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Bulletin of the American Physical Society

Time-Resolved Dynamics in Exact TDDFT: Studies of Two-Electron Systems

Emilio Muñoz‐Sandoval, Johanna I. Fuks, Kai Luo, Neepa T. Maitra, Peter D. T. A. Elliott

Published Mar 4, 2014• 0 citations
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Ultrafast electronic dynamics in solids lies at the core of modern condensed matter and materials physics. To build up a practical \textit{ab initio} method for studying solids under photoexcitation, we develop momentum-resolved real-time time dependent density functional theory (rt-TDDFT) algorithm using numerical atomic basis, together with the implementation of both length and vector gauge of electromagnetic field. When applied to simulate elementary excitations in graphene, different excitation modes, only distinguishable in momentum space, are observed. The momentum-resolved rt-TDDFT is important and computationally efficient for the study of ultrafast dynamics in extended systems.
The foundation of many approximations in time-dependent density functional theory (TDDFT) lies in the theory of the homogeneous electron gas. However, unlike the ground-state DFT, in which the exchange-correlation potential of the homogeneous electron gas is known exactly via the quantum Monte Carlo calculation, the time-dependent or frequency-dependent dynamical potential of the homogeneous electron gas has not been known exactly, due to the absence of a similar variational principle for excited states. In this work, we present a simple geometric derivation of the time-dependent dynamical exchange-correlation potential for the homogeneous system. With this derivation, the dynamical potential can be expressed in terms of the stress tensor, offering an alternative to calculate the bulk and shear moduli, two key input quantities in TDDFT.
Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. We investigate the possibility of using the linear response formalism of time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron-interaction alone. Nearest-neighbor level-spacing statistics are in principle exactly and directly accessible from TDDFT. We discuss how the TDDFT linear response procedure can reveal information about the mechanism of chaos induced by electron-interaction alone. A simple model of a two-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.