Entanglement transfer from quantum matter to classical geometry in an emergent holographic dual description of a scalar field theory

Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic Einstein-Klein-Gordon type action. Here, the dynamics of both the dual order-parameter field and the metric tensor field originate from density-density and energy-momentum tensor-tensor effective interactions, respectively, in the recursive renormalization group transformation, performed approximately in the Gaussian level. This linear approximation in the recursive renormalization group transformation for the gravity sector gives rise to a linearized quantum Einstein-scalar theory along the z-directional emergent space. In the large N limit, where N is the flavor number of the original scalar fields, quantum fluctuations of both dynamical metric and dual scalar fields are suppressed, leading to a classical field theory of the Einstein-scalar type in (D+1)-spacetime dimensions. We show that this emergent background gravity describes the renormalization group flows of coupling functions in the UV quantum field theory through the extra dimension. More precisely, the IR boundary conditions of the gravity equations correspond to the renormalization group β-functions of the quantum field theory, where the infinitesimal distance in the extra-dimensional space is identified with an energy scale for the renormalization group transformation. Finally, we also show that this dual holographic formulation describes quantum entanglement in a geometrical way, encoding the transfer of quantum entanglement from quantum matter to classical gravity in the large N limit. We claim that this entanglement transfer serves as a microscopic foundation for the emergent holographic duality description.

Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface

The Lie symmetry group transformation method was used to investigate the partial differential equations that model the motion of a natural convective unsteady flow past to a non-isothermal vertical flat surface. The one-parameter Lie group transformation was applied twice consecutively to convert the motion governing equations into a system of ordinary differential equations. The obtained system of ordinary differential equations was solved numerically using the Lobatto IIIA formula (implicit Runge–Kutta method). The effect of the Prandtl number on the temperature and velocity profiles is illustrated graphically.

Selective electrocatalytic hydroboration of aryl alkenes

A CH3CN-involved electrochemical mono- or di-functional borylation reaction with alkenes and HBpin as substrates was reported. Functional group transformation and gram-scale synthesis demonstrated the utility of this method and showed great potential application.

HYDROGEN ROLE IN SELECTIVITY OF SUBSTITUTED NITRO-AZOBENENES HYDROGENI-ZATION ON SKELETAL NICKEL IN 2-PROPANOL AQUEOUS SOLUTIONS

Elucidation of the substituted nitrobenzenes transformations sequence, in particular, containing several reactive groups and the development of approaches to the control of the selectivity of processes involving them is of interest from both theoretical and practical points of view. The article is devoted to the analysis of the hydrogenation kinetics of 2-nitro-2'-hydroxy-5'-methylazobenzene, 4-nitro-2'-hydroxy-5'-methyl-isobenzene, 4-nitroaniline, 4-amino-2'-hydroxy-5'-methylazobenzene on skeletal nickel in 2-propanol aqueous solutions of different composition, including with the addition of acetic acid or sodium hydroxide with various initial amounts of organic compound. The rise in the 4-nitro-2'-hydroxy-5'-methylazobenzene initial amount leads to increase in the nitro group transformation rate in the starting compound and to decrease in the azo-group transformation rate. The effect of sodium hydroxide additives in the 2-propanol aqueous solution on the nitro- and azo-groups conversion rate into 4-nitro-2'-hydroxy-5'-methyl-isobenzene is analogous to the change in the individual compounds hydrogenation rates (4-nitroaniline and 4-amino-2'-hydroxy-5'-methylazobenzene). Obtained results do not contradict the parallel-sequential scheme concept for the 4-nitro-2'-hydroxy-5'-methylazobenzene transformations. One of the directions is associated with the azo-group transformation into 4-nitro-2'-hydroxy-5'-methylazobenzene and 4-nitroaniline and 2-amino-4-methylphenol formation, and the second with the 4-nitro-2'-hydroxy-5'-methyl-isobenzene conversion through 4-amino-2'-hydroxy-5'-methyl-isobenzene by the nitro-group reducing. At the reaction end, all intermediate compounds are reduced to 2-amino-4-methylphenol and 1,4-phenylenediamine. When 2-nitro-2'-hydroxy-5'-methylazobenzene is hydrogenated, one of the directions leads to the 2-nitro-2'-hydroxy-5'-methylhydrazobenzene formation, and the second to the product containing the triazole cycle - N-oxide 2-2'-hydroxy-5'-methylphenylbenzotriazole. At the reaction end, these compounds are reduced to 2-2'-hydroxy-5'-methylphenylbenzotriazole and 2-amino-4-methylphenol and 1,2-phenylenediamine, respectively. In the solution at the sodium hydroxide presence, 2-nitro-2'-hydroxy-5'-methylhydrazobenzene transforms into the N-oxide 2-2'-hydroxy-5'-methylphenylbenzotriazole as a result of intramolecular rearrangement.