Quantum computation of multifractal exponents through the quantum wavelet transform

We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum algorithms for multifractal exponents with a polynomial gain compared to classical simulations. Numerical results indicate that a rough estimate of fractality could be obtained exponentially fast. Our findings are relevant e.g. for quantum simulations of multifractal quantum maps and of the Anderson model at the metal-insulator transition.Comment: 9 pages, 9 figure

Multifractality of quantum wave packets

We study a version of the mathematical Ruijsenaars-Schneider model, and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets, and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, different from the mulifractality of eigenvectors, but related to it, as is the rate of the decrease. Our results could guide the study of experimental situations where multifractality is present in quantum systems.Comment: 6 pages, 4 figures, final version including a new figure (figure 1

Tailored gamification and serious game framework based on fuzzy logic for saving energy in connected thermostats

Connected thermostats (CTs) often save less energy than predicted because consumers may not know how to use them and may not be engaged in saving energy. Additionally, several models perform contrary to consumers’ expectations and are thus not used the way they are intended to. As a result, CTs save less energy and are underused in households. This paper reviews aspects of gamification and serious games focused on engaging consumers. A gamification and serious games framework is proposed for saving energy that is tailored by a fuzzy logic system to motivate connected thermostat consumers. This intelligent gamification framework can be used to customize the gamification and serious game strategy to each consumer so that fuzzy logic systems can be adapted according to the requirements of each consumer. The framework is designed to teach, engage, and motivate consumers while helping them save electrical energy when using their thermostats. It is described the proposed framework as well as a mockup that can be run on a cellphone. Although this framework is designed to be implemented in CTs, it can be translated to their energy devices in smart homes

Multifractality of quantum wave functions in the presence of perturbations

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases, and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems.Comment: 20 pages, 27 figure