Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

We consider chaotic billiards in d dimensions, and study the matrix elements M_{nm} corresponding to general deformations of the boundary. We analyze the dependence of |M_{nm}|^2 on \omega = (E_n-E_m)/\hbar using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency \omega. We show that for dilations and translations of the boundary, |M_{nm}|^2 vanishes like \omega^4 as \omega -> 0, for rotations like \omega^2, whereas for generic deformations it goes to a constant. Such special cases lead to quasi-orthogonality of the eigenstates on the boundary.Comment: 4 pages, 3 figure

Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems

Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving $x(t)=A\sin(\Omega t)$. It is assumed that the classical dynamics is chaotic, and that its power-spectrum extends over some frequency range $|\omega|<\omega_{cl}$. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for $\Omega<\omega_{cl}$, and a relatively small response otherwise, independently of the driving amplitude $A$. We define a non-perturbative regime in the $(\Omega,A)$ space, where LRT fails, and demonstrate this failure numerically. For $A>A_{prt}$, where $A_{prt}\propto\hbar$, the system may have a relatively strong response for $\Omega>\omega_{cl}$, and the shape of the response function becomes $A$ dependent.Comment: 4 pages, 2 figures, revised version with much better introductio

Financial incentives to discontinue long-term benzodiazepine use: a discrete choice experiment investigating patient preferences and willingness to participate.

OBJECTIVES: Investigate the acceptability of financial incentives for initiating a medically supervised benzodiazepine discontinuation programme among people with long-term benzodiazepine use and to identify programme features that influence willingness to participate. METHODS: We conducted a discrete choice experiment in which we presented a variety of incentive-based programs to a sample of older adults with long-term benzodiazepine use identified using the outpatient electronic health record of a university-owned health system. We studied four programme variables: incentive amount for initiating the programme, incentive amount for successful benzodiazepine discontinuation, lottery versus certain payment and whether partial payment was given for dose reduction. Respondents reported their willingness to participate in the programmes and additional information was collected on demographics, history of use and anxiety symptoms. RESULTS: The overall response rate was 28.4%. Among the 126 respondents, all four programme variables influenced stated preferences. Respondents strongly preferred guaranteed cash-based incentives as opposed to a lottery, and the dollar amount of both the starting and conditional incentives had a substantial impact on choice. Willingness to participate increased with the amount of conditional incentive. Programme participation also varied by gender, duration of use and income. CONCLUSIONS: Participation in an incentive-based benzodiazepine discontinuation programme might be relatively low, but is modifiable by programme variables including incentive amounts. These results will be helpful to inform the design of future trials of benzodiazepine discontinuation programmes. Further research is needed to assess the financial viability and potential cost-effectiveness of such economic incentives

Rate of energy absorption by a closed ballistic ring

We make a distinction between the spectroscopic and the mesoscopic conductance of closed systems. We show that the latter is not simply related to the Landauer conductance of the corresponding open system. A new ingredient in the theory is related to the non-universal structure of the perturbation matrix which is generic for quantum chaotic systems. These structures may created bottlenecks that suppress the diffusion in energy space, and hence the rate of energy absorption. The resulting effect is not merely quantitative: For a ring-dot system we find that a smaller Landauer conductance implies a smaller spectroscopic conductance, while the mesoscopic conductance increases. Our considerations open the way towards a realistic theory of dissipation in closed mesoscopic ballistic devices.Comment: 18 pages, 5 figures, published version with updated ref

The Bloch-Okounkov correlation functions, a classical half-integral case

Bloch and Okounkov's correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of \hgl_\infty-modules of level one. Recent works have calculated these character functions for higher levels for \hgl_\infty and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.Comment: v2: minor changes to the introduction; accepted for publication in Letters in Mathematical Physic

An accelerator mode based technique for studying quantum chaos

We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wavepackets with localized spatial and momentum distributions. The potential used to create the accelerator mode and subsequently realize the kicked rotor system is formed by a set of off-resonant standing wave light pulses. We also propose a method for testing whether a selected region of phase space exhibits chaotic or regular behavior using a Ramsey type separated field experiment.Comment: 5 pages, 3 figures, some modest revisions to previous version (esp. to the figures) to aid clarity; accepted for publication in Physical Review A (due out on January 1st 2003

Global Diffusion in a Realistic Three-Dimensional Time-Dependent Nonturbulent Fluid Flow

We introduce and study the first model of an experimentally realizable three-dimensional time-dependent nonturbulent fluid flow to display the phenomenon of global diffusion of passive-scalar particles at arbitrarily small values of the nonintegrable perturbation. This type of chaotic advection, termed {\it resonance-induced diffusion\/}, is generic for a large class of flows.Comment: 4 pages, uuencoded compressed postscript file, to appear in Phys. Rev. Lett. Also available on the WWW from http://formentor.uib.es/~julyan/, or on paper by reques

Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we compute the Melnikov function for a perturbation of a three-dimensional map that has a heteroclinic connection between a pair of invariant circles. The intersection curves of the manifolds are shown to undergo bifurcations in homologyComment: LaTex with 10 eps figure

Quadratic Volume Preserving Maps

We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family of quadratic volume preserving maps in three space for which we find a normal form and study invariant sets. We also give an alternative proof of a theorem by Moser classifying quadratic symplectic maps.Comment: Ams LaTeX file with 4 figures (figure 2 is gif, the others are ps

Sequencing the potato genome: outline and first results to come from the elucidation of the sequence of the world's third most important food crop

Potato is a member of the Solanaceae, a plant family that includes several other economically important species, such as tomato, eggplant, petunia, tobacco and pepper. The Potato Genome Sequencing Consortium (PGSC) aims to elucidate the complete genome sequence of potato, the third most important food crop in the world. The PGSC is a collaboration between 13 research groups from China, India, Poland, Russia, the Netherlands, Ireland, Argentina, Brazil, Chile, Peru, USA, New Zealand and the UK. The potato genome consists of 12 chromosomes and has a (haploid) length of approximately 840 million base pairs, making it a medium-sized plant genome. The sequencing project builds on a diploid potato genomic bacterial artificial chromosome (BAC) clone library of 78000 clones, which has been fingerprinted and aligned into ~7000 physical map contigs. In addition, the BAC-ends have been sequenced and are publicly available. Approximately 30000 BACs are anchored to the Ultra High Density genetic map of potato, composed of 10000 unique AFLPTM markers. From this integrated genetic-physical map, between 50 to 150 seed BACs have currently been identified for every chromosome. Fluorescent in situ hybridization experiments on selected BAC clones confirm these anchor points. The seed clones provide the starting point for a BAC-by-BAC sequencing strategy. This strategy is being complemented by whole genome shotgun sequencing approaches using both 454 GS FLX and Illumina GA2 instruments. Assembly and annotation of the sequence data will be performed using publicly available and tailor-made tools. The availability of the annotated data will help to characterize germplasm collections based on allelic variance and to assist potato breeders to more fully exploit the genetic potential of potat