Entanglement entropy of two disjoint blocks in critical Ising models

We study the scaling of the Renyi and entanglement entropy of two disjoint blocks of critical Ising models, as function of their sizes and separations. We present analytic results based on conformal field theory that are quantitatively checked in numerical simulations of both the quantum spin chain and the classical two dimensional Ising model. Theoretical results match the ones obtained from numerical simulations only after taking properly into account the corrections induced by the finite length of the blocks to their leading scaling behavior.Comment: 4 pages, 5 figures. Revised version accepted for publication in PR

From viability to sustainability: the contribution of the viable systems approach (VSA)

The current dynamics of business systems require new ways of conceiving the role of single entities. On this basis, a complex of interactions between the company and the reference context must be activated to guarantee survival dynamics. From these considerations re-emerge the ideas of Peccei (2013) and King (2013) that recognise in the systemic thought the foundations for a sustainable society. The present study derives from these considerations, and aims at contributing to the advancement of the knowledge necessary to overcome the challenges in the sustainability field. The methodological approach, albeit heuristic, can be traced back to the positive scientific and constructivist method. The results of the study showed the prevalence of qualitative and subjective techniques, accompanied by the so-called inductive method, testifying to the intense interaction between the scholar and the object investigated. With regard to future research, it would be interesting to construct a flexible, scalable and extensible model to recover both a database and an ontology for the theoretical framework

Entanglement dynamics after quantum quenches in generic integrable systems

The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations

Negativity spectrum of one-dimensional conformal field theories

The partial transpose \u3c1T2A of the reduced density matrix \u3c1A is the key object to quantify the entanglement in mixed states, in particular through the presence of negative eigenvalues in its spectrum. Here we derive analytically the distribution of the eigenvalues of \u3c1T2A, that we dub negativity spectrum, in the ground sate of gapless one-dimensional systems described by a Conformal Field Theory (CFT), focusing on the case of two adjacent intervals. We show that the negativity spectrum is universal and depends only on the central charge of the CFT, similarly to the entanglement spectrum. The precise form of the negativity spectrum depends on whether the two intervals are in a pure or mixed state, and in both cases, a dependence on the sign of the eigenvalues is found. This dependence is weak for bulk eigenvalues, whereas it is strong at the spectrum edges. We also investigate the scaling of the smallest (negative) and largest (positive) eigenvalues of \u3c1T2A. We check our results against DMRG simulations for the critical Ising and Heisenberg chains, and against exact results for the harmonic chain, finding good agreement for the spectrum, but showing that the smallest eigenvalue is affected by very large scaling corrections

Alignment-Rheology Relationship of Biosourced Rod-Like Colloids and Polymers under Flow

Fluids composed of biosourced rod-like colloids (RC) and rod-like polymers (RP) have been extensively studied due to various promising applications relying on their flow-induced orientation (e.g., fiber spinning). However, the relationship between RC and RP alignment and the resulting rheological properties is unclear due to experimental challenges. We investigate the alignment-rheology relationship for a variety of biosourced RC and RP, including cellulose-based particles, filamentous viruses, and xanthan gum, by simultaneous measurements of the shear viscosity and fluid anisotropy under rheometric shear flows. For each system, the RC and RP contribution to the fluid viscosity, captured by the specific viscosity ηsp, follows a universal trend with the extent of the RC and RP alignment independent of concentration. We further exploit this unique rheological-structural link to retrieve a dimensionless parameter (β) directly proportional to ηsp at zero shear rate (η0,sp), a parameter often difficult to access from experimental rheometry for RC and RP with relatively long contour lengths. Our results highlight the unique link between the flow-induced structural and rheological changes occurring in RC and RP fluids. We envision that our findings will be relevant in building and testing microstructural constitutive models to predict the flow-induced structural and rheological evolution of fluids containing RC and RP.</p

Redox modulation by plant polyphenols targeting vitagenes for chemoprevention and therapy: Relevance to novel anti-cancer interventions and mini-brain organoid technology

The scientific community, recently, has focused notable attention on the chemopreventive and therapeutic effects of dietary polyphenols for human health. Emerging evidence demonstrates that polyphenols, flavonoids and vitamins counteract and neutralize genetic and environmental stressors, particularly oxidative stress and inflammatory process closely connected to cancer initiation, promotion and progression. Interestingly, polyphenols can exert antioxidant or pro-oxidant cytotoxic effects depending on their endogenous concentration. Notably, polyphenols at high dose act as pro-oxidants in a wide type of cancer cells by inhibiting Nrf2 pathway and the expression of antioxidant vitagenes, such as NAD(P)H-quinone oxidoreductase (NQO1), glutathione transferase (GT), GPx, heme oxygenase-1 (HO-1), sirtuin-1 (Sirt1) and thioredoxin (Trx) system which play an essential role in the metabolism of reactive oxygen species (ROS), detoxification of xenobiotics and inhibition of cancer progression, by inducing apoptosis and cell cycle arrest according to the hormesis approach. Importantly, mutagenesis of Nrf2 pathway can exacerbate its "dark side" role, representing a crucial event in the initiation stage of carcinogenesis. Herein, we review the hormetic effects of polyphenols and nanoincapsulated-polyphenols in chemoprevention and treatment of brain tumors via activation or inhibition of Nrf2/vitagenes to suppress carcinogenesis in the early stages, and thus inhibit its progression. Lastly, we discuss innovative preclinical approaches through mini-brain tumor organoids to study human carcinogenesis, from basic cancer research to clinical practice, as promising tools to recapitulate the arrangement of structural neuronal tissues and biological functions of the human brain, as well as test drug toxicity and drive personalized and precision medicine in brain cancer