ABSTRACT Accurate estimation of structural properties is essential for understanding the behavior of atomic systems, particularly in confined environments where they display unique physical phenomena. Amongst these, the correlation energy plays a pivotal role in shaping the overall dynamics of the system. In this study, we investigate the influence of external confinement on both correlation energy and Collins' conjecture by evaluating different quantum information and quantum entanglement entropies. For this purpose, we model a two‐electron quantum dot using an isotropic harmonic potential to explore these effects. Various geometrical properties are estimated to showcase the acceptability and viability of the present method. Additionally, we investigate the impact of harmonic confinement on the quantum similarity measures e.g. quantum similarity index and quantum dissimilarity between He(1) and He(1 and 1), as well as between He(1) and He(1). These results for both ground and singly excited states of two‐electron system are reported here for first time.
ABSTRACT Accurate estimation of structural properties is essential for understanding the behavior of atomic systems, particularly in confined environments where they display unique physical phenomena. Amongst these, the correlation energy plays a pivotal role in shaping the overall dynamics of the system. In this study, we investigate the influence of external confinement on both correlation energy and Collins' conjecture by evaluating different quantum information and quantum entanglement entropies. For this purpose, we model a two‐electron quantum dot using an isotropic harmonic potential to explore these effects. Various geometrical properties are estimated to showcase the acceptability and viability of the present method. Additionally, we investigate the impact of harmonic confinement on the quantum similarity measures e.g. quantum similarity index and quantum dissimilarity between He(1) and He(1 and 1), as well as between He(1) and He(1). These results for both ground and singly excited states of two‐electron system are reported here for first time.
Abstract This study investigates the quantum correlation and information‐theoretic measures of coupled double‐well systems, modeled using Razavy's hyperbolic potential. By employing numerical techniques, including the finite difference method and Kronecker tensor product, the time‐independent equation is solved to determine energy eigenvalues and eigenfunctions for quantum states, such as , , , and of the bipartite quantum system. The analysis focuses on quantum information measures, such as Shannon entropy, mutual information, and statistical correlation coefficients, to understand how potential parameters and and the coupling strength influence correlations. The results reveal intricate dependencies between quantum states, highlighting symmetry and asymmetry in correlation measures for mixed states under opposite coupling potentials. Further, the different behaviors of the statistical correlation coefficients are found in position and momentum space and their information‐theoretic measures as functions of potential parameters, which is very helpful for understanding the dynamics of quantum particles in the coupled system. Additionally, the study investigates the entanglement properties of bipartite quantum states, employing von Neumann, and linear entropy to measure quantum correlations. The results provide critical insights into the dynamics of quantum particles in confined systems, connecting quantum mechanics and information theory. This work opens new avenues to exploring quantum information dynamics in Razavy double‐well systems, which gives novel insights into the role of spatial and momentum correlations in particle interactions.
Abstract We investigate the influence of quartic anharmonic confinement on spatial entanglement in two-electron quantum dots. By transforming the Hamiltonian into center-of-mass and relative coordinates, we develop a computational framework combining variational methods, Numerov integration, and Monte Carlo evaluation of linear entropy. We demonstrate that anharmonicity reduces the equilibrium inter-electronic separation, leading to enhanced Coulomb correlations and increased entanglement. In the weakly anharmonic regime, the linear entropy exhibits an approximately linear dependence on the anharmonicity parameter. The results are validated through convergence analysis and comparison with known harmonic-limit results. These findings establish anharmonic confinement as a controllable mechanism for tuning entanglement in semiconductor quantum dots, with potential applications in quantum information processing.
Atomic systems subjected to external confinement exhibit a range of intriguing physical properties. In this work, we employ a well-established work-function-based Kohn-Sham density functional theory (DFT) within a generalized pseudospectral (GPS) method to determine the energy eigenvalues and eigenfunctions of Hookium (a two-electron system bound by a harmonic potential). We consider the two cases, viz. (i) Hookium and (ii) Hookium under the influence of a spherical cavity confinement. Two correlation energy functionals like Wigner and Lee-Yang-Parr (LYP) are considered to include explicit correlation energy in the calculation. Furthermore, we provide a comprehensive analysis of the quantum information-theoretic aspects of confined systems by examining the position-space Shannon and Fisher entropies.
The effect of impenetrable confinement has been rigorously tested on the information-theoretic measures of Shannon information entropy, Fisher measure, Onicescu energy, and entanglement measures, such as von Neumann and linear entropy, corresponding to ${\mathrm{H}}^{\ensuremath{-}}$, He, and Li+ in their ground electronic state. High-quality variational Hylleraas-like expansion as well as the accurate numerical Hartree-Fock wave functions have been employed for the chosen set of two-electron Zee systems. The impenetrable confinement has been mimicked with a spherical cavity model potential of varying radius R, which in turn, is used to quantify thermodynamic pressure within the adiabatic approximation. The structural properties such as total energy, energy components, and geometrical properties (expectation values electron-electron separation and electron-nuclear distance) have been estimated to test the accuracy and viability of the present calculation. Some intriguing scaling laws related to von Neumann, linear, and Shannon entropy as a function of pressure are proposed. The influence of impenetrable confinement on the transition probability of He $\ensuremath{\rightarrow}{\mathrm{Li}}^{+}$ during nuclear $\ensuremath{\beta}$ decay is quantitatively assessed.
The entanglement dynamics of spin–subband states for an electron in a 2D isotropic Rashba quantum dot, with an applied magnetic field of arbitrary strength, is studied. We explicitly include the confining (gate) effects as a two-dimensional isotropic harmonic oscillator. The von Neumann entropy, as a measure of entanglement, is calculated as a function of time, by going to the Fock–Darwin representation. Our results indicate that the period and amplitude of the collapse–revival behavior of the entanglement between the spin states and the structural subbands strongly depend upon the size of the quantum dot (confining length) and choice of heterostructural materials. Our results, thereby, provide means of controlling the degree of entanglement by adjusting these factors.
We calculate the spatial entanglement between two electrons trapped in a nanostructure for a broad class of confinement potentials, including single and double quantum dots, and core-shell quantum dot structures. By using a parametrized confinement potential, we are able to switch from one structure to the others with continuity and to analyze how the entanglement is influenced by the changes in the confinement geometry. We calculate the many-body wave function by ``exact'' diagonalization of the time-independent Schr\"odinger equation. We discuss the relationship between the entanglement and specific cuts of the wave function, and show that the wave function at a single highly symmetric point could be a good indicator for the entanglement content of the system. We analyze the counterintuitive relationship between spatial entanglement and Coulomb interaction, which connects maxima (minima) of the first to minima (maxima) of the latter. We introduce a potential quantum phase transition which relates quantum states characterized by different spatial topology. Finally we show that by varying shape, range, and strength of the confinement potential, it is possible to induce strong and rapid variations in the entanglement between the two electrons. This property may be used to tailor nanostructures according to the level of entanglement required by a specific application.