Vibration-transit theory of self-dynamic response in a monatomic liquid.

A theoretical model for self-dynamic response is developed using vibration-transit theory, and is applied to liquid sodium at all wave vectors q from the hydrodynamic regime to the free particle limit. In this theory the zeroth-order Hamiltonian describes the vibrational motion in a single random valley harmonically extended to infinity. This Hamiltonian is tractable, is evaluated a priori for monatomic liquids, and the same Hamiltonian (the same set of eigenvalues and eigenvectors) is used for equilibrium and nonequilibrium theory. Here, for the self-intermediate scattering function F;{s}(q,t) , we find the vibrational contribution is in near perfect agreement with molecular dynamics (MD) through short and intermediate times, at all q . This is direct confirmation that normal mode vibrational correlations are present in the motion of the liquid state. The primary transit effect is the diffusive motion of the vibrational equilibrium positions, as the liquid transits rapidly among random valleys. This motion is modeled as a standard random walk, and the resulting theoretical F;{s}(q,t) is in excellent agreement with MD results at all q and t . In the limit q-->infinity , the theory automatically exhibits the correct approach to the free-particle limit. Also, in the limit q-->0 , the hydrodynamic limit emerges as well. In contrast to the benchmark theories of generalized hydrodynamics and mode coupling, the present theory is near a priori, while achieving modestly better accuracy. Therefore, in our view, it constitutes an improvement over the traditional theories.