Spectroscopic characteristics of simple systems in a spherical cavity

Пупышев, В.И.; Stepanov, N. F.

doi:10.1134/s0036024414110132

Cited by 9 publications

(14 citation statements)

References 34 publications

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“…As both the boundary conditions and normalization conditions Equation are independent of D , one can also use more formal arguments to prove this statement presented for the discussion of similar problems for atom into the sphere in Corollary 2 of the Lemma proved in the Appendix of Ref. ).…”

Section: Wave Functionsmentioning

confidence: 91%

“…To some extent this tendency is clear from the right-hand side ofFigure 4.Dependence of the wave function with respect to D values can be described in the following way: for the functions ψ normalized with weight 1 it is clear from the form of the Hamiltonian (1.9) that D growth is followed by localization of the wave function near the external boundary of the region Ω(R int , R ext ). As both the boundary conditions and normalization conditions Equation (1.8) are independent of D, one can also use more formal arguments to prove this statement presented for the discussion of similar problems for atom into the sphere in Corollary 2 of the Lemma proved in the Appendix of Ref [39]…”

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confidence: 94%

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On the shell‐confined atom problem

Пупышев

Montgomery

2018

Int J of Quantum Chemistry

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The properties of spherically symmetric, one‐electron atomic systems are analyzed for the systems where the electron is placed in the region between two impenetrable concentric spheres of radii Rint and Rext. The changes in the structure of the energy levels of low‐lying electron states and the corresponding variations in radial wave functions are analyzed for different types of changes in Rint and Rext. Special attention is paid to the changes in electric dipole polarizability for problems with varied dimension, D, of the space. The form and the quality of some simple classical estimates for polarizability are also studied for various space dimensions.

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Section: Wave Functionsmentioning

confidence: 91%

mentioning

confidence: 94%

On the shell‐confined atom problem

Пупышев

Montgomery

2018

Int J of Quantum Chemistry

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“…11, Eq. (11.16)], [70,Theorem 7.3.1] which in essence is just a result of first-order perturbation theory for self-adjoint linear operators [71][72][73][74].…”

Section: Appendix A: Energy Velocity and Group Velocity Of Electromagmentioning

confidence: 99%

Speed-of-light limitations in passive linear media

2014

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We prove that well-known speed-of-light restrictions on electromagnetic energy velocity can be extended to a new level of generality, encompassing even nonlocal chiral media in periodic geometries, while at the same time weakening the underlying assumptions to only passivity and linearity of the medium (either with a transparency window or with dissipation). As was also shown by other authors under more limiting assumptions, passivity alone is sufficient to guarantee causality and positivity of the energy density (with no thermodynamic assumptions). Our proof is general enough to include a very broad range of material properties, including anisotropy, bianisotropy (chirality), nonlocality, dispersion, periodicity, and even delta functions or similar generalized functions. We also show that the "dynamical energy density" used by some previous authors in dissipative media reduces to the standard Brillouin formula for dispersive energy density in a transparency window. The results in this paper are proved by exploiting deep results from linear-response theory, harmonic analysis, and functional analysis that had previously not been brought together in the context of electrodynamics.

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“…The general approach to description of a "not going out" state for a particle in a vacuum cavity Ω with boundary Σ starts with the following energy functional [17]- [21]…”

Section: General Treatment Of a "Not Going Out" Statementioning

confidence: 99%

“…therein). However, actually general boundary conditions of "not going out" imply a quite different pic- * Electronic address: costa@bog.msu.ru † Electronic address: Tolokonnikov@physics.msu.ru ture, where the particle WF doesn't unavoidably vanish at the box boundary ( [17]- [22] and refs. therein).…”

Section: Introductionmentioning

confidence: 99%

Spontaneous spherical symmetry breaking in atomic confinement

Sveshnikov

Tolokonnikov

2017

Eur. Phys. J. D

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The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The reason is that such boundary conditions could yield a large magnitude of electronic wavefunction in some sector of the box boundary, what in turn promotes atomic displacement from the box center towards this part of the boundary, and so the underlying SO(3) symmetry spontaneously breaks. The emerging Goldstone modes, coinciding with rotations around the box center, restore the symmetry by spreading the atom over a spherical shell localized at some distances from the box center. Atomic confinement inside the cavity proceeds dynamically -due to the boundary condition the deformation of electronic wavefunction near the boundary works as a spring, that returns the atomic nuclei back into the box volume.

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Spectroscopic characteristics of simple systems in a spherical cavity

Cited by 9 publications

References 34 publications

On the shell‐confined atom problem

On the shell‐confined atom problem

Speed-of-light limitations in passive linear media

Spontaneous spherical symmetry breaking in atomic confinement

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