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Extended phase-space symplectic integration for electron dynamics
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DOI：10.1103/7ghc-htf8.png)
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Abstract
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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.
Keywords:
DIFFERENTIAL-EQUATIONS
NUMERICAL-INTEGRATION
ALGORITHMS
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