Electronegativity under Confinement

The electronegativity concept was first formulated by Pauling in the first half of the 20th century to explain quantitatively the properties of chemical bonds between different types of atoms. Today, it is widely known that, in high-pressure regimes, the reactivity properties of atoms can change, and, thus, the bond patterns in molecules and solids are affected. In this work, we studied the effects of high pressure modeled by a confining potential on different definitions of electronegativity and, additionally, tested the accuracy of first-order perturbation theory in the context of density functional theory for confined atoms of the second row at the Hartree–Fock level. As expected, the electronegativity of atoms at high confinement is very different than that of their free counterparts since it depends on the electronic configuration of the atom, and, thus, its periodicity is modified at higher pressures.

Linearized General Relativity

A complete theory of weak-field gravity is described: the linearized approximation. This is a form of first-order perturbation theory. The concept of a gauge transformation, as applied to the curvature tensor and the field equation, is explained, and it is shown how to reduce the field equation to a wave equation in the Lorenz gauge (under the linear approximation). Thus a huge variety of gravitational calculations become accessible.

An inverse problem on determining second order symmetric tensor for perturbed biharmonic operator

This article offers a study of the Calderón type inverse problem of determining up to second order coefficients of higher order elliptic operators. Here we show that it is possible to determine an anisotropic second order perturbation given by a symmetric matrix, along with a first order perturbation given by a vector field and a zero-th order potential function inside a bounded domain, by measuring the Dirichlet to Neumann map of the perturbed biharmonic operator on the boundary of that domain.

First law and quantum correction for holographic entanglement contour

Entanglement entropy satisfies a first law-like relation, which equates the first order perturbation of the entanglement entropy for the region AA to the first order perturbation of the expectation value of the modular Hamiltonian, \delta S_{A}=\delta \langle K_A \rangleδSA=δ⟨KA⟩. We propose that this relation has a finer version which states that, the first order perturbation of the entanglement contour equals to the first order perturbation of the contour of the modular Hamiltonian, i.e. \delta s_{A}(\textbf{x})=\delta \langle k_{A}(\textbf{x})\rangleδsA(𝐱)=δ⟨kA(𝐱)⟩. Here the contour functions s_{A}(\textbf{x})sA(𝐱) and k_{A}(\textbf{x})kA(𝐱) capture the contribution from the degrees of freedom at \textbf{x}𝐱 to S_{A}SA and K_AKA respectively. In some simple cases k_{A}(\textbf{x})kA(𝐱) is determined by the stress tensor. We also evaluate the quantum correction to the entanglement contour using the fine structure of the entanglement wedge and the additive linear combination (ALC) proposal for partial entanglement entropy (PEE) respectively. The fine structure picture shows that, the quantum correction to the boundary PEE can be identified as a bulk PEE of certain bulk region. While the shows that the quantum correction to the boundary PEE comes from the linear combination of bulk entanglement entropy. We focus on holographic theories with local modular Hamiltonian and configurations of quantum field theories where the applies.

The Fixed Angle Scattering Problem with a First-Order Perturbation

We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by 2n measurements up to a natural gauge. We also show that one can recover the full first-order term for a related equation having no gauge invariance, and that it is possible to reduce the number of measurements if the coefficients have certain symmetries. This work extends the fixed angle scattering results of Rakesh and Salo (SIAM J Math Anal 52(6):5467–5499, 2020) and (Inverse Probl 36(3):035005, 2020) to Hamiltonians with first-order perturbations, and it is based on wave equation methods and Carleman estimates.

Prediction of the density-pressure-temperature behavior of the 5CB Liquid Crystal, at the Isotropic-Nematic phase transition

In this work, we have analyzed of density-pressure-temperature behavior at the Isotropic-Nematic phase transition of the 5CB liquid crystal at 1 atm by using a first-order perturbation theory for Convex Peg HERSW model. We predicted quantitatively the experimental behavior in this region of the diagram phase.

Einstein–Yang–Mills theory: gauge invariant charges and linearization instability

We construct the gauge-invariant electric and magnetic charges in Yang–Mills theory coupled to cosmological general relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser (Phys Lett B 116:259–263, 1982). For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part. In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.

Quantum many-body effects on Rydberg excitons in cuprous oxide

We investigate quantum many-body effects on Rydberg excitons in cuprous oxide induced by the surrounding electron-hole plasma. Line shifts and widths are calculated by full diagonalisation of the plasma Hamiltonian and compared to results in first order perturbation theory, and the oscillator strength of the exciton lines is analysed.