Black holes, complexity and quantum chaos

We study aspects of black holes and quantum chaos through the behavior of computational costs, which are distance notions in the manifold of unitaries of the theory. To this end, we enlarge Nielsen geometric approach to quantum computation and provide metrics for finite temperature/energy scenarios and CFT's. From the framework, it is clear that costs can grow in two different ways: operator vs `simple' growths. The first type mixes operators associated to different penalties, while the second does not. Important examples of simple growths are those related to symmetry transformations, and we describe the costs of rotations, translations, and boosts. For black holes, this analysis shows how infalling particle costs are controlled by the maximal Lyapunov exponent, and motivates a further bound on the growth of chaos. The analysis also suggests a correspondence between proper energies in the bulk and average `local' scaling dimensions in the boundary. Finally, we describe these complexity features from a dual perspective. Using recent results on SYK we compute a lower bound to the computational cost growth in SYK at infinite temperature. At intermediate times it is controlled by the Lyapunov exponent, while at long times it saturates to a linear growth, as expected from the gravity description.Comment: 30 page

Codification Volume of an operator algebra and its irreversible growth through thermal processes

Given a many-body system, we define a quantity, the Codification Volume of an operator algebra, which measures the size of the subspace with whom a given algebra is correlated. We explicitly calculate it for some limit cases, including vacuum states of local Hamiltonians and random states taken from the Haar ensemble. We argue that this volume should grow irreversibly in a thermalization process, and illustrate it numerically on a non-integrable quantum spin chain

Black holes as random particles: entanglement dynamics in infinite range and matrix models

We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large-$\mathcal{N}$ matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large-$\mathcal{N}$ matrix models, where we provide a gauge invariant entanglement entropy for `generalized free fields', again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.Comment: Journal versio

Foreword: mycotoxins in a changing world

This special issue arose because of the changes in the global landscape in relation to the impact and implications of our changing climate on food security and quality, consumer habits, trade and economics, regulations and scientific thinking. The EU green paper (EC, 2007) on climate change (CC) has suggested significant hot spots in different regions where food production will be considerably affected both in quality and quantity. Indeed, a recent UNEP report on ‘Emerging Issues of Environmental Concern’ (UNEP, 2016) has included a section entitled ‘Poisoned chalice: Toxin accumulation in crops in an era of climate change’ which refers to the impact that aflatoxin contamination is having in low and middle income countries (LMICs)

Alternaria in food: Ecophysiology, mycotoxin production and toxicology

Alternaria species are common saprophytes or pathogens of a wide range of plants pre- and post-harvest. This review considers the relative importance of Alternaria species, their ecology, competitiveness, production of mycotoxins and the prevalence of the predominant mycotoxins in different food products. The available toxicity data on these toxins and the potential future impacts of Alternaria species and their toxicity in food products pre- and post-harvest are discussed. The growth of Alternaria species is influenced by interacting abiotic factors, especially water activity (a w ), temperature and pH. The boundary conditions which allow growth and toxin production have been identified in relation to different matrices including cereal grain, sorghum, cottonseed, tomato, and soya beans. The competitiveness of Alternaria species is related to their water stress tolerance, hydrolytic enzyme production and ability to produce mycotoxins. The relationship between A. tenuissima and other phyllosphere fungi has been examined and the relative competitiveness determined using both an Index of Dominance (I D ) and the Niche Overlap Index (NOI) based on carbon-utilisation patterns. The toxicology of some of the Alternaria mycotoxins have been studied; however, some data are still lacking. The isolation of Alternaria toxins in different food products including processed products is reviewed. The future implications of Alternaria colonization/infection and the role of their mycotoxins in food production chains pre- and post-harvest are discussed

Complex regulation of the aflatoxin biosynthesis gene cluster of Aspergillus flavus in relation to various combinations of water activity and temperature

A microarray analysis was performed to study the effect of varying combinations of water activity and temperature on the activation of aflatoxin biosynthesis genes in Aspergillus flavus grown on YES medium. Generally A. flavus showed expression of the aflatoxin biosynthetic genes at all parameter combinations tested. Certain combinations of aw and temperature, especially combinations which imposed stress on the fungus resulted in a significant reduction of the growth rate. At these conditions induction of the whole aflatoxin biosynthesis gene cluster occurred, however the produced aflatoxin B1 was low. At all other combinations (25 °C/0.95 and 0.99; 30 °C/0.95 and 0.99; 35 °C/0.95 and 0.99) a reduced basal level of cluster gene expression occurred. At these combinations a high growth rate was obtained as well as high aflatoxin production. When single genes were compared, two groups with different expression profiles in relation to water activity/temperature combinations occurred. These two groups were co-ordinately localized within the aflatoxin gene cluster. The ratio of aflR/aflJ expression was correlated with increased aflatoxin biosynthesis