Type: Article
Publication Date: 2004-12-28
Citations: 50
DOI: https://doi.org/10.1103/physreve.70.066141
Cold ions in anisotropic harmonic potentials can form ion chains of various sizes. Here, the density of ions is not uniform, and thus the eigenmodes are not phononic-like waves. We study chains of $N⪢1$ ions and evaluate analytically the long-wavelength modes and the density of states in the short-wavelength limit. These results reproduce with good approximation the dynamics of chains consisting of dozens of ions. Moreover, they allow one to determine the critical transverse frequency required for the stability of the linear structure, which is found to be in agreement with results obtained by different theoretical methods [D. H. E. Dubin, Phys. Rev. Lett. 71, 2753 (1993)] and by numerical simulations [J. P. Schiffer, Phys. Rev. Lett. 70, 818 (1993)]. We introduce and explore the thermodynamic limit for the ion chain. The thermodynamic functions are found to exhibit deviations from extensivity.