Localization constraints in Gaussian wave packet molecular dynamics of nonideal plasmas

Abstract

The problem of wave packet broadening in the method of wave packet molecular dynamics simulations of electron–ion nonideal plasmas is discussed. It is shown that when using a harmonic restrictive potential for the packet widths, simulation results depend strongly on the constraint parameter. Two new approaches to constraining the packet broadening in a less stringent way are analyzed: periodic boundary conditions for widths and a dynamic constraint, based on filtering close particle collisions. These different ways to localize electrons are compared by calculating the dynamical plasma collision rate and the particle pair distribution functions.

Wave packet spreading and localization in electron-nuclear scattering

“…The Gaussian ansatz seemed reasonable because at high temperatures, electrons were expected to approximate classical behavior [20]. However, electrons as simulated by WPMD feature divergent width parameters leading to wave packet spreading [22][23][24][25][26][27][28][29]. Electrons then overlap all ions, with no mechanism to localize near nuclei, producing a nearly constant electron background at large times.…”

“…Morozov and Valuev [29] showed that by varying the constraint, they could obtain any value of the dynamical collision rate; including the constraint makes WPMD an empirical model.…”

Reflecting Boundary Conditions for Classical and Quantum Molecular Dynamics Simulations of Nonideal Plasmas

“…In the following we simulate this quantum system using the Wave Packet Molecular Dynamics (WPMD) method. In contrast to earlier WPMD plasma models [8,12,17,29], the confined system formally does not introduce any wave packet broadening problem, since the width of the wave packets is naturally limited by the confinement walls. Moreover, the confined quantum system with infinite walls has no continuum spectrum of eigenstates, thus the partition function of this system can be unambiguously defined and calculated with controllable accuracy.…”

“…The peak at larger widths corresponds to propagating electrons. Their mean wave function width determines the strength of the effective interaction with ions and the electron-ion collision frequency [29]. This distribution may be accumulated by both Monte Carlo and dynamical versions of the method.…”

“…In WPMD simulations there is another issue related to the boundary conditions. Application of this method to rather dilute nondegenerate extended systems leads to the known problem of unrestricted wave packet spreading [29]. Although this spreading is a natural effect for the Gaussian wave function in an unrestricted space, the model of an extended system should also provide correct limitations on the density of allowed quantum states, which remains arbitrary when the wave packets are allowed to spread.…”