Scale invariant distribution functions in quantum systems with few degrees of freedom

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.Comment: 8+10 pages. Scipost Submissio

EDITORIAL

<p>To make comparisons among the different modes for each strain gauge, each strain was normalized with respect to the average among the fixation modes. The average and standard deviation of the seven specimens are plotted.</p

Retrofitting sustainable urban drainage systems (SuDS): a cost-benefit analysis appraisal

Sustainable Urban Drainage Systems (SuDS) are known to help mitigate flooding whilst simultaneously delivering other positive outcomes, such as the provision of environmental, economic, educational, and business benefits. Despite this, there has been a relatively low uptake of SuDS in new developments and even less of an uptake in the opportunities for retrofitting SuDS in existing buildings. A major barrier to uptake has been a lack of understanding regarding the value of the benefits provided by SuDS. This study presents an appraisal of the costs and benefits derived from the retrofitting of SuDS in existing buildings and reveals some of the key decision-making considerations during the design and installation of such schemes. A qualitative research approach that included a number of case studies of successfully retrofitted SuDS schemes within public buildings was conducted. A novel feature of the research was the use of the Willingness to Pay (WTP) approach to value the tangible and intangible benefits provided by the various schemes from the perspectives of the property owners. The findings revealed that the retrofit provided a net value to the client of over £100,000 over 10 years, a mean CBA ratio of 5.3/10, and a return on investment (ROI) that would be achieved in less than 3 years. The importance of stakeholder engagement during the decision-making process was highlighted in helping to overcome many of the design, installation, and maintenance challenges. The findings demonstrate a significant ROI for these SuDs retrofit schemes and highlight useful approaches to overcoming the barriers in valuing the importance of the intangible benefits. In supporting the uptake of the retrofitting of SuDS, it is recommended that these benefits are given full consideration by property owners, urban planners, and architects during the design of retrofit schemes and throughout the decision-making stage.</p

A anti-jamming method for satellite navigation system based on multi-objective optimization technique

<div><p>In this paper, an anti-jamming method, which turns the single objective optimization problem into a multi-objective optimization problem by utilizing 2-norm, is proposed. The proposed jamming suppression method can reduce the wide nulls and wrong nulls problems, which are generated by the common adaptive nulling methods. Therefore a better signal-noise-ratio (SNR) can be achieved, especially when the jammers are close to satellite signals. It can also improve the robustness of the algorithm. The effectiveness of the proposed method is evaluated by simulation and practical outdoor experiments with the GPS L1 band C/A signals. The experimental results show that with the dedicated method, the nulls targeting at the corresponding jammers become narrower and the wrong nulls can be eliminated.</p></div

Simulation procedure of the experiments.

<p>Simulation procedure of the experiments.</p

The pattern in azimuth view of the array patterns of the original PI and the proposed PI with a wide- band jammer.

<p>The pattern in azimuth view of the array patterns of the original PI and the proposed PI with a wide- band jammer.</p

The experimental results of multiple satellites comparison.

<p>The experimental results of multiple satellites comparison.</p

The experiment setup.

<p>The experiment setup.</p

The 2-dimensional array pattern by using contour lines after the adaptive processing of the original MUSIC algorithm.

<p>The 2-dimensional array pattern by using contour lines after the adaptive processing of the original MUSIC algorithm.</p

The 2-dimensional array pattern by using contour lines after the adaptive processing of the proposed 2-norm matrix constrained MUSIC algorithm.

<p>The 2-dimensional array pattern by using contour lines after the adaptive processing of the proposed 2-norm matrix constrained MUSIC algorithm.</p