Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality.

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

Tensor representation of spin States.

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.

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.

Distribution of the ratio of consecutive level spacings in random matrix ensembles.

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.

Eigenfunction entropy and spectral compressibility for critical random matrix ensembles.

Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D(1) and the spectral compressibility χ are related by the simple equation χ+D(1)/d=1, where d is system dimensionality.

Semiclassical evaluation of expectation values.

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.

Chaos-assisted tunneling resonances in a synthetic Floquet superlattice.

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.

Quantum computing of semiclassical formulas.

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.

Multifractality and intermediate statistics in quantum maps.

We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical computations and provide analytical arguments showing that the generalized fractal dimensions are directly related to the parameter of the underlying classical map, and thus to other properties such as spectral statistics. Our results could be relevant for Anderson and quantum Hall transitions, where wave functions also show multifractality.

Grafting both acute wound site and adjacent donor site with the same graft: an easy and safe procedure to improve healing and minimize pain in elderly and bedridden patients.

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.

Lors du prélèvement de peau mince pour couvrir une plaie causée par une brûlure, une seconde plaie est créée, le site donneur. Voici une méthode alternative pour la gestion du site donneur: prélever une greffe de peau mince GPM à partir d'un site donneur adjacent à la brûlure, l'expandre avec un ratio de 3:1 pour couvrir les deux sites à la fois. Ici l'objectif principal est d'évaluer l'efficacité de la couverture simultanée d'une petite brûlure et du site donneur adjacent avec la même GPM chez les patients âgés et alités. Nous avons étudié rétrospectivement les dossiers de 6 patients traités par couverture simultanée de la brûlure et du site donneur adjacent avec la même GPM entre avril 2016 et novembre 2016 dans le Service de Chirurgie Plastique de l'hôpital militaire Percy (France). Les données ont été comparées à un groupe similaire de patients qui ont subi une procédure habituelle durant la même période. Il y avait une différence statistiquement significative entre les patients qui ont subi une procédure de GPM du site donneur adjacent et ceux qui ont subi une procédure habituelle sur la durée (jours) moyenne (écart-type, SD) de cicatrisation (7,33 ± 1,03 vs 16,2 ± 0,83; p = 0,007) et de la douleur sur l'échelle numérique au jour 2 (0,33 ± 0,33 vs 2,4 ± 1,35; p = 0,04). Greffer la plaie liée à la brûlure aiguë et le site donneur adjacent avec une même GPM semble être une méthode simple pour améliorer la guérison et minimiser la douleur du site donneur.

Quantum computing of delocalization in small-world networks.

We study a quantum small-world network with disorder and show that the system exhibits a delocalization transition. A quantum algorithm is built up which simulates the evolution operator of the model in a polynomial number of gates for an exponential number of vertices in the network. The total computational gain is shown to depend on the parameters of the network and a larger than quadratic speedup can be reached. We also investigate the robustness of the algorithm in presence of imperfections.

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.

Activation of mu opioid receptors in the nucleus raphe dorsalis blocks apomorphine-induced aggression in rats: serotonin appears not to be involved.

The role of mu opioid receptors in the nucleus raphe dorsalis (DR) in the control of apomorphine-induced aggression was studied in rats. Administration in the DR of a selective mu opioid receptor agonist, (D-Ala2,N-Me-Phe4,Gly5-ol)-enkephalin (DAGO), in doses ranging from 0.01 to 1 microgram/0.5 microliter, dose-dependently reduced aggression caused by apomorphine 20 mg/kg intraperitoneally. 0.01 microgram DAGO significantly reduced the time spent by the animals in aggressive posture and 0.1 and 1 microgram markedly reduced both aggressive postures and attacks. 5 micrograms (in 0.5 microliter) naloxone in the DR completely antagonized the anti-aggressive effect of DAGO (0.1 microgram/0.5 microliter) injected in the same area. 0.1 and 1 microgram but not 0.01 microgram DAGO significantly increased serotonin (5-HT) metabolism in the striatum, a terminal area almost exclusively innervated by DR, indicating that the activity of 5-HT cells in the DR was modified by DAGO. In animals given 6 micrograms/3 microliters 5,7-dihydroxytryptamine in the DR 11 days before, in which striatal 5-HT levels were markedly depleted, no significant changes were found in the time spent by the apomorphine-treated animals in aggressive postures, numbers of attacks or anti-aggressive effect of 0.1 and 1 microgram DAGO administered in the DR. The study shows for the first time that activation of mu opioid receptors in the DR has a powerful anti-aggressive effect in one model of experimental aggression by a mechanism apparently not involving changes in the activity of 5-HT cells in this area.

Nearest-neighbor distribution for singular billiards.

The exact computation of the nearest-neighbor spacing distribution P(s) is performed for a rectangular billiard with a pointlike scatterer inside for periodic and Dirichlet boundary conditions, and it is demonstrated that when s-->infinity this function decreases exponentially. Together with the results of Bogomolny, Gerland, and Schmit [Phys. Rev. E 63, 036206 (2001)], it proves that spectral statistics of such systems is of intermediate type characterized by level repulsion at small distances and exponential fall-off of the nearest-neighbor distribution at large distances. The calculation of the nth nearest-neighbor spacing distribution P(n)(s) and its asymptotics is performed as well for any boundary conditions.

Difference in learning and retention by Albino-Swiss mice. Part IV. Effect of some nutrients.

According to the preceding papers, the possible difference in activity of some nutrients on memory retrieval of "good" and "poor" learning mice was studied. Among the substances used, only phenylalanine significantly improved memory recall of poor learning mice. On the contrary, tryptophan, tyrosine, phosphatidylserine and choline did not influence memory retention of previously learned avoidance of both poor and good learning mice.

Difference in learning and retention by Albino Swiss mice. Part III. Effect of some brain stimulants.

According to the two preceding papers, the possible difference in activity of brain stimulants on memory retrieval of "good" and "poor" learning mice was studied. Among the drugs studied, caffeine, oxiracetam and nicotine significantly improved memory recall of poor learning mice. On the contrary, methylphenidate, fipexide and piracetam did not significantly modify memory retention of previously learned avoidance of both poor and good learning mice.

Exploratory behavior and the dual activity of some psychoactive drugs. Part 1.

Animal behavior in a free environment involves the orienting reflex, a major component of which is exploratory behavior. Exploration is an essential, life-preserving component of animal higher nervous functions and the experiments presented here show that exploratory behavior may differ according to the experimental subjects' emotional baseline. Exploratory performance may accordingly be affected differently by psychoactive drugs.

[A cause of intubation failure: a subglottic bridge]. / Une cause d'intubation impossible: la bride sous-glottique.

We report the case of a patient with a history of facio-thoracic burns, the treatment of which included prolonged intubation, whose trachea could not be intubated because of a subglottic obstacle. The ventilation was easily controlled with a laryngeal mask. At the end of surgery for postburn cheloids, laryngoscopy through the laryngeal mask showed a transversal subglottic laryngeal band, a probable sequela of the previous prolonged intubation. The band was resected one week later. The conventional indicators for difficult intubation cannot detect the laryngotracheal obstacles to tracheal tube insertion.

[Value of fasciocutaneous tensor fasciae latae island flap in the treatment of large abdominal hernias. Apropos of a case]. / Intérêt du lambeau en îlot fascio-cutané de tensor fasciae latae dans le traitement des grandes éventrations abdominales. A propos d'une observation.

One case of repeated incisional hernia is reported. This hernia was initially repaired but repeated infection occurred. This hernia was then successfully treated with a fasciocutaneous tensor fasciae latae island flap. The patient was reexamined two years after surgery and presented a functional abdominal wall. Other different reconstructive possibilities of regional myocutaneous flaps are described.

Calculation of mean spectral density for statistically uniform treelike random models.

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.