Anharmonic Effects In Ion-Electron Chains

It is shown that a Fröhlich Hamiltonian for a chain of ions and conduction electrons leads to an effective quartic anharmonic phonon Hamiltonian characterized by a dimensionless parameter a²_e ≈ (3/64)(ξ/ε_F)⁴ (e_F/ 1/2 Ms², where ξ≈ε_F is an electron-phonon coupling parameter, M the ion mass, and s the speed of Sound. This electronic anharmonicity is ordinarily negligible (α²_e ≈ 0.01) but may become large and dominant in light-ion systems with high Fermi energies, for example, in filamentary metallic hydrogen.