# Absence of diagonal force constants in cubic Coulomb crystals

@article{Andrews2020AbsenceOD, title={Absence of diagonal force constants in cubic Coulomb crystals}, author={B. Andrews and G. Conduit}, journal={Proceedings. Mathematical, Physical, and Engineering Sciences}, year={2020}, volume={476} }

The quasi-harmonic model proposes that a crystal can be modelled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss’s law shows that the ion–ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modelled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tight-binding and density nearly-free… Expand

#### Figures and Tables from this paper

#### References

SHOWING 1-10 OF 73 REFERENCES

Control of the conformations of ion Coulomb crystals in a Penning trap

- Physics, Medicine
- Nature communications
- 2013

In a Penning trap the creation and manipulation of a wide variety of ion Coulomb crystals formed from small numbers of ions is demonstrated, which has potential applications for quantum simulation, quantum information processing and tests of fundamental physics models from quantum field theory to cosmology. Expand

Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects.

- Physics, Medicine
- Physical review. B, Condensed matter
- 1995

The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wave function and the collective excitations in the… Expand

Lattice instabilities in metallic elements

- Physics
- 2012

Most metallic elements have a crystal structure that is either body-centered cubic (bcc), face-centered close packed, or hexagonal close packed. If the bcc lattice is the thermodynamically most… Expand

Direct evaluation of the force constant matrix in quantum Monte Carlo.

- Physics, Medicine
- The Journal of chemical physics
- 2019

A formalism to directly evaluate the matrix of force constants within a Quantum Monte Carlo calculation is developed and fundamental vibrational frequencies are obtained within 0.1% of experimental results and ∼10 times more accurate than leading computational methods. Expand

Statistical Mechanics of Dense Ionized Matter. I. Equilibrium Properties of the Classical One-Component Plasma

- Physics
- 1973

The equilibrium properties of a classical one-component plasma, in a uniform background of opposite charge, are computed for systems of various sizes by the Monte Carlo method of Metropolis et al.… Expand

Structural properties of two-component coulomb crystals in linear paul traps.

- Materials Science, Medicine
- Physical review letters
- 2001

Structural properties of two-component Coulomb crystals in a linear Paul trap with observed changes in the radial separation of the two ion species with the radius of the inner cylindrical crystal are reported on. Expand

Zero‐Point Energy of an Electron Lattice

- Physics
- 1960

At very low densities an electron gas in a compensating uniform background of positive charge crystallizes into a bcc lattice for which the correlation energy per electron is (−1.792/rs) ry. At… Expand

Structural stability analysis of Wigner crystal with Gaussian and Yukawa‐type positive background

- Physics
- 2002

Calculations of the ground-state energies of Wigner crystals having simple cubic (sc), body-centered cubic (bcc), face-centered cubic (fcc), diamond, and perovskite structures and (hence) the… Expand

Stability, dynamical properties, and melting of a classical bilayer Wigner crystal.

- Materials Science, Medicine
- Physical review. B, Condensed matter
- 1996

The stability, the dynamical properties and melting of a two-dimensional Wigner crystal of classical Coulombic particles in a bi-layer structure and the harmonic free-energy of the system is minimized, and no temperature-induced structural phase transition is found. Expand

On the crystalline states of the dilute jellium model

- Physics
- 2009

Strongly localized quantum crystalline states (SLQCS) are determinantal wave-functions made up of the single-particle wave-functions that are obtained from all the distinct crystalline translations… Expand