Suplemento de la Revista Mexicana de Física

Information theoretic measures of Hookium using generalized pseudo-spectral technique within density functional theory

2025-04-12T01:47:14+00:00

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.

On the numerical integration of two-particle functions for pair entropies of diatomic molecules

2025-03-05T01:47:29+00:00

In order to compute two-electron informational entropies of atoms or molecules, highly-accurate numerical integration methods are needed. In this contribution, we describe the details of a numerical algorithm specific for diatomic molecules, originally designed to numerically integrate 3D functions. The algorithm is adapted to integrate functions of two particles, i.e., to integrate functions in domains of the form Ω × Ω, where Ω ∈ R³ . The diatomic integration scheme is a cubature rule that combines Gauss-Legendre quadratures for the radial and angular parts, and the domain Ω is split into two semi-spheres, each with its own local center of coordinates. In addition, we compare the performance of the diatomic integration scheme vs. a Monte Carlo integrator, both for the 3D and 6D cases.

Applications of information theory to compact objects: configurational entropy as a stability criterion

2025-03-06T17:42:18+00:00

M. Gleiser and N. Jiang [Phys. Rev. D 92, 044046, 2015] established that, within the simple Fermi gas model and self-gravitating complex scalar field configurations, the stability regions of neutron stars—determined using conventional perturbation techniques—align with the critical points of the configurational entropy, with deviations of only a few percent. Extending their work, we employ a range of realistic equations of state, suitable to describe neutron stars, quark stars, and hybrid stars (twin stars), to explore the potential correlation. Our findings indicate that, at least quantitatively, the proposed stability prediction lacks universal validity for neutron and quark stars. Furthermore, to enrich our analysis, we compute the configurational entropy for bosonic and fermionic systems (interacting boson and Fermi gases), revealing a strong correlation between the stability points predicted by configurational entropy and those obtained through traditional methods, with a slight dependence on interaction strength. In conclusion, configurational entropy can be a valuable tool for studying compact object stability, though its predictive accuracy depends on the specific equation of state.

Uncertainties and statistical correlations in quantum systems

2025-03-05T01:34:14+00:00

A survey of recent ideas and goals, along with a brief history behind the quantification of uncertainties and statistical correlation in quantum systems is presented. The focus is on ideas and connections taken from information theory, in particular, the quantification of uncertainties via Shannon entropies, the entropic uncertainty relation, and statistical correlation by mutual information. A discussion of phase-space distributions and their use in information theory is also given. An incomplete list of applications, with emphasis on confined quantum systems, is provided. The article concludes by addressing future challenges in these directions.

Shannon entropy as an indicator for the orbital shape manipulation of a hydrogen atom under a repulsive single barrier potential

2025-02-27T20:44:02+00:00

The effect of a penetrable repulsive single-barrier potential on the structural properties of hydrogen atom in ground and different excited (n,l) states [n=1-3, l=0-2] is studied. The Lagrange mesh method is adopted to solve the corresponding Schrodinger equation numerically for energy eigenvalues and eigenfunctions. Different novel features and phenomena e.g. shrinking the size of the atom, atomic swelling, orbital fusion and fission etc. are noted when the strength of the barrier is changed by tuning its position and height. It is remarkable that all such alterations of the atomic orbital are well articulated from the Shannon entropy profile.

Towards entropic uncertainty relations for non-regular Hilbert spaces

2025-03-12T02:34:33+00:00

The Entropic Uncertainty Relations (EUR) result from inequalities that are intrinsic to the Hilbert space and its dual with no direct connection to the Canonical Commutation Relations. Bialynicky-Mielcisnky obtained them in [1] attending Hilbert spaces with a Lebesgue measure. The analysis of these EUR in the context of singular Hilbert spaces has not been addressed. Singular Hilbert spaces are widely used in scenarios where some discretization of the space (or spacetime) is considered, e.g., loop quantum gravity, loop quantum cosmology and polymer quantum mechanics. In this work, we present an overview of the essential literature background and the road map we plan to follow to obtain the EUR in polymer quantum mechanics.

Information-theoretical quantities in the thermodynamical transcription of the density functional theory

2025-02-27T20:07:14+00:00

The Ghosh-Berkowitz-Parr idea of density functional theory as local thermodynamics is revisited. It is emphasized that the kinetic energy density and consequently the local temperature are not unique. It is highlighted that the extremal principle for the Shannon entropy and the Fisher information leads to constant temperature. Relations for the phase-space Fisher information, fidelity and relative Rényi entropy are summarized.

An information-theoretical take on electron-nuclear wave packet dynamics

2025-03-20T23:40:05+00:00

Applications of information-theoretic measures to a time-dependent coupled electron-nuclear system to analyze the dynamics and correlation between both particles are presented. For this, differential Shannon entropies that are derived from time-dependent coordinate-space and momentum-space probability densities are calculated. Two distinct scenarios are investigated: one exhibiting adiabatic Born-Oppenheimer dynamics and the other involving strong non-adiabatic transitions. The total and single-particle entropies, as well as the mutual information are analyzed and compared to semi-analytical expressions. The results reveal that in the adiabatic regime, correlations manifest differently in coordinate and momentum spaces, which is related to the formation of nodes. In the non-adiabatic case, entropies can be decomposed into state-specific contributions, revealing information about the transition between adiabatic states.

Quantum entropy production rate of quantum markov semigroups

2025-04-30T17:37:24+00:00

This paper explores various perspectives on Quantum Detailed Balance and the Entropy Production Rate within the framework of Quantum Markov Semigroups. Using the generators of these semigroups, formulated according to the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) theorem, and their respective adjoints, we identify two contrasting families of Quantum Markov Semigroups. The first family demonstrates a situation where the condition for Quantum Detailed Balance is violated, yet the entropy production rate is zero. In contrast, the second family reveals cases where the quantum entropy production rate aligns with an interpretation of Quantum Detailed Balance. These findings provide insights into the relationship between quantum detailed balance and entropy production rate in open systems.

Construction and analysis of statistical correlation measures through Diophantine equations

2025-04-12T00:58:33+00:00

In this work, we explore the connection between Diophantine equations and the construction of informational measures, particularly mutual information, total correlation, and higher-order interaction information. These information measures are calculated in continuous variable quantum systems comprised of three to fifty harmonic oscillators, and their behaviour was compared among them. By analyzing the ground state of quantum harmonic oscillators, we establish a mathematical framework where Diophantine constraints emerge naturally in the computation of these quantities. There is an overall consistency in the behaviour of the introduced measures as function of the parameters of pairwise potential and the number of oscillators. Our results provide new insights into the interplay between number theory and quantum information, suggesting novel approaches to quantifying higher-order correlations in many-body quantum systems.

Spherically confined hydrogen atom: variational cut-off factor

2025-05-15T17:20:27+00:00

The hydrogen atom confined within an impenetrable spherical cavity of radius R under the influence of a uniform constant magnetic field B is considered. For the ground state, using the variational method, we employ a physically meaningful trial wavefunction characterized by three variational parameters, including a novel cut-off factor that acts as an additional degree of freedom in the optimization process. This approach allows us to systematically analyze the interplay between quantum confinement and the external magnetic field, providing insights into their combined effects on the energy spectrum and wavefunction behavior. Our results reveal how the ground state energy E and eigenfunction evolve as functions of the cavity radius R ∈ [1, 5] a.u. and magnetic field strength B ∈ [0, 1] a.u., offering a deeper understanding of quantum confinement in atomic systems subjected to external fields. These findings have potential implications for confined quantum systems in astrophysical and nanotechnological applications.

Preface

2025-05-21T20:25:52+00:00

Proceedings of the International Symposium Commemorating the 50th Anniversary of the Universidad Aut´onoma Metropolitana: Applications of Information Theory in Natural Sciences.