Non-parametric application of Tsallis statistics to systems consisting of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e1133" altimg="si259.gif"><mml:mi>M</mml:mi></mml:math> hydrogen molecules

Drzazga, E.A.; Szczȩśniak, R.; Domagalska, I. A.; Durajski, A. P.; Kostrzewa, M.

doi:10.1016/j.physa.2018.11.050

Cited by 3 publications

(2 citation statements)

References 59 publications

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“…It can be easily seen that the ground state is the degenerated one, this being related to the existence of two directions of the electronic spin projections. The degeneration can be removed by the constant external magnetic field (H) applied to the cations: ĤH = −2H Ŝz 1 + Ŝz 2 , where Ŝz j = 1 2 (n j↑ − nj↓ ) [30,31]. The eigenvectors have the form:…”

Section: Description Of the Ground State Of Cations With One-electron...mentioning

confidence: 99%

Chaotic evolution of the energy of the electron orbital and the hopping integral in diatomic molecule cations subjected to harmonic excitation

Domagalska¹,

Jarosik²,

Durajski³

et al. 2019

Preprint

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We analysed the dynamics of the positively charged ions of diatomic molecules (X + 2 and XY + ), in which the bond is realised by a single electron. We assumed that the atomic cores separated by a distance R were subjected to the external excitation of a harmonic type with the amplitude A and frequency Ω. We found the ground states of ions using the variational approach within the formalism of second quantization (the Wannier function was reproduced by means of Gaussian orbitals). It occurred that, on the account of the highly non-linear dependence of the total energy on R, the chaotic dynamics of cores induced the chaotic evolution of the electronic Hamiltonian energetic parameters (i.e. the energy of the electron orbital ε and the hopping integral t). Changes in cation masses or in the charge arrangement does not affect qualitatively the values of Lyapunov exponents in the A-Ω parameter space.

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Section: Description Of the Ground State Of Cations With One-electron...mentioning

confidence: 99%

Chaotic evolution of the energy of the electron orbital and the hopping integral in diatomic molecule cations subjected to harmonic excitation

Domagalska¹,

Jarosik²,

Durajski³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Other research investigates the localization of the entanglement of two interacting distinguishable particles in the configuration space by sampling a preliminary calculated reduced density matrix for known wave functions over a uniform grid and next calculating the von Neumann entropy [3]. It is also worth mentioning the use of the Tsallis approach to characterize the entropy properties of a single hydrogen molecule as well as of systems of three and more such molecules [4]. From the chemistry viewpoint, the local entanglement entropy considered as information entropy may find application in analysis of electron density and as correlation measure in atoms and molecules where mostly global measures have been used so far [5,6].…”

Section: Introductionmentioning

confidence: 99%

Local Entanglement of Electrons in 1D Hydrogen Molecule

Christov

2023

Entropy

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The quantum entanglement entropy of the electrons in a one-dimensional hydrogen molecule is quantified locally using an appropriate partitioning of the two-dimensional configuration space. Both the global and the local entanglement entropy exhibit a monotonic increase when increasing the inter-nuclear distance, while the local entropy remains peaked in the middle between the nuclei with its width decreasing. Our findings show that at the inter-nuclear distance where a stable hydrogen molecule is formed, the quantum entropy shows no peculiarity thus indicating that the entropy and the energy measures display different sensitivity with respect to the interaction between the two identical electrons involved. One possible explanation is that the calculation of the quantum entropy does not account explicitly for the distance between the nuclei, which contrasts to the total energy calculation where the energy minimum depends decisively on that distance. The numerically exact and the time-dependent quantum Monte Carlo calculations show close results.

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Open Problems within Nonextensive Statistical Mechanics

Nelson

2024

Entropy

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Nonextensive statistical mechanics has developed into an important framework for modeling the thermodynamics of complex systems and the information of complex signals. To mark the 80th birthday of the field’s founder, Constantino Tsallis, a review of open problems that can stimulate future research is provided. Over the thirty-year development of NSM, a variety of criticisms have been published ranging from questions about the justification for generalizing the entropy function to the interpretation of the generalizing parameter q. While these criticisms have been addressed in the past and the breadth of applications has demonstrated the utility of the NSM methodologies, this review provides insights into how the field can continue to improve the understanding and application of complex system models. The review starts by grounding q-statistics within scale-shape distributions and then frames a series of open problems for investigation. The open problems include using the degrees of freedom to quantify the difference between entropy and its generalization, clarifying the physical interpretation of the parameter q, improving the definition of the generalized product using multidimensional analysis, defining a generalized Fourier transform applicable to signal processing applications, and re-examining the normalization of nonextensive entropy. This review concludes with a proposal that the shape parameter is a candidate for defining the statistical complexity of a system.

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Non-parametric application of Tsallis statistics to systems consisting of M hydrogen molecules

Cited by 3 publications

References 59 publications

Chaotic evolution of the energy of the electron orbital and the hopping integral in diatomic molecule cations subjected to harmonic excitation

Chaotic evolution of the energy of the electron orbital and the hopping integral in diatomic molecule cations subjected to harmonic excitation

Local Entanglement of Electrons in 1D Hydrogen Molecule

Open Problems within Nonextensive Statistical Mechanics

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