In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holographic entanglement entropy. In addition, we study the effect of a relevant perturbation in the Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic term shows up. This new term is proportional to both the dimension of the relevant operator and the Gauss-Bonnet coupling. We also introduce the renormalized entanglement entropy for a kink region which in the UV limit reduces to a universal positive finite term.
The effects of the preharvest application of calcium chloride (1 and 2%), salicylic acid (1 and 2 mM), and putrescine (1 and 2 mM) on the quality attributes and biochemical changes of two ber (Ziziphus mauritiana Lamk.) genotypes ("Sibi" and "Khormaee") were investigated at harvest and after 30 days of storage (5 ± 1°C and 85 ± 5% RH). The results showed that softening and weight loss in the treated fruit were significantly lower in comparison with the control. The antioxidant capacity of the fruit was higher in treated fruit than the control. Moreover, all the treatments significantly reduced the polyphenol oxidase (PPO) activity, increased the catalase (CAT) and peroxidase (POD) activities, and prevented the quick color change of ber fruit. The best overall visual quality (OVQ) was observed in the fruit treated with calcium chloride (1.5%) and putrescine (2 mM). Compared to the two genotypes, "Khormaee" showed a better appearance, relative to the "Sibi" genotypes. Practical applications Ber (Ziziphus mauritiana Lamk.) fruit is a popular fruit which is cultivated widely in the tropical and subtropical countries of the world, due to its high nutritional value. It is rich in bioactive compounds and minerals. However, Indian jujube as a climacteric fruit is highly perishable and have a limited shelf life due to softening, browning, and shrinking. So that, the researchers still need more challenge to keep the quality of this fruit for consumers. In this study, the results showed that the preharvest application of calcium chloride (1.5%), putrescine (2 mM), and salicylic acid (2 mM) effectively kept the total quality of the Indian jujube fruit during storage by improving the firmness of the fruit, retarding the color change and browning, increasing the antioxidant enzymes such as; CAT and POD, and preserving the higher ascorbic acid. Therefore, these treatments can be useful to maintain the quality of Indian jujube during storage.
We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for the thermofield double (TFD) states in free scalar quantum field theories using the covariance matrix approach. To have mixed states, we choose non-complementary subsystems, either adjacent or disjoint intervals on each side of the TFD. We find that the time evolution pattern of OEE is a linear growth followed by saturation. On a circular lattice, for longer times the finite size effect demonstrates itself as oscillatory behavior. In the limit of vanishing mass, for a subsystem containing a single degree of freedom on each side of the TFD, we analytically find the effect of zero-mode on the time evolution of OEE which leads to logarithmic growth in the intermediate times. Moreover, for adjacent intervals we find that the LN is zero for times t < β/2 (half of the inverse temperature) and after that, it begins to grow linearly. For disjoint intervals at fixed temperature, the vanishing of LN is observed for times t < d/2 (half of the distance between intervals). We also find a similar delay to see linear growth of ∆S = SOEE− SEE. All these results show that the dynamics of these measures are consistent with the quasi-particle picture, of course apart from the logarithmic growth.
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