A Network Orange

Crandall, Richard S.; Levich, Marvin

doi:10.1007/978-1-4612-2172-2

Cited by 5 publications

(3 citation statements)

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“…Here, sums are over all integers, positive, negative, and zero, excluding the single point where all are zero. They are summed numerically using Ewald's method [23,30,31]. A few specific values needed for calculations: Z 3 (2; 1, 1, 1) = 16.5323159598, (B5) Z 3b (2; 1, 1, 1) = −3.8631638072, (B6) Z 3c (2; 1, 1, 1) = −1.8973804658, (B7)…”

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confidence: 99%

Scalar Casimir energies of tetrahedra and prisms

Abalo¹,

Milton²,

Kaplan³

2012

J. Phys. A: Math. Theor.

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New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a point-splitting regulator, which amounts to evaluation of the cylinder kernel. The correct Weyl divergences, depending on the volume, surface area, and the edges, are obtained, which is strong evidence that the counting of modes is correct. Because there is no curvature, the finite part of the quantum energy may be unambiguously extracted. Cubic, rectangular parallelepipedal, triangular prismatic, and spherical geometries are also revisited.Dirichlet and Neumann boundary conditions are considered for all geometries. Systematic behavior of the energy in terms of geometric invariants for these different cavities is explored. Smooth interpolation between short and long prisms is further demonstrated. When scaled by the ratio of the volume to the surface area, the energies for the tetrahedra and the prisms of maximal isoareal quotient lie very close to a universal curve. The physical significance of these results is discussed.

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confidence: 99%

Scalar Casimir energies of tetrahedra and prisms

Abalo¹,

Milton²,

Kaplan³

2012

J. Phys. A: Math. Theor.

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“…a Coulomb potential) within the N-dimensional crystal [33], but computations are quite involved and results presented were only up to three dimensions. For the N-dimensional case one can explore expansions known for example for the Epstein zeta function [15,34,35] or similar techniques [36]. In this work, we introduce a general formula for the N-dimensional Madelung constant for a simple cubic crystal in terms of a fast convergent Bessel function expansion allowing for analytical continuation, which gives deep insight into the functional behaviour of the N-dimensional Madelung constant.…”

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confidence: 99%

The Madelung constant in N dimensions

Burrows¹,

Cooper

Schwerdtfeger³

2022

Proc. R. Soc. A.

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We introduce two convergent series expansions (direct and recursive) in terms of Bessel functions and the number of representations of an integer as a sum of squares for N -dimensional Madelung constants, M N ( s ) , where s is the exponent of the Madelung series (usually chosen as s = 1 / 2 ). The convergence of the Bessel function expansion is discussed in detail. Values for M N ( s ) for s = 1 2 , 3 2 , 3 and 6 for dimension up to N = 20 are presented. This work extends Zucker’s original analysis on N -dimensional Madelung constants for even dimensions up to N = 8 .

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“…2, corresponding to the best-fit value of η = 0.036). In principle, the value of η can be calculated on the basis of the present model (by also including the repulsion between the layers due to exchange interaction), but, while its introduction results in a better fit to the data, it is methodologically wrong to try to model the macroscopic interaction inside the microscopic Hamiltonian (6).…”

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confidence: 99%

Model for flexural phonon dispersion in graphite and graphene

Metlov

2010

Phys. Rev. B

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A simple model for flexural phonons in graphite (and graphene, corresponding to the limiting case of infinite distance between carbon planes) is proposed, in which the local dipolar moment is assumed to be proportional to the curvature of the carbon sheets. Explicit expressions for dispersion curves with full account for the long-range dipolar interaction forces are obtained and fitted to the experimental data using a single adjustable parameter of the model. The parameter is expected to depend on the ground state configuration of molecular π-orbitals, the same both for graphite and for graphene. At decreasing carbon sheet separation (high pressures) the phonon spectrum displays instability, corresponding to the graphite to diamond transition. Being explicitly based on the local dipolar moments, the proposed simple model may prove useful for considering electron-phonon interaction.

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A Network Orange

Cited by 5 publications

References 0 publications

Scalar Casimir energies of tetrahedra and prisms

Scalar Casimir energies of tetrahedra and prisms

The Madelung constant in N dimensions

Model for flexural phonon dispersion in graphite and graphene

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