Isomorphs and isomorph invariants in dusty plasmas
Abstract
For physical systems with the strong correlation between the virial and potential energy, in addition to isotherms, isobars, and isochores in their thermodynamic phase diagrams, there are also the so-called isomorphs, along which the structural and dynamical properties of these systems in reduced units are approximately invariant. In this paper, the isomorphs of two-dimensional (2D) and three-dimensional (3D) dusty plasmas are derived analytically using the effective coupling parameter of Yukawa systems, which are found to be the same as the isomorphs derived analytically from the effective power-law exponent of the Yukawa potential when the reduced nearest-neighbor distance is constant. The analytically derived isomorphs are verified by the calculated results of the radial distribution function and the mean squared displacement from the computer simulations of 2D and 3D Yukawa liquids. Furthermore, based on both the computer simulations and the corresponding theories, the two-particle entropy, the instantaneous transverse sound speed, and the excess isochoric specific heat are all demonstrated to be isomorph invariants in 2D and 3D dusty plasmas, so that the corresponding scaling laws of these three physical quantities are also presented.
