Extended phase-space symplectic integration for electron dynamics

We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical dynamics of a charged particle in a strong, constant, and uniform magnetic field perturbed by a turbulent electrostatic potential. The second one, with an infinite number of degrees of freedom, comes from physical chemistry and corresponds to Kohn-Sham time-dependent density-functional theory. For both we lay out the extension procedure and stability condition for numerical integration of the dynamics using high-order symplectic split-operator schemes. We also identify a computationally inexpensive metric that can be used for on-the-fly estimation of the accuracy of simulations. Our work paves the way for broad application of symplectic split-operator integration of classical and quantum Hamiltonian systems with finite and infinite number of degrees of freedom by comparing different modes of implementation of extended phase space integration.