier works, we find that the globular cluster population
in NGC 1399 is highly X-ray active, extending to globulars which may in fact be
intra-cluster systems. We have also found a remarkable correlation between the
location of giant and dwarf cluster galaxies and the presence of X-ray
counterparts, such that systems inhabiting regions of low gas density are more
likely to show X-ray activity. Not only does this correlate with the asymmetry
of the intra-cluster gas but also with the axis joining the center of Fornax to
an infalling group 1 Mpc to the South-West. We suggest that Fornax may be
experiencing an intergalactic ``headwind'' due to motion relative to the
surrounding large-scale structure.Comment: 35 pages, 15 figures, submitted to ApJ. Most figures not included
owing to severe compression degradation - we strongly recommend downloading
the full resolution paper from
http://www.astro.columbia.edu/~caleb/ms_highres.pdf (1.9Mb
Constraints on Scalar Asymmetric Dark Matter from Black Hole Formation in Neutron Stars
We consider possibly observable effects of asymmetric dark matter (ADM) in
neutron stars. Since dark matter does not self-annihilate in the ADM scenario,
dark matter accumulates in neutron stars, eventually reaching the Chandrasekhar
limit and forming a black hole. We focus on the case of scalar ADM, where the
constraints from Bose-Einstein condensation and subsequent black hole formation
are most severe due to the absence of Fermi degeneracy pressure. We also note
that in some portions of this constrained parameter space, non-trivial effects
from Hawking radiation can modify our limits. We find that for scalar ADM with
mass between 100 keV and 10^5 GeV, the constraint from pulsars in globular
clusters on the scattering cross-section with neutrons ranges from \sigma_n <
10^{-45} cm^2 to 10^{-52} cm}^2. In particular, for scalar ADM with mass
between 1 GeV and 1 TeV (in the case where black hole evaporation due to
Hawking radiation is unimportant), the constraint on the scattering
cross-section is below what is reachable with ton scale direct detection
experiments.Comment: 24 pages, 5 figures; updated to match published versio
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