Dimensional interpolation for metallic hydrogen

Ghosh, Kumar; Kais, Sabre; Herschbach, D. R.

doi:10.1039/d0cp05301e

Cited by 10 publications

(13 citation statements)

References 62 publications

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“…A very important point is here that all the data of T c obtained fall on a common, straight line (blue), which follows the equation for a particle in a box [24] with the slope h 2 /(2πk B ) = 5.061 × 10 −45 m 2 kg K. This result enables the Roeser-Huber formalism to act as a test for given predictions of T c , e.g., for the case of metallic hydrogen as was done recently in Ref. [37].…”

Section: Elementsupporting

confidence: 64%

Calculation of Tc of Superconducting Elements with the Roeser–Huber Formalism

Koblischka

Koblischka-Veneva

2022

Metals

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The superconducting transition temperature, Tc, can be calculated for practically all superconducting elements using the Roeser–Huber formalism. Superconductivity is treated as a resonance effect between the charge carrier wave, i.e., the Cooper pairs, and a characteristic distance, x, in the crystal structure. To calculate Tc for element superconductors, only x and information on the electronic configuration is required. Here, we lay out the principles to find the characteristic lengths, which may require us to sum up the results stemming from several possible paths in the case of more complicated crystal structures. In this way, we establish a non-trivial relation between superconductivity and the respective crystal structure. The model enables a detailed study of polymorphic elements showing superconductivity in different types of crystal structures like Hg or La, or the calculation of Tc under applied pressure. Using the Roeser–Huber approach, the structure-dependent different Tc’s of practically all superconducting elements can nicely be reproduced, demonstrating the usefulness of this approach offering an easy and relatively simple calculation procedure, which can be straightforwardly incorporated in machine-learning approaches.

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Section: Elementsupporting

confidence: 64%

Calculation of Tc of Superconducting Elements with the Roeser–Huber Formalism

Koblischka

Koblischka-Veneva

2022

Metals

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“…To recapitulate, we start with the dimensional interpolation formula for atomic, molecular, and extended systems. , For dimensional scaling of atoms and molecules, the energy erupts to infinity as D → 1 and vanishes as D → ∞. Hence, we adopt scaled units (with hartree atomic units) whereby E D = ( Z /β) 2 ϵ D and β = ( 1 / 2 )( D – 1), so the reduced energy ϵ D remains finite in both limits.…”

Section: Basic Dimensional Interpolation Formulamentioning

confidence: 99%

“…Dimensional scaling offers simple solutions at the limits D = 1 and D → ∞, where D is the number of spacial dimensions. Using these limits, we interpolate between them to obtain accurate results for chemical physics at D = 3. − Recently, a dimensional interpolation formula was developed to obtain the ground state energies for few electron atoms, simple diatomic molecules and extended systems like metallic hydrogen . Rudnick et al studied the random walks in high spacial dimensions , and developed 1/ D expansion to study the shape of a random walk in three dimensions.…”

Section: Introductionmentioning

confidence: 99%

Dimensional Interpolation for Random Walk

2021

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We employ a simple and accurate dimensional interpolation formula for the shapes of random walks at D = 3 and D = 2 based on the analytically known solutions at both limits D = ∞ and D = 1. The results obtained for the radius of gyration of an arbitrary shaped object have about 2% error compared with accurate numerical results at D = 3 and D = 2. We also calculated the asphericity for a three-dimensional random walk using the dimensional interpolation formula. The results agree very well with the numerically simulated results. The method is general and can be used to estimate other properties of random walks.

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“…Ever since this has been a major quest for condensed matter physics, pursuing theory [68][69][70][71][72] and extreme high-pressure experiments [73][74][75][76][77][78]. Dimensional scaling and interpolation as applied to metallic hydrogen was investigated in articles [68,79]. With appropriate scaling, energies will be in units of 4/(D − 1) 2 hartrees, and distances in units of D(D − 1)/6 Bohr radii.…”

Section: Electron Correlation and The Surface Area For Metallic Hydro...mentioning

confidence: 99%

“…We optimize the above Hamiltonian (15) with respect to the parameters γ 100 , γ 110 , γ 111 keeping the values of ρ and R from the HF-Hamiltonian [79]. In Fig.…”

Section: Electron Correlation and The Surface Area For Metallic Hydro...mentioning

confidence: 99%

Geometrical picture of the electron-electron correlation at the large-D limit

Ghosh,

Kais,

Herschbach

2021

Preprint

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In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electronelectron correlations and might give a bound on the correlation energy. The results at the large-D limit and at D= 3 indicate the feasibility of using the geometrical picture to get a bound on the electron-electron correlations.

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Dimensional interpolation for metallic hydrogen

Abstract: We employ a simple and mostly accurate dimensional interpolation formula using dimensional limits D = 1 and D = ¥ to obtain D = 3 ground-state energy of metallic hydrogen....

Cited by 10 publications

References 62 publications

Calculation of Tc of Superconducting Elements with the Roeser–Huber Formalism

Calculation of Tc of Superconducting Elements with the Roeser–Huber Formalism

Dimensional Interpolation for Random Walk

Geometrical picture of the electron-electron correlation at the large-D limit

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