On the fate of the Hoop Conjecture in quantum gravity

We consider a closed region $R$ of 3d quantum space modeled by $SU(2)$ spin-networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary $\partial R$ and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interprete such phenomenon as a pre-geometric analogue of Thorne's "Hoop conjecture", at the core of the formation of a horizon in General Relativity.Comment: 7 pages, 2 figures, minor improvement

Typicality in spin network states of quantum geometry

In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network; however, they are mainly motivated by the fact that spin-network states can describe states of quantum geometry, providing a gauge-invariant basis for the kinematical Hilbert space of several background-independent approaches to quantum gravity. The first result is, by itself, the existence of a regime in which we show the emergence of a typical state. We interpret this as the proof that in that regime there are certain (local) properties of quantum geometry which are "universal". Such a set of properties is heralded by the typical state, of which we give the explicit form. This is our second result. In the end, we study some interesting properties of the typical state, proving that the area law for the entropy of a surface must be satisfied at the local level, up to logarithmic corrections which we are able to bound.Comment: Typos and mistakes fixe

Dynamics of a particle confined in a two-dimensional dilating and deforming domain

Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving, by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the "pantographic", case (same shape of the box through all the process) and the case with deformation.Comment: 13 pages, 2 figure

Quantifying the difference between many-body quantum states

The quantum state overlap is the textbook measure of the difference between two quantum states. Yet, it is inadequate to compare the complex configurations of many-body systems. The problem is inherited by the widely employed quantum state fidelity and related distances. We introduce the weighted distances, a new class of information-theoretic measures that overcome these limitations. They quantify how hard it is to discriminate between two quantum states of many particles, factoring in the structure of the required measurement apparatus. Therefore, they can be used to evaluate both the theoretical and the experimental performances of complex quantum devices. We also show that the newly defined "weighted Bures length" between the input and output states of a quantum process is a lower bound to the experimental cost of the transformation. The result uncovers an exact quantum limit to our ability to convert physical resources into computational ones.Comment: 4+2 pages, change from previous version: the contractivity of weighted distances holds only for single site operation

Tripartite thermal correlations in an inhomogeneous spin-star system

We exploit the tripartite negativity to study the thermal correlations in a tripartite system, that is the three outer spins interacting with the central one in a spin-star system. We analyze the dependence of such correlations on the homogeneity of the interactions, starting from the case where central-outer spin interactions are identical and then focusing on the case where the three coupling constants are different. We single out some important differences between the negativity and the concurrence.Comment: 8 pages, 9 figure

Quantifying within-group variation in sociality—covariation among metrics and patterns across primate groups and species

It has long been recognized that the patterning of social interactions within a group can give rise to a social structure that holds very different places for different individuals. Such within-group variation in sociality correlates with fitness proxies in fish, birds, and mammals. Broader integration of this research has been hampered by the lack of agreement on how to integrate information from a plethora of dyadic interactions into individual-level metrics. As a step towards standardization, we collected comparative data on affinitive and affiliative interactions from multiple groups each of five species of primates to assess whether the same aspects of sociality are measured by different metrics and indices. We calculated 16 different sociality metrics used in previous research and thought to represent three different sociality concepts. We assessed covariation of metrics within groups and then summarized covariation patterns across all 15 study groups, which varied in size from 5 to 41 adults. With some methodological and conceptual caveats, we found that the number of weak ties individuals formed within their groups represented a dimension of sociality that was largely independent from the overall number of ties as well as from the number and strength of the strong ties they formed. Metrics quantifying indirect connectedness exhibited strong covariation with strong tie metrics and thus failed to capture a third aspect of sociality. Future research linking affiliation and affinity to fitness or other individual level outcomes should quantify inter-individual variation in three aspects: the overall number of ties, the number of weak ties, and the number or strength of strong ties individuals form, after taking into account effects of social network density. Significance statement: In recent years, long-term studies of individually known animals have revealed strong correlations between individual social bonds and social integration, on the one hand, and reproductive success and survival on the other hand, suggesting strong natural selection on affiliative and affinitive behavior within groups. It proved difficult to generalize from these studies because they all measured sociality in slightly different ways. Analyzing covariation between 16 previously used metrics identified only three rather independent dimensions of variation. Thus, different studies have tapped into the same biological phenomenon. How individuals are weakly connected within their group needs further attention.Peer Reviewe

Intensive physiotherapic respiratory care in critically ill patients with tracheostomy after cardiac surgery

Background. Patients following major cardiac surgery are increasingly elderly and present many comorbidities. For these reasons their post-operative phase is often burdened by several complications requiring a long stay in Critical Care and prolonged mechanical ventilation. Most of these patients, when transferred to our Intensive Cardiac Rehabilitation Unit, still have a percutaneous tracheostomy due to respiratory mechanical dysfunction. The aim of our work is to present new rehabilitative care strategies in such compromised patients. Methods and materials. We studied 27 elderly critically ill tracheostomized patients who were split into 2 Groups (A = 11 and B = 16). The Groups were homogeneous for age and for left ventricular ejection fraction. Group A received a standard treatment including cautious mobilisation and respiratory unspecific physiotherapy. Group B received an earlier and more aggressive treatment with a specific respiratory physiotherapy including Positive Expiration Pressure (PEP) directly connected to the tracheostomy cannula. A protocol for tracheostomy decannulation by assessment of the Peak Expiratory Flow during cough (PCEF≥ 180 L/min.) has been defined in order to verify the patients ability to develop a mechanically effective cough to obtain weaning from tracheostomy. Besides, in the patients of Group B, we carried out a screening of the swallowing dysfunction. Results. Four patients of Group A deceased while in Group B there were no deaths. Furthermore patients of Group B showed a statistically significant improvement of mobility and respiratory indexes. In Group B only one patient was discharged with tracheostomy cannula in site because he did not reach standard criteria for decannulation and his PCEF value was not satisfactory. This patient underwent percutaneous gastrostomy. Conclusions. A precocious and intensive rehabilitation, based on specific respiratory physiotherapy, significantly improves mobility and respiratory indexes of patients with tracheostomy. The PCEF and the swallowing deficit evaluation allows an earlier tracheostomy decannulation with lower risk of complications

Information-theoretic equilibrium and observable thermalization

A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light

A note on the secondary simplicity constraints in loop quantum gravity

15 pagesInternational audienceA debate has appeared in the literature on loop quantum gravity and spin foams, over whether secondary simplicity constraints should imply the shape matching conditions reducing twisted geometries to Regge geometries. We address the question using a model in which secondary simplicity constraints arise from a dynamical preservation of the primary ones, and answer it in the affirmative. The origin of the extra condition is to be found in the different graph localisations of the various constraints. Our results are consistent with previous claims by Dittrich and Ryan, and extend their validity to Lorentzian signature and a priori arbitrary cellular decompositions. Finally, we show how the (gauge-invariant version of the) twist angle {\xi} featuring in twisted geometries equals on-shell the Regge dihedral angle multiplied by the Immirzi parameter, thus recovering the discrete extrinsic geometry from the Ashtekar-Barbero holonomy

Sex and grooming as exchange commodities in female bonobos’ daily biological market

The Biological Market Theory (BMT) posits that cooperation between non-human animals can be seen as a mutually beneficial exchange of commodities similarly to what observed in human economic markets. Positive social interactions are commodities in non-human animals, and mutual exchanges fulfilling the criteria of the BMT have been shown in several species. However, the study of biological markets suffers from methodological limitations that are mainly linked to the difficulty of clearly identifying the currencies and their exchanges in the short-term. Here, we test whether bonobo females are more attractive during their maximum swelling phase, whether they exchange grooming and Genito-Genital Rubbing (GGR) on a daily level of analysis, and whether these daily exchanges fulfil the BMT criteria. Females engaged more in GGR when their sexual swelling was in the maximum phase. Moreover, they exchanged grooming and sex according to the daily “market fluctuations” associated with swelling status. Females in the minimum phase (low-value) increased their probability to engage in GGR with females in the maximum phase (high-value) by grooming them preferentially. In line with the supply/demand law, the female grooming strategy varied depending on the daily number of swollen females present: the higher the number of swollen females, the lower the individual grooming preference. As a whole, our study confirms BMT as a valid model to explain daily commodity exchanges as a function of the temporary value of traders, and underlines the importance of a day-by-day approach to unveil the presence of a biological market when the value of traders frequently change