1,831 research outputs found
A study of quantum decoherence in a system with Kolmogorov-Arnol'd-Moser tori
We present an experimental and numerical study of the effects of decoherence
on a quantum system whose classical analogue has Kolmogorov-Arnol'd-Moser (KAM)
tori in its phase space. Atoms are prepared in a caesium magneto-optical trap
at temperatures and densities which necessitate a quantum description. This
real quantum system is coupled to the environment via spontaneous emission. The
degree of coupling is varied and the effects of this coupling on the quantum
coherence of the system are studied. When the classical diffusion through a
partially broken torus is < hbar, diffusion of quantum particles is inhibited.
We find that increasing decoherence via spontaneous emission increases the
transport of quantum particles through the boundary.Comment: 19 pages including 6 figure
Regularity for eigenfunctions of Schr\"odinger operators
We prove a regularity result in weighted Sobolev spaces (or
Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator.
More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space
obtained by blowing up the set of singular points of the Coulomb type potential
V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N}
\frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u
in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution
sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0.
Our result extends to the case when b_j and c_{ij} are suitable bounded
functions on the blown-up space. In the single-electron, multi-nuclei case, we
obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy
Experimental evidence for the role of cantori as barriers in a quantum system
We investigate the effect of cantori on momentum diffusion in a quantum
system. Ultracold caesium atoms are subjected to a specifically designed
periodically pulsed standing wave. A cantorus separates two chaotic regions of
the classical phase space. Diffusion through the cantorus is classically
predicted. Quantum diffusion is only significant when the classical phase-space
area escaping through the cantorus per period greatly exceeds Planck's
constant. Experimental data and a quantum analysis confirm that the cantori act
as barriers.Comment: 19 pages including 9 figures, Accepted for publication in Physical
Review E in March 199
The Cauchy problems for Einstein metrics and parallel spinors
We show that in the analytic category, given a Riemannian metric on a
hypersurface and a symmetric tensor on , the metric
can be locally extended to a Riemannian Einstein metric on with second
fundamental form , provided that and satisfy the constraints on
imposed by the contracted Codazzi equations. We use this fact to study the
Cauchy problem for metrics with parallel spinors in the real analytic category
and give an affirmative answer to a question raised in B\"ar, Gauduchon,
Moroianu (2005). We also answer negatively the corresponding questions in the
smooth category.Comment: 28 pages; final versio
Surgery and the spinorial tau-invariant
We associate to a compact spin manifold M a real-valued invariant \tau(M) by
taking the supremum over all conformal classes over the infimum inside each
conformal class of the first positive Dirac eigenvalue, normalized to volume 1.
This invariant is a spinorial analogue of Schoen's -constant, also
known as the smooth Yamabe number. We prove that if N is obtained from M by
surgery of codimension at least 2, then with . Various topological conclusions
can be drawn, in particular that \tau is a spin-bordism invariant below
. Below , the values of cannot accumulate from
above when varied over all manifolds of a fixed dimension.Comment: to appear in CPD
Climate Forcing by the Volcanic Eruption of Mount Pinatubo. Revised edition
We determine the volcano climate sensitivity and response time for the Mount
Pinatubo eruption. This is achieved using observational measurements of the
temperature anomalies of the lower troposphere and the aerosol optical density
(AOD) in combination with a radiative forcing proxy for AOD. Using standard
linear response theory we find sensitivity = 0.18 +- 0.04 K/(W/m2), which
implies a negative feedback of -1.0 +- 0.4. The intrinsic response time is
5.8+-1.0 months. Both results are contrary to the conventional paradigm that
includes long response times and positive feedback. In addition, we analyze the
outgoing longwave radiation during the Pinatubo eruption and find that its time
dependence follows the forcing much more closely than the temperature, and even
has an amplitude equal to that of the AOD proxy. This finding is independent of
the response time and feedback results.Comment: 22 pages, including 4 figures. Revised version of a paper [Douglass
D. H. and R. S. Knox (2005), Climate forcing by the volcano eruption of Mount
Pinatubo. Geophys. Res. Lett. 32, L05710.doi: 10.1029/2004GL022119]. Revision
is based on subsequent comments and replies to appear in the same journal.
Quantitative results have only minor change
Modelling the climate of the last millennium: what causes the differences between simulations?
An ensemble of simulations performed with a coarse resolution 3-D climate model driven by various combinations of external forcing is used to investigate possible causes for differences noticed in two recent simulations of the climate of the past millennium using General Circulation Models (GCMs). Our results strongly suggest that differences in sensitivity (equilibrium and transient climate response) could be responsible for temperature changes that differ by more than a factor of two between two models. In addition, the spin-up procedure could explain some differences between the simulations during the first centuries of the second millennium. The choice of the forcing reconstruction is found to play a smaller role for the differences in the simulated climate, in the model configurations analyzed here. Furthermore, at decadal scale, internal climate variability can mask the differences associated with different forcing reconstructrions. Copyright 2005 by the American Geophysical Union
Changes in extracellular pH during electrical stimulation of isolated rat vagus nerve
Double-barrelled pH-sensitive micro-electrodes were used to record changes of extracellular pH during repetitive stimulation of isolated rat vagus nerves. It was found that a small initial alkaline shift was followed by a prolonged acidification. The acidification was correlated in time with the poststimulus undershoot of the extracellular K+ activity and with the recovery phase of the nerve conduction velocity. In the presence of ouabain, the acid component of the pH change was completely abolished (indicating a metabolic origin), whereas the alkaline component remained unaltered. These pH changes were too small to make a significant contribution to the activity-related changes in conduction velocity of the vagal C-fibres
A Numerical Investigation of the Effects of Classical Phase Space Structure on a Quantum System
We present a detailed numerical study of a chaotic classical system and its
quantum counterpart. The system is a special case of a kicked rotor and for
certain parameter values possesses cantori dividing chaotic regions of the
classical phase space. We investigate the diffusion of particles through a
cantorus; classical diffusion is observed but quantum diffusion is only
significant when the classical phase space area escaping through the cantorus
per kicking period greatly exceeds Planck's constant. A quantum analysis
confirms that the cantori act as barriers. We numerically estimate the
classical phase space flux through the cantorus per kick and relate this
quantity to the behaviour of the quantum system. We introduce decoherence via
environmental interactions with the quantum system and observe the subsequent
increase in the transport of quantum particles through the boundary.Comment: 15 pages, 22 figure
Invertible Dirac operators and handle attachments on manifolds with boundary
For spin manifolds with boundary we consider Riemannian metrics which are
product near the boundary and are such that the corresponding Dirac operator is
invertible when half-infinite cylinders are attached at the boundary. The main
result of this paper is that these properties of a metric can be preserved when
the metric is extended over a handle of codimension at least two attached at
the boundary. Applications of this result include the construction of
non-isotopic metrics with invertible Dirac operator, and a concordance
existence and classification theorem.Comment: Accepted for publication in Journal of Topology and Analysi
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