Journal of Atomic, Molecular, Condensed Matter and Nano Physics

Analytical Derivation and Perturbative Structure of Entanglement Entropy in Quantum Field Theory: Covariance Matrix Formalism and Noncommutative Corrections

Vaidik A. Sharma — 2024-12-31

Entanglement entropy (EE) is a pivotal quantity in quantum field theory (QFT) that captures the nonlocal correlations between subsystems, offering deep insights into the quantum structure of spacetime, field dynamics, and phase transitions. This work derives EE in QFT using the covariance matrix formalism, establishing its foundations through the von Neumann entropy of reduced density matrices. We analytically compute EE for coupled harmonic oscillators as a prototypical model, extending the results to quantum fields via perturbative expansions. In the context of Maxwell QFT, we analyze entropy corrections induced by external perturbations, revealing their fractal dynamics through the emergence of Julia sets. The study further incorporates noncommutative geometry, where the deformation of spacetime modifies the covariance matrix, field strength tensors, and modular indices. Numerical simulations validate the derived scaling laws, entropy corrections, and noncommutative effects. These findings provide a mathematically rigorous framework to explore the interplay between EE, field theory, and geometric structures in high-energy physics.

Hybrid Theory of Scattering of Positrons from Helium Atoms

Anand K. Bhatia — 2024-12-31

Hybrid theory of $L$-wave scattering of positrons from helium atoms is developed. Phase shifts are calculated for the incident positron momentum from $0.1$ to $1.2$ for $L=0, 1, 2, 3$ before the~onset of excitation, and positronium formation. The phase shifts are compared with phase shifts obtained by Drachman, and by Campeanu and Humberston.

Energy Eigenvalues, Dipole Polarizability, Electron Pressure and Effect of Dielectrics on the Confined Hydrogen Atom

Rupachandra Maibam — 2024-12-31

In this work, we used an efficient computational technique to solve the Schrödinger equation for the confined hydrogen atom (CHA) which is confined inside a hard spherical cavity with impenetrable wall. The wavefunctions, energy eigenvalues, polarizability and pressure have been calculated for different confinement radius. The energy eigenvalues and expectation values obtained are in good agreement with those calculated values obtained by Aquino et al. [2]. The hydrogen atoms under high pressure are real physical systems which can be found inside astrophysical objects.

Excitations of the 4F and 5F States of Atomic Hydrogen by Positron Impact

Anand K. Bhatia — 2024-12-31

The excitation cross sections of the 4F and 5F states of atomic hydrogen by positron impact have been calculated at low incident energies (from 1.00 to 4.41 Ry), using the variational polarized method, also called the hybrid theory. Partial waves ranged from $L=3$$to 20 to obtain converged cross sections. The importance of the long-range interaction in the threshold region is discussed. A comparison of $S$, $P$, $D$, and $F$ cross sections is given. These cross sections are needed because of cascades from higher states to the $S$ state when the cross sections of the $S$ state in hydrogen are measured or in diagnostics of solar and astrophysical observations. The phase shifts at low energies are also given.