Stochastic quantum molecular dynamics

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 21, 2009, Pages

  Appel, Heiko ^a   Di Ventra, Massimiliano ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954745351     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.212303     Document Type: Article

References (20)

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6. See, e.g., R. D'Agosta and M. Di Ventra, J. Phys.: Condens. Matter 20, 374102 (2008). 10.1088/0953-8984/20/37/374102
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8. R. D'Agosta and M. Di Ventra, Phys. Rev. B 78, 165105 (2008). 10.1103/PhysRevB.78.165105
9. Note that both the electron-phonon and the electron-photon interaction can be cast in the form of H SB.
10. P. Gaspard and N. Nagaoka, J. Chem. Phys. 111, 5676 (1999). 10.1063/1.479868
11. The reasons why we work with a stochastic Schrödinger equation and not with a density-matrix approach are due to both the possible loss of positivity of the density matrix during dynamics, and the fact that a Kohn-Sham Hamiltonian depends on the density and/or current density, and is thus generally stochastic (Refs.).
12. T. Kreibich and E. K. U. Gross, Phys. Rev. Lett. 86, 2984 (2001). 10.1103/PhysRevLett.86.2984
13. T. Kreibich, R. van Leeuwen, and E. K. U. Gross, Phys. Rev. A 78, 022501 (2008). 10.1103/PhysRevA.78.022501
14. As in Refs., we are implicitly assuming that given an initial condition, bath operator, and ensemble-averaged current density, a unique ensemble-averaged density can be obtained from its equation of motion. Therefore, the density is not independent of the current density, and our theorem establishes a one-to-one correspondence between current density and vector potential.
15. G. Vignale, Phys. Rev. B 70, 201102 (R) (2004). 10.1103/PhysRevB.70. 201102
16. We have implemented a quantum-jump algorithm (Ref.) in the real-space real-time package octopus (Ref.) to integrate the KS equations of motion. We have used the bath operators as in Ref., and the adiabatic local-density approximation for the xc potential. We note that the jumps introduced by the bath in the quantum-jump algorithm appear like a "surface hopping." The relaxation rates derived from H SB and the jumps induced by the bath, however, provide a solid framework for a surface hopping scheme. More details of the numerics will be given in a forthcoming publication.
17. S. I. Druzhinin, J. Phys. Chem. A 110, 2955 (2006). 10.1021/jp054496o
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