Research ArticlePHYSICS

Fast nonadiabatic dynamics of many-body quantum systems

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Science Advances  22 Nov 2019:
Vol. 5, no. 11, eaaw1634
DOI: 10.1126/sciadv.aaw1634
  • Fig. 1 Static ion-ion structure factors for aluminum.

    The static structure factor is defined as S(k) = ∫ S(k, ω)dω. The main graph compares our results from Bohmian dynamics with data obtained by density functional theory molecular dynamics (DFT-MD) with orbital-free DFT (OFDFT) (21) for a density of 5.2 g cm−3 and a temperature of 3.5 eV. The lower insets compare our results to data from full Kohn-Sham DFT (KS-DFT) simulations at solid density and two different temperatures. The excellent agreement of the methods is also demonstrated by the very small differences in pressure as quantified by the parameter R: These values give the difference in ionic pressure between the methods normalized to the difference of the DFT pressures and the pressure of an ideal gas, that is, R = (PBohmPDFT)/(PDFTP0).

  • Fig. 2 Results for the dynamic ion structure for aluminum at 3.5 eV and 5.2 g cm−3.

    (A) The frequency-resolved DSF from the Bohmian dynamics. (B) Comparison of the dispersion relation of the ion acoustic modes from our Bohmian approach with the data from the Langevin model of (21).

  • Fig. 3 Schematic of the applied linearization approximation.

    (A) The time evolution of an N-trajectory in an exact Bohmian representation of a pure quantum state (top) and the Bohm potential, VB, that it experiences (bottom). VB isa functional of the density of N-trajectories in configuration space, Φ. At each time step, all of the N-trajectories in the ensemble must be updated, Φ calculated, and the updated Bohm potential determined. (B) The time evolution of an N-trajectory in our linearized Bohmian representation of a thermal state (top) and the Bohm potential that it experiences (bottom). We need only to track a single N-trajectory: Its coupling to a heat bath ensures its ergodicity, so that Φ becomes equal, in equilibrium, to its time-averaged density in configuration space. As a result, the N-trajectory evolves with a time-independent Bohm potential, generated self-consistently by its own time-integrated density. (C) The block panel summarizes our scheme to determine the Bohmian dynamics and gives the sources for the different potentials needed as input.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/11/eaaw1634/DC1

    Bohm’s theory of quantum mechanics

    Correlation closure

    Fermi statistical corrections

    Pseudopotentials

    Generalized IMC parameter search

    Modified thermostats

    Simulation parameters

    Fig. S1. Reproduction of a Fermi kinetic energy distribution using our modified thermostat.

    References (3252)

  • Supplementary Materials

    This PDF file includes:

    • Bohm’s theory of quantum mechanics
    • Correlation closure
    • Fermi statistical corrections
    • Pseudopotentials
    • Generalized IMC parameter search
    • Modified thermostats
    • Simulation parameters
    • Fig. S1. Reproduction of a Fermi kinetic energy distribution using our modified thermostat.
    • References (3252)

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