Two Hundred Years after Hamilton: Exploring New Formulations of Classical and Quantum Mechanics
David J. Tannor, Weizmann Institute of Science, Rehovot, Israel
Thursday, December 15, 2022, 11:00 AM, Los Angeles Seminar Room
Abstract: Density functional theory (DFT) can yield excited state properties as functionals of the density, by working from ensemble instead of pure states. Facilitating excited states requires exact functionals to be carefully generalized to weight-dependent forms, to avoid spurious interactions from misapplied ansatze. This talk will discuss recent advances on rigorous definitions for the kinetic, Hartree and exchange [1] and correlation [2] ensemble energy functionals, which together yield a complete generalisation of pure state DFT. These works reveal unusual (yet tractable) properties of density functionals -- notably the need for multi-configurational Kohn-Sham states, and strong absence of weight-dependence in the low density limit. Ensemble generalized Kohn-Sham theory based on these functionals, and its successful applications to excited state chemical problems [3], will finally be discussed.
1. W. R. Hamilton, On a General Method in Dynamics, Philosophical Transactions, Part 2, p. 247 (1834); ibid., Second Essay on a General Method in Dynamics, Part 1, p. 95 (1835).
2. M. Nakane and C. G. Fraser, The Early History of Hamilton-Jacobi Dynamics 1834-1837, Centaurus 44, 161 (2002); C. Lanczos, The Variational Principles of Mechanics (Oxford, 1949)
3. D. J. Tannor, New derivation of Hamilton’s three formulations of classical mechanics (preprint); ibid, Duality of the Principle of Least Action: A New Formulation of Classical Mechanics, arXiv:2109.09094 (2021).
4. Y. Goldfarb, I. Degani and D. J. Tannor, Bohmian mechanics with complex action: A new trajectory based formulation of quantum mechanics, J. Chem. Phys. 125, 231103 (2006); J. Schiff, Y. Goldfarb and D. J. Tannor, Path integral derivations of complex trajectory methods, Phys. Rev. A 83, 012104 (2011); N. Zamstein and D. J. Tannor, Overcoming the root search problem in complex quantum trajectory calculations, J. Chem. Phys. 140, 041105(2014).
5. N. Zamstein and D. J. Tannor, Non-adiabatic molecular dynamics with complex quantum trajectories. I. The adiabatic representation, J. Chem. Phys. 137, 22A518 (2012); W. Koch and D. J. Tannor, Wavepacket revivals via complex trajectory propagation, Chem. Phys. Lett. 683, 306 (2017); W. Koch and D. J. Tannor, A three-step model of high harmonic generation using complex classical trajectories, Annals of Physics, 427, 168288 (2021).