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

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

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]

Mu2e Technical Design Report

The Mu2e experiment at Fermilab will search for charged lepton flavor violation via the coherent conversion process mu- N --> e- N with a sensitivity approximately four orders of magnitude better than the current world's best limits for this process. The experiment's sensitivity offers discovery potential over a wide array of new physics models and probes mass scales well beyond the reach of the LHC. We describe herein the preliminary design of the proposed Mu2e experiment. This document was created in partial fulfillment of the requirements necessary to obtain DOE CD-2 approval.Comment: compressed file, 888 pages, 621 figures, 126 tables; full resolution available at http://mu2e.fnal.gov; corrected typo in background summary, Table 3.

Drying colloidal systems: laboratory models for a wide range of applications

The drying of complex fluids provides a powerful insight into phenomena that take place on time and length scales not normally accessible. An important feature of complex fluids, colloidal dispersions and polymer solutions is their high sensitivity to weak external actions. Thus, the drying of complex fluids involves a large number of physical and chemical processes. The scope of this review is the capacity to tune such systems to reproduce and explore specific properties in a physics laboratory. A wide variety of systems are presented, ranging from functional coatings, food science, cosmetology, medical diagnostics and forensics to geophysics and art

Kyoto protocol cooperation: does government corruption facilitate environmental lobbying?

Does environmental lobbying affect the probability of environmental treaty ratification? Does the level of government corruption play a role for the success of such lobbying? In this paper, we propose that a more corruptible government may be more responsive to the demands of the environmental lobby. We use several stratified hazard models and panel data from 170 countries on the timing of Kyoto Protocol ratification to test this hypothesis. We find that increased environmental lobby group activity raises the probability of ratification, and the effect rises with the degree of corruption