Simulating Quantum High Energy Density Plasmas: Approximations According to the Time-Dependent Variational Principle

Paul Grabowski
Los Alamos National Laboratory
Computational Physics Group

Despite very high temperatures, quantum effects are important in high energy density plasmas, including Heisenberg uncertainty, quantum diffraction and degeneracy. It is necessary to include these effects in electron-electron and electron-ion interactions. Except for rare fusion events, ion-ion interactions are classical. These systems can also be strongly coupled; so a precise treatment of particle-particle collisions is needed.

Uncertainties remain in calculations of ion-electron temperature equilibration times, stopping power, and thermal conductivity. It is difficult for any theory to accurately treat both strong coupling and quantum effects. Furthermore, these high densities and temperatures are very difficult to reach experimentally, necessitating ab initio computer simulations.

Quantum calculations for high energy density systems can be done with path integral Monte Carlo or molecular dynamics using quantum statistical potentials in equilibrium or density functional theory molecular dynamics in the adiabatic limit, but these methods cannot be used to calculate non-equilibrium or time-dependent observables. Solving the full many-body time-dependent Schrödinger equation is intractable, but simple approximations can be made at high temperatures and high densities.

The time-dependent variational principle gives a rigorous framework for non-equilibrium systems by producing the best solution given an ansatz for the wave function. A review of this method, in particular using the isotropic Gaussian ansatz (wave packet molecular dynamics) will be given. A well-known problem is wave packet spreading. The origin and implications of this spreading will be presented as well as an improvement to the ansatz using a plane wave basis.
Victor S. Batista(2); Lorin X. Benedict(3); Michael P. Desjarlais(4);
Frank R. Graziani(3); Andreas Markmann(2); Michael S. Murillo(1);
David F. Richards(3); Michael P. Surh(3); Heather D. Whitley(3);

(1)Los Alamos National Laboratory
(2)Yale University
(3)Lawrence Livermore National Laboratory
(4)Sandia National Laboratory

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