Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potential

Details Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potential Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potential

2004-02-18

arxiv.org/abs/cond-mat/0402462v1

Phys. Rev. Lett. 93, 170602 (2004).

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.93.170602

The density of ions trapped in a harmonic potential in one dimension is not uniform. Consequently the eigenmodes are not phonons. We calculate the long wavelength modes in the continuum limit, and evaluate the density of states in the short wavelength limit for chains of $N\gg 1$ ions. Remarkably, the results that are found analytically in the thermodynamic limit provide a good estimate of the spectrum of excitations of small chains down to few tens of ions. The spectra are used to compute the thermodynamic functions of the chain. Deviations from extensivity of the thermodynamic quantities are found. An analytic expression for the critical transverse frequency determining the stability of a linear chain is derived.

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