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 $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ 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 $\sigma$-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 $\tau(N) \geq \min\{\tau(M),\Lambda_n\}$ with $\Lambda_n>0$. Various topological conclusions can be drawn, in particular that \tau is a spin-bordism invariant below $\Lambda_n$. Below $\Lambda_n$, the values of $\tau$ 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