Autocorrelation function of eigenstates in chaotic and mixed systems

We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation length. For localized states, like bouncing ball modes or states living on tori, a simple model using only classical input gives good agreement with the exact result. In particular, a prediction for irregular eigenfunctions in mixed systems is derived and tested. For chaotic systems, the expansion of the autocorrelation function can be used to test quantum ergodicity on different length scales.Comment: 30 pages, 12 figures. Some of the pictures are included in low resolution only. For a version with pictures in high resolution see http://www.physik.uni-ulm.de/theo/qc/ or http://www.maths.bris.ac.uk/~maab

Public Benefits of Undeveloped Lands on Urban Outskirts: Non-Market Valuation Studies and their Role in Land Use Plans

Over the past three decades, the economics profession has developed methods for estimating the public benefits of green spaces, providing an opportunity to incorporate such information into land-use planning. While federal regulations routinely require such estimates for major regulations, the extent to which they are used in local land use plans is not clear. This paper reviews the literature on public values for lands on urban outskirts, not just to survey their methods or empirical findings, but to evaluate the role they have played--or have the potential to play-- in actual land use plans. Based on interviews with authors and representatives of funding agencies and local land trusts, it appears that academic work has had a mixed reception in the policy world. Reasons for this include a lack of interest in making academic work accessible to policy makers, emphasizing revealed preference methods which are inconsistent with policy priorities related to nonuse values, and emphasis on benefit-cost analyses. Nevertheless, there are examples of success stories that illustrate how such information can play a vital role in the design of conservation policies. Working Paper 07-2

Chaotic eigenfunctions in momentum space

We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated momentum distribution, and the angular integrated momentum distribution explicit formulae in terms of the normal derivative along the billiard boundary are derived. We present a detailed numerical study for the stadium and the cardioid billiard, which shows in several cases that the radially integrated momentum distribution is a good indicator of localized eigenstates, such as scars, or bouncing ball modes. We also find examples, where the localization is more strongly pronounced in position space than in momentum space, which we discuss in detail. Finally applications and generalizations are discussed.Comment: 30 pages. The figures are included in low resolution only. For a version with figures in high resolution see http://www.physik.uni-ulm.de/theo/qc/ulm-tp/tp99-2.htm

On the rate of quantum ergodicity in Euclidean billiards

For a large class of quantized ergodic flows the quantum ergodicity theorem due to Shnirelman, Zelditch, Colin de Verdi\`ere and others states that almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we first give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the Wigner function in the case of ergodic systems. Of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value. This is studied numerically for three Euclidean billiards (stadium, cosine and cardioid billiard) using up to 6000 eigenfunctions. We find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions like bouncing ball modes or scarred eigenfunctions. We give a detailed discussion and explanation of these effects using a simple but powerful model. For the rate of quantum ergodicity in momentum space we observe a slower decay. We also study the suitably normalized fluctuations of the expectation values around their mean, and find good agreement with a Gaussian distribution.Comment: 40 pages, LaTeX2e. This version does not contain any figures. A version with all figures can be obtained from http://www.physik.uni-ulm.de/theo/qc/ (File: http://www.physik.uni-ulm.de/theo/qc/ulm-tp/tp97-8.ps.gz) In case of any problems contact Arnd B\"acker (e-mail: [email protected]) or Roman Schubert (e-mail: [email protected]

Regional clusters of innovative activity in Europe: Are social capital and geographical proximity the key determinants?

Finding proper policy instruments to promote productivity growth features prominently on the Lisbon agenda and is central in many national as well as European policy debates. In view of the increased mobility of high-skilled workers in Europe, ongoing globalization and increased interregional and international co-operation, location patterns of innovative activity may be subject to drastic changes. A proper understanding of location patterns of innovative outputs can enhance the effectiveness and efficiency of national and European innovation policies. Building on the literature on the knowledge production function the aim of this paper is to explain the observed differences in the production of innovative output across European regions. Our main research question is whether geographical proximity and social capital are important vehicles of knowledge transmission for the production of innovative output in Europe. Several other variables are used to control for structural differences across European regions. We find support for the hypothesis that both social capital and geographical proximity are important factors in explaining the differences in the production of innovative output across European regions

Is Transition Experience Enough? The Donor-side Effectiveness of Czech and Polish Democracy Aid to Georgia

The paper examines the democracy aid practices of the Czech Republic and Poland in Georgia. These two countries have recently emerged as promoters of democracy, and have argued that their own transition experience puts them in a unique position to support democratization and the consolidation of democracy in the EU’s Eastern Neighbourhood. The paper evaluates how these two countries provide democracy aid to Georgia along three criteria, derived from the aid effectiveness literature: supporting locally driven change, learning from results and coordination. The results indicate that both countries have plenty of space to improve the way their democracy aid is delivered. Neither country has formal systems in place to ensure that they actually support Georgian priorities; evaluations are ad hoc and feedback loops missing; and there is significant scope to improve coordination with other donors. Nonetheless, there seems to be a general perception among stakeholders that the democracy aid provided by the Czech Republic and Poland is relevant to Georgia’s needs

Human papillomavirus 16 is an aetiological factor of scrotal cancer

Background: Squamous cell scrotal carcinoma (SCSC) is an infrequent skin cancer associated historically with occupational carcinogens. Human papillomavirus (HPV) DNA has been associated with SCSC but there is no definitive proof of its oncogenic role. Methods: Human papillomavirus-DNA and -E6*I mRNA were analysed in six invasive histologically typed SCSC. LCM-PCR was used to localise HPV DNA to tumour cells. P16(INK4a)and p53 expression were studied by immunohistochemistry. Results: In three warty or basaloid SCSC HPV16-DNA and E6*I-mRNA were detected. LCM-PCR confirmed HPV16 was in p16(INK4a)-positive malignant cells. However, of three usual-type SCSC, all were HPV-negative and two expressed p53 protein but not p16(INK4a). Conclusions: Human papillomavirus 16 was present in tumour cells and oncogenically active in basaloid and warty SCSC, whereas usual SCSC was HPV-negative and showed immunostaining, suggesting p53 mutation. The dual pathways of oncogenesis and relation between histological type of SCSC and HPV are similar to that in penile cancers