Confinement of atoms with Robin’s condition: Spontaneous symmetry breaking

Sveshnikov, K. A.; Silaev, P. K.; Tolokonnikov, A. V.

doi:10.3103/s0027134917010155

Cited by 5 publications

(21 citation statements)

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“…In a cavity with finite R, such situation also takes place when the equilibrium position of H shifts from the center to the border, that happens whenever λ < q with q being the nucleus charge. [34,35] In ℜ 3 / 2 the spherical symmetry restores only for infinite distances between the atom and plane and only in the case, when the atomic electron is localized in the nucleus vicinity, where it falls into the eigenstates of the free atom. But this is not the general case.…”

Section: The Problem Statement For Atomic H In ℜ 3 /mentioning

confidence: 99%

“…[25][26][27][28][29][30][31][32][33] Moreover, such conditions are able to take into account the interaction of confined particles with medium, surrounding the cavity or demarcating the half-space. [29][30][31][32]34,35] It would be worth to note that the term "not going through," used here, underlines that these conditions do not necessarily originate from the actual confinement of particles inside the given volume, rather they may be caused by a significantly wider number of reasons, as it takes place, in particular, in the Wigner-Seitz model of an alkali metal, [4,5] where the valence electron state is principally delocalized. The latter circumstance turns out to be quite important, because in some cases the cavities, where a particle or an atom could reside, form a lattice, similar to that of an alkali metal, like certain interstitial sites of a metal supercell, for example, next-to-nearest octahedral positions of palladium face-centered-cubic lattice.…”

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confidence: 99%

“…[36] In this case a particle (or a valence electron, provided that the whole lattice of cavities is occupied by identical atoms) finds itself in a periodic potential of a cubic lattice, and so the description of its ground state could be based on the first principles of the Wigner-Seitz model. [31,32,34,35] Another approach to atomic confinement by means of "not going through" condition has been considered recently by Burrows and Cohen [37] in terms of the electronic flux, which is assumed to vanish on some notional bounding surface of arbitrary shape.…”

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confidence: 99%

“…with growing R the equilibrium position of the atom in the center of cavity ceases to be stable and it shifts to the border. [34,35] When the curvature of the border becomes much larger than a B , then the problem of an H over plane with Robin boundary condition for the electronic WF appears in a natural way. In this problem there are two most important questions.…”

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confidence: 99%

“…The first one is under which conditions imposed on the surface interaction the effective atomic potential, treated as a function of the distance h to the plane, reveals a minimum for finite and nonzero h. A preliminary, rather rough estimate for this effect has been considered in Refs. [34,35]. The second concerns the additional "power-like" levels, which appear always under Robin boundary condition with attractive surface interaction and become the lowest ones, when the attraction is sufficiently strong.…”

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Atomic H over plane: Effective potential and level reconstruction

Artyukova

Sveshnikov

Tolokonnikov

2019

Int J of Quantum Chemistry

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The behavior of atomic H in a semi-bounded space z ≥ 0 with the condition of "not going through" the boundary (the surface z = 0) for the electronic wavefunction (WF) is considered. It is shown that in a wide range of "not going through" condition parameters the effective atomic potential, treated as a function of the distance h from H to the boundary plane, reveals a well pronounced minimum at certain finite but nonzero h, which describes the mode of "soaring" of the atom above the plane. In particular cases of Dirichlet and Neumann conditions, the analysis of the soaring effect is based on the exact analytical solutions of the problem in terms of generalized spheroidal Coulomb functions. For h varying between the regions h ) a B and h ( a B , both the deformation of the electronic WF and the atomic state are studied in detail. For a more general case of Robin (third type) condition, the variational estimates and direct numerical tools are used. By means of the latter it is also shown that in the case of a sufficiently large positive affinity of the atom to the boundary plane a significant reconstruction of the lowest levels takes place, including the change of both the asymptotics and the general dependence on h. K E Y W O R D S confined quantum systems, levels reconstruction, soaring effect 1 | INTRODUCTIONConsiderable amount of theoretical and experimental activity has been focused recently on spatially confined atoms and molecules. [1][2][3] The interest is largely due to the nontrivial physical and chemical properties that arise for quantum systems in such a state of complete or incomplete confinement. The interaction of confined particles with the environment, forming the cavity or volume boundary, is usually simulated by means of a suitable boundary condition, imposed on their wavefunctions (WF). The pioneering works on quantum system in a closed cavity are the Wigner-Seitz model [4,5] and the papers [6,7] on atomic H in a spherical cavity. More concretely, in the Wigner-Seitz model the metallic bond formation in alkali metals has been considered in terms of the Neumann condition for the valence electron on the boundary of the corresponding Wigner-Seitz cell. In Ref.[6] the exact solution for atomic H in a spherical cavity with the Dirichlet boundary condition was found, while in Ref.[7] such a model has been used for description of atomic H under high pressure.Atoms in the Euclidean half-space ℜ 3 / 2 have been first explored by Levine, [8] devoted to the properties of the impurity donor atom placed on the plane boundary of the dielectric crystal. Due to a large positive affinity it is energetically favorable for the valence electron to reside inside the crystal that allows to simulate the crystal boundary by means of the Dirichlet condition imposed on the electronic WF. Afterwards, this model All authors contributed equally to this work.

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Section: The Problem Statement For Atomic H In ℜ 3 /mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Atomic H over plane: Effective potential and level reconstruction

Artyukova

Sveshnikov

Tolokonnikov

2019

Int J of Quantum Chemistry

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Atomic H over crystal surface: effective potential dependence on sample properties

Silaev,

Tolokonnikov

2024

Phys. Scr.

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We considered the behavior of the lowest electronic level of atomic H in a semi-infinite space bounded by a flat surface. We impose a third kind boundary condition on the electronic wave functions, where the boundary condition parameter models the adsorbent properties of the surface.For the crystal surface, the double periodic function as the boundary parameter seems reasonable; therefore, this case is considered.It is shown that there are two modes of atom adsorption on the sample surface depending on the parameters of the boundary condition. In the first case the effective atomic potential, considered as a function of the distance between H and the boundary plane, exhibits a well pronounced minimum at some finite distance and a relatively small effective range of interaction distances between the atoms and samples.The second case occurs under the condition of a large positive affinity of the atomic electron to the sample boundary and low initial H-concentration inside the sample. In such a situation, the minimum of the effective potential is close to the sample surface, and a significant amount of energy can be emitted throughout the adsorption process.

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