arXiv subjects

Boris Maulén

Publications and source records attributed to Boris Maulén.

5 recordsLinked to original sources

arXiv2026

Quantum Expectation Identities for the Three-State Model of a Molecular Domain

The electronic distribution of a molecular domain is examined in this study. A theoretical formulation of quantum molecular properties is presented using the Quantum Expectation Identity theorem (QEI), with a focus on the three-state model of the density matrix for the quantum state of a molecular domain as an open system. The report examines the relationship between ab initio statistical fluctuation-correlation theorems for quantum observables and their derivatives. We focus on three main quantities of a domain: the electronic population, its chemical potential, and its maximum capacity for accepting or donating charge with the neighbors. The analytical expressions for the quantities are presented and discussed in detail. At the end, we explore the concept of quantum purity and its proper application in the molecular domain.

quant-ph↗

arXiv2026

Configurational density of states of finite classical systems

The configurational density of states (CDOS) encodes all the relevant thermodynamic information contained in the interaction potentials for statistical mechanical systems. However, its explicit computation is usually a challenge for non-trivial systems, and numerical algorithms such as Wang-Landau simulation are often used. In this work we use a microcanonical framework to provide an explicit inversion formula for the calculation of the CDOS from the total density of states (DOS) without resorting to the inversion of the Laplace transform. From this formula, several results can be obtained for the thermodynamics of finite classical systems composed of a few degrees of freedom, while also recovering the well-known asymptotic results for the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2024

A quantum expectation identity: Applications to statistical mechanics

In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between different quantum observables depending on a continuous parameter. Such a parameter can be contained in the observables itself (e.g. perturbative parameter) or may appear as a Lagrange multiplier (inverse temperature, chemical potential, etc.) in the density matrix, excluding parameters that modify the underlying Hilbert space. In this way, using both canonical and grand canonical density matrices along with certain quantum observables (Hamiltonian, number operator, the density matrix itself, etc.) we found new identities in the field, showing not only its derivation but also their meaning. Additionally, we found that some theorems of traditional quantum statistics and quantum chemistry, such as the thermodynamical fluctuation-dissipation theorem, the Ehrenfest, and the Hellmann-Feynman theorems, among others, are particular instances of our aforementioned quantum expectation identity. At last, using a generalized density matrix arising from the Maximum-Entropy principle, we derive generalized quantum expectation identities: these generalized identities allow us to group all the previous cases in a unitary scheme.

quant-ph↗

arXiv2023

Quantum states of physical domains in molecular systems: A three-state model approach

The physical regions (domains or basins) within the molecular structure are open systems that exchange charge between them and consequently house a fractional number of electrons (net charge). The natural framework describing the quantum states for these domains is the density matrix (DM) in its grand-canonical version which corresponds to a convex expansion into a set of basis states of an integer number of electrons. In this report, it is shown that the solution for these quantities is supported by the DM expansion into three states of different number of particles, the neutral and two (edge) ionic states. The states and the average number of particles in the domains (fractional occupation population) are determined by the coefficients of the expansion in terms of the fundamental transference magnitudes revealing the donor/acceptor character of the domains by which the quantum accessible states are discussed.

quant-ph↗

arXiv2021

Lie algebraic solution of the Kratzer oscillator in diatomic molecules

The study of diatomic molecules plays a central role in the understanding of the chemical bond. For their simplicity, they serve as a model for the study of more complex molecular systems. In this article, we solve the rovibrational Schrödinger equation for diatomic molecules using the Kratzer oscillator, by means of so(2,1) Lie algebra. The energies and bound states for this simple model are obtained through a canonical transformation of the molecular Hamiltonian. The main contribution of the Lie-algebraic approach is that this allows us to reduce the degree of Schrödinger equation, obtaining a first-order differential equation whose resolution is considerably simpler than the original one. Additionally, we give the physical insight of the symmetry transformation of the SO(2,1) Lie group and show the relationship between this group and its associated Lie algebra. Finally, as an illustrative example, we calculated the selection rules for the vibrational quantum number by the use of transformation rules of SO(2,1) Lie group.

quant-ph↗