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Quantum multifractality is a fundamental property of systems such as noninteracting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension Δ_{q} is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation Δ_{q}=Δ_{1−q} is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that this is the result of two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.

In cerebrovascular networks, some vertices are more connected to each other than with the rest of the vasculature, defining a community structure. Here, we introduce a class of model networks built by rewiring Random Regular Graphs, which enables reproduction of this community structure and other topological properties of cerebrovascular networks. We use these model networks to study the global flow reduction induced by the removal of a single edge. We analytically show that this global flow reduction can be expressed as a function of the initial flow rate in the removed edge and of a topological quantity, both of which display probability distributions following Cauchy laws, i.e. with large tails. As a result, we show that the distribution of blood flow reductions is strongly influenced by the community structure. In particular, the probability of large flow reductions increases substantially when the community structure is stronger, weakening the network resilience to single capillary occlusions. We discuss the implications of these findings in the context of Alzheimers Disease, in which the importance of vascular mechanisms, including capillary occlusions, is beginning to be uncovered. Statement of significance: “Occlusions of capillary vessels, the smallest blood vessels in the brain, are involved in major diseases, including Alzheimers Disease and ischemic stroke. To better understand their impact on cerebral blood flow, we theoretically study the vessel network response to a single occlusion. We show that the reduction of blood flow at network scale is a function of the initial blood flow in the occluded vessel and of a topological quantity, both of which have broad distributions, that is, with significant probabilities of extreme values. Using model networks built from Random Regular Graphs, we show that the presence of communities in the network (subparts more connected to each other than with the rest of the vasculature) yield a broader distribution of the topological quantity. This weakens the resilience of brain vessel networks to single capillary occlusions, which may contribute to the pathogenicity of capillary occlusions in the brain”.

We present a full description of the nonergodic properties of wave functions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization lengths: the largest one describes localization along rare branches and diverges with a critical exponent ν_{∥}=1 at the transition. The second length, which describes localization along typical branches, reaches at the transition a finite universal value (which depends only on the connectivity of the graph), with a singularity controlled by a new critical exponent ν_{⊥}=1/2. We show numerically that these two localization lengths control the finite-size scaling properties of key observables: wave-function moments, correlation functions, and spectral statistics. Our results are identical to the theoretical predictions for the typical localization length in the many-body localization transition, with the same critical exponent. This strongly suggests that the two transitions are in the same universality class and that our techniques could be directly applied in this context.

OBJECTIVE: To assess the role of odors in triggering or worsening migraine in men. METHOD: Ninety-eight male migraineurs from the general population were assessed individually through questionnaires. Environmental factors relating to their migraine were reported, with special focus on the role of odors. RESULTS: Odors were the second most frequent triggering factor for migraine attacks (48%), behind stressful situations (59%). Likewise, odors were the second most frequent worsening factor (73%), just behind excessive light (74%). Thirty-three individuals (33.4%) stated that odors were both triggering and worsening factors for their migraine attacks. Perfume, cigarette smoke and cleaning products were the most frequent migraine-related odors reported by these male migraineurs. CONCLUSION: This was the first study to assess the role of odors in migraine exclusively in men. There was a high degree of odor-related migraine among these men, thus suggesting that patient education could alert such individuals to gender-related factors, since different triggering and worsening factors have been reported by males and females.

We compare complex networks built from the game of go and obtained from databases of human-played games with those obtained from computer-played games. Our investigations show that statistical features of the human-based networks and the computer-based networks differ, and that these differences can be statistically significant on a relatively small number of games using specific estimators. We show that the deterministic or stochastic nature of the computer algorithm playing the game can also be distinguished from these quantities. This can be seen as a tool to implement a Turing-like test for go simulators. [ABSTRACT FROM AUTHOR]

The ability to actually implement epidemic models is a crucial stake for public institutions, as they may be overtaken by the increasing complexity of current models and sometimes tend to revert to less elaborate models such as the susceptible-infected-recovered (SIR) model. In our work, we study a simple epidemic propagation model, called SIR-k, which is based on a homogeneous network of degree k, where each individual has the same number k of neighbors. This model represents a refined version of the basic SIR which assumes a completely homogeneous population. We show that nevertheless, analytical expressions, simpler and richer than the ones existing for the SIR model, can be derived for this SIR-k model. In particular, we obtain an exact implicit analytical solution for any k, from which quantities such as the epidemic threshold or the total number of agents infected during the epidemic can be obtained. We furthermore obtain simple exact explicit solutions for small ks, and in the large k limit we find a new formulation of the analytical solution of the basic SIR model, which comes with new insights.

We study the time evolution of mean values of quantum operators in a regime plagued by two difficulties: the smallness of ℏ and the presence of strong and ubiquitous classical chaos. While numerics become too computationally expensive for purely quantum calculations as ℏ→0, methods that take advantage of the smallness of ℏ-that is, semiclassical methods-suffer from both conceptual and practical difficulties in the deep chaotic regime. We implement an approach which addresses these conceptual problems, leading to a deeper understanding of the origin of the interference contributions to the operator's mean value. We show that in the deep chaotic regime our approach is capable of unprecedented accuracy, while a standard semiclassical method (the Herman-Kluk propagator) produces only numerical noise. Our work paves the way to the development and employment of more efficient and accurate methods for quantum simulations of systems with strongly chaotic classical limits.

We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with chaos-induced long-range hoppings t_{n}∝1/n between sites at a distance n. We provide a numerical demonstration of the robustness of the results and derive an analytical prediction for the hopping term law. Such systems can thus be used to enlarge the scope of quantum simulations to experimentally realize long-range models of condensed matter.

Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral statistics of all these low-complexity random matrices is of the intermediate type, characterized by: (i) level repulsion at short distances, (ii) an exponential decrease in the nearest-neighbor distributions at long distances, (iii) a nontrivial value of the spectral compressibility, and (iv) the existence of nontrivial fractal dimensions of eigenvectors in Fourier space. Our findings show that intermediate-type statistics is more ubiquitous and universal than was considered so far and open a new direction in random matrix theory.

Semiclassical mechanics allows for a description of quantum systems which preserves their phase information, and thus interference effects, while using only the system's classical dynamics as an input. In particular one of the strengths of a semiclassical description is to present a coherent picture which (to negligible higher-order ℏ corrections) is independent of the particular canonical coordinates used. However, this coherence relies heavily on the use of the stationary phase approximation. It turns out, however, that in some important cases, a brutal application of stationary phase approximation washes out all interference, and thus quantum, effects. In this paper, we address this issue in detail in one of its simplest instantiations, namely the evaluation of the time evolution of the expectation value of an operator. We explain why it is necessary to include contributions which are not in the neighborhood of stationary points and provide new semiclassical expressions for the evolution of the expectation values. The efficiency of our approach is based on the fact that we treat analytically all the integrals that can be performed within the stationary phase approximation, implying that the remaining integrals are simple integrals, in the sense that the integrand has no significant variations on the quantum scale (and thus they are very easy to perform numerically). This to be contrasted with other approaches such as the ones based on initial value representation, popular in chemical and molecular physics, which avoid a root search for the classical dynamics, but at the cost of performing numerically integrals whose evaluation requires a sampling on the quantum scale, and which are therefore not well designed to address the deep semiclassical regime. Along the way, we get a deeper understanding of the origin of these interference effects and an intuitive geometric picture associated with them.

The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to the all-purpose quantum computer. So far, most efforts in this domain have been directed to either fully regular or fully chaotic systems. Here, we focus on the intermediate regime, where regular orbits are surrounded by a large sea of chaotic trajectories. We observe a quantum chaos transport mechanism, called chaos-assisted tunneling, that translates in sharp resonances of the tunneling rate and provides previously unexplored possibilities for quantum simulation. More specifically, using Bose-Einstein condensates in a driven optical lattice, we experimentally demonstrate and characterize these resonances. Our work paves the way for quantum simulations with long-range transport and quantum control through complexity., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify the relationship between the eigenstates and the classical structures, and we quantify their multifractality at different scales. Based on this study, we conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but these states are multifractal instead of ergodic at each level of the hierarchy. This is visible for sufficiently long-lived resonance states at scales smaller than the classical structures. Our results can guide experimentalists in order to observe multifractal behavior in open systems.

We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1

In harvesting skin to cover the defect caused by a burn, a second wound is created, the donor site wound. We propose an alternative method to manage the donor site: taking a split-thickness skin graft (STSG) from a donor site adjacent to the burn wound to be treated, and meshing at a 3:1 ratio to cover both sites at once. The main objective of this study is to evaluate the effectiveness of covering both burn wound and adjacent donor site with the same STSG in elderly and bedridden patients. We retrospectively reviewed the medical records of 6 patients over 60 years old or/and bedridden presenting with a small burn wound who underwent STSG of both burn wound and adjacent donor site between April 2016 and November 2016 in the Department of Plastic Surgery and Burn Treatment at Percy Military Hospital (France). Their data were compared with data of five patients who had undergone the usual STSG procedure during the same period. There was a statistically significant difference between patients who underwent adjacent STSG procedure and those who underwent usual STSG procedure in healing time (days) mean (SD) (7,33 ± 1,03 vs. 16,2 ± 0,83; p = 0,007) and Numeric Rating Scale pain mean (SD) at day 2 (0,33 ± 0,33 vs. 2,4 ± 1,35; p = 0,04). Grafting both acute burn wound and adjacent donor site with the same graft seems to be an easy method to improve healing and minimize pain in the STSG donor site in elderly and bedridden patients.

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 quantum systems. Our calculations elucidate various heuristic relations proposed recently in the literature.

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.

We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light.

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.

For random matrices with treelike structure there exists a recursive relation for the local Green functions whose solution permits us to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this article is to investigate and compare expressions for the spectral density of random regular graphs, based on easy approximations for real solutions of the recursive relation valid for trees with large coordination number. The obtained formulas are in a good agreement with the results of numerical calculations even for small coordination number.

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.

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, which is different from the multifractality 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.

We construct perturbation series for the qth moment of eigenfunctions of various critical random-matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the region q<1/2. Our findings allow one to verify, at first leading orders in the strong multifractality limit, the symmetry relation for anomalous fractal dimensions Δ(q)=Δ(1-q), recently conjectured for critical models where an analog of the metal-insulator transition takes place. It is known that this relation is verified at leading order in the weak multifractality regime. Our results thus indicate that this symmetry holds in both limits of small and large coupling constant. For general values of the coupling constant we present careful numerical verifications of this symmetry relation for different critical random-matrix ensembles. We also present an example of a system closely related to one of these critical ensembles, but where the symmetry relation, at least numerically, is not fulfilled.

Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes, we obtain expressions similar to those of the critical banded random matrix ensemble extensively discussed in the literature. For certain ensembles, the leading-order term for weak multifractality can be calculated within standard perturbation theory. For other models, such a direct approach requires modifications, which are briefly discussed. Our analytical formulas are in good agreement with numerical calculations.