We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are Λ–shaped and driven at two-photon resonance by a pair of lasers, which cool the center–of–mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser–cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb–Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second order perturbation theory. We find that the spectrum of resonance fluorescence is composed by two narrow sidebands — the Stokes and anti-Stokes components of the scattered light — while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow–type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behaviour of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two-levels.

The IWA Performance Indicator System for water services is now recognized as a worldwide reference. Since it first appearance in 2000, the system has been widely quoted, adapted and used in a large number of projects both for internal performance assessment and metric benchmarking. Water professionals have benefited from a coherent and flexible system, with precise and detailed definitions that in many cases have become a standard. The system has proven to be adaptable and it has been used in very different contexts for diverse purposes. The Performance Indicators System can be used in any organization regardless of its size, nature (public, private, etc.) or degree of complexity and development.The second edition of Performance Indicators for Water Supply Services represents a further improvement of the original manual. It contains a reviewed and consolidated version of the indicators, resulting from the real needs of water companies worldwide that were expressed during the extensive field testing of the original system. The indicators now properly cover bulk distribution and the needs of developing countries, and all definitions have been thoroughly revised. The confidence grading scheme has been simplified and the procedure to assess the results- uncertainty has been significantly enhanced.In addition to the updated contents of the original edition, a large part of the manual is now devoted to the practical application of the system. Complete with simplified step-by-step implementation procedures and case studies, the manual provides guidelines on how to adapt the IWA concepts and indicators to specific contexts and objectives.The manual includes a new version of the software Sigma Lite incorporating all the new developments and an improved graphical user interface.This new edition of Performance Indicators for Water Supply Services will be an invaluable reference source for all those concerned with managing the performance of the water supply industry, including those in the water utilities as well as regulators, policy-makers and financial agencies.This title belongs to Manual of Best Practice Series.ISBN: 9781780405292 (eBook)ISBN: 9781843390510 (Print)

Water suppliers worldwide are challenged by climate variations, but so far only the qualitative change in boundary conditions has become clear but not yet the degree and impact on the water supply systems. Short-term quality changes in surface waters can, e.g. be caused by extreme rainfalls after dry periods. Longer heat periods without rain can induce middle-term quality changes in surface waters due to lacking dilution. Furthermore, unsustainable management of groundwater can lead to long-term quality changes and to water shortages, especially in times with higher water demand. Depending on the individual situation, the expected effects on the supply system differ widely, so a general adaptation strategy will not suit the individual problems. The purpose of our work is to enable water supply companies to systematically identify potential risks resulting from climate change and other external factors in a water safety plan approach, and to adapt the supply system in a most effective way by taking advantage of ongoing modernization measures and ‘no-regret’-measures. A suitable adaptation strategy should address climate change conditions as well as other external factors like changing water demand and also to take into account possible effects on every part of the supply system.

Concerns regarding security in water supply have been addressed after the 9/11 terrorist attack on the World Trade Centre and following natural disasters in various places of the world. The yearly geo hazards report accounts for 820 natural catastrophes in 2011, with 50 major and 5 great natural catastrophes. Dominating natural threats for water infrastructure are seismic, meteorological, climatological and hydrological events, summarising storms, tornadoes, floods, wildfires, heat waves, droughts, earthquakes and tsunamis.

We present two physical systems which make Gauß sums experimentally accessible. The probability amplitude for a two-photon transition in an appropriate ladder system driven by a chirped laser pulse is determined by a Gauß sum. The autocorrelation function of a quantum rotor is also of the form of a Gauß sum. These examples suggest rules for determining prime factor components on the basis of the properties of Gauß sums. Moreover, we show how Gauß sums are related to the Riemann Zeta function.

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.

Against the background of price controls for drinking water supply utilities in Germany, the comparability of utilities with regard to their specific structural conditions comes into focus. Relevant structural conditions were identified for the two main technical processes, namely water production (WP) and treatment, storage and distribution (TSD). A defined clustering process for comparable utilities has been developed. At the end of the process, groups of comparable utilities are obtained including information to what extent and in which structural condition these utilities are similar. These sets of relevant structural conditions and the clustering process were verified in a data assessment study with 45 German utilities. Applying the clustering process to the sample, WP and TSD peer groups of a certain utility are obtained, where structural similarities are above a certain threshold value. Performance and cost indicators of comparable utilities have been evaluated, providing interesting data on general performance levels and spread among individual utilities. The survey underlines the high standard of German water supply in terms of reliability, quality, customer service, sustainability and economic efficiency.

According to the recommendations of the World Health Organization (WHO) for Water Safety Plans (WSP), a Technical Risk Management was developed, which considers standard demands in drinking water treatment in Germany. It was already implemented at several drinking water treatment plants of different size and treatment processes in Germany. Hazards affecting water quality, continuity, and the reliability of supply from catchment to treatment and distribution could be identified by a systematic approach, and suitable control measures were defined. Experiences are presented by detailed examples covering methods, practical consequences, and further outcomes. The method and the benefits for the water suppliers are discussed and an outlook on the future role of WSPs in German water supply is given.

The importance of performance assessment in the water industry is demonstrated by the increasing number of initiatives taking place around the world. Since the first initiatives, which started 15 years ago, the topic has evolved significantly although it still presents challenges to be tackled.Five years ago, a project on performance assessment of urban infrastructure services was submitted to the European Union under the COST programme. As a consequence, the COST C18 Action was created. This paper presents the main conclusions and future key research areas from the project. In the solid waste sector, existing practical experience is less advanced, but methodologies and conclusions will be equally applicable in performance assessment projects.

We generalize the concept of factorization using truncated Gauss sums to exponential sums where the phase increases with the jth power of the summation index. For such sums the number of terms needed to suppress ghost factors of N scales as . Unfortunately, this advantageous scaling law is accompanied by a disadvantage: the gap between factors and non-factors decreases rapidly with increasing power j and as a consequence it gets more difficult to identify factors. This feature serves as our motivation to study sums with an exponential phase. Our numerical simulations indicate that in this case the scaling law is logarithmic and that we retain a significant gap between factors and non-factors.

idea of factorizing numbers with Gauss sums. Motivated by the questionof resources we then turn in Section 3 to exponential sums. Finally, inSection 4 we propose an NMR method to implement such exponential sums.We conclude in Section 5 by presenting a brief summary and an outlook.2. Factorization with Gauss sums: the central ideaOur factorization algorithm relies on the truncated Gauss sum

Recent experiments have shown that truncated Gauss sums allow us to find the factors of an integer N. This method relies on the fact that for a factor the absolute value of the Gauss sum is unity. However, for every integer N there exist integers which are not factors, but where the Gauss sum reaches a value which is arbitrarily close to unity. In order to distinguish such ghost factors from real factors we need to amplify this difference. We show that a proper choice of the truncation parameter of the Gauss sum suppresses the ghost factors below a threshold value. We derive the scaling law of the truncation parameter on the number to be factored. Moreover, we show that this scaling law is also necessary for the success of our factorization scheme, even if we relax the threshold or allow limited error tolerance.

We consider a two-photon transition in a specific ladder system driven by a chirped laser pulse. In the weak field limit, we find that the excited state probability amplitude arises due to interference of multiple quantum paths which are weighted by quadratic phase factors. The excited state population has the form of a Gauss sum which plays a prominent role in number theory.

We describe a technique for transferring a two-level atom between two adjacent potential wells of an optical lattice, using pairs of pump and Stokes pulses, each resonantly coupling the same pair of internal atomic states to form a Raman transition. Starting from a vibrational eigenstate of one well the atom slowly moves under the action of the pulse pair, to the vibrational eigenstate with the same quantum number in the neighboring well. The transfer takes place in two stages: A conventional stimulated Raman adiabatic passage (STIRAP) technique, in which Stokes precedes pump pulse, is followed by a pulse sequence where pump precedes Stokes and with an inverted sign of the Stokes envelope. In the first step the atom is accelerated toward the adjacent well and in the second step decelerated to the initial vibrational energy. The STIRAP technique avoids the introduction of stochastic motion caused by spontaneous emission from the excited internal atomic state.

The periodicity properties of Gauss sums allow us to factor integer numbers. We show that the excitation probability amplitudes of appropriate quantum systems interacting with specific laser fields are determined by Gauss sums. The resulting probabilities are experimentally accessible by measuring the fluorescence from this level. In particular, we discuss a two-photon transition in a ladder system driven by a chirped laser pulse. In addition, we consider two realizations of laser driven one-photon transitions. For each quantum system we demonstrate the power of this factorization scheme using numerical examples.

The light scattered by a cold trapped ion, which is in the stationary state of laser cooling, presents features due to the mechanical effects of atom-photon interactions. These features appear as additional peaks (sidebands) in the spectrum of resonance fluorescence. Among these sidebands the literature has discussed the Stokes and anti-Stokes components: namely, the sidebands of the elastic peak. We show that the motion also gives rise to sidebands of the inelastic peaks. These are not always visible, but, as we show, can be measured in parameter regimes which are experimentally accessible.