Average diagonal entropy in non-equilibrium isolated quantum systems

The diagonal entropy was introduced as a good entropy candidate especially for isolated quantum systems out of equilibrium. Here we present an analytical calculation of the average diagonal entropy for systems undergoing unitary evolution and an external perturbation in the form of a cyclic quench. We compare our analytical findings with numerical simulations of various many-body quantum systems. Our calculations elucidate various heuristic relations proposed recently in the literature.Comment: 5 pages + 4 page "Supplemental material", 2 figure

Relaxation of isolated quantum systems beyond chaos

In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is -- to say the least -- fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many body quantum systems that can be parametrically tuned from regular to chaotic. We show that a universal relation between relaxation and delocalization of the initial state in the perturbed basis can be established regardless of the chaotic nature of system.Comment: 4+ pages, 4 figs. Closest to published versio

O estado da arte e a polinização cruzada na indústria joalheira: um caso promissor

The present article intends to participate in the debate on the concept of design as a process that is approached differently by Latin countries and Anglo-Saxon countries. Many authors, particularly English or American, propose design methodologies that are borrowed from other disciplines such as engineering and try to adapt them to product design. However, no consensus has been reached. This paper will discuss the current panorama of the design methodologies present in Mexico, which is strongly influenced by the Hfg Ulm. The second part of the article is a case study of an industry that is considered promising in Mexico: the jewelry industry, mainly that which uses silver as its main raw material, describing the fundamental role that design is playing for this industry, emphasizing the fact that the methodology used by these designers tilts towards fashion design. The result strongly reflects the influence of fashion design methods and processes in a sort of involuntary cross-fertilization. Key words: design methodologies, design methods, cross fertilization, Mexico.Este artigo pretende participar do debate sobre o conceito de design como um processo abordado de forma diferente pelos países de cultura latina e pelos países anglo-saxões. Muitos autores, principalmente americanos e britânicos, propõem metodologias de desenvolvimento de projetos emprestadas de outras ciências, tais como a engenharia, e tentam adaptá-las à concepção de produto. Entretanto, não se chegou a um consenso nesse debate. O presente artigo dará uma visão geral das metodologias presentes no discurso do design mexicano, fortemente permeado pela influência da escola de Ulm. A segunda parte do trabalho é um estudo de caso onde se considera um setor promissor no México: a indústria de joias, em particular a que utiliza a prata como matéria-prima principal, descrevendo o papel fundamental desempenhado pelo design para esta indústria e destacando o fato de que a metodologia utilizada por esses designers tende mais para a moda e estilo. O resultado reflete a forte influência de métodos e processos de design de moda em uma espécie de fertilização cruzada involuntária. Palavras-chave: metodologias de design, métodos de design, polinização cruzada, México

Weyl law for fat fractals

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.Comment: 8 pages, 4 figures, IOP forma

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

Multifractal wave functions of simple quantum maps

We study numerically multifractal properties of two models of one-dimensional quantum maps, a map with pseudointegrable dynamics and intermediate spectral statistics, and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting method and wavelet method). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects.Comment: 15 pages, 21 figure

Two scenarios for quantum multifractality breakdown

We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications.Comment: 5 pages, 4 figures, minor modifications, published versio

Non-Markovian Quantum Dynamics and Classical Chaos

We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude-a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.Comment: Closest to the published versio