Analysis of collective diffusion by a variational method

Abstract: I will present a variational method of calculating diffusion coefficients [1] for particles in complex energy landscapes. The approach is based on the master equation and allows to obtain diffusion coefficients as functions of the jump rates between the potential minima, interaction constants [2], the system’s temperature and coverage at lattices of various geometry [3]. In particular I will show a general expression for the collective diffusion coefficient of interacting particles in an arbitrary one-dimensional energetic potential [4]. The diffusion coefficient obtained in the variational approach takes into account corrections due to long-range correlations, which, as we show, are particularly important in non-homogeneous systems. Such correlations are not taken into account by other methods [5]. Contribution from long-range correlations causes that the diffusion depends not only on the height of the barriers in the system but also on the sequence in which they are ordered. Additionally, I will show solutions for two-dimensional cases including real systems such as Ga atoms on GaAs(001) [6] or Cu monomers and dimers on Cu(111) and Ag(111) [7]. The variational method allows to compare contributions from various diffusive paths in such systems to the total diffusion coefficient.

[1] M. A. Załuska-Kotur, Z. W. Gortel, Phys. Rev. B 76, 245401 (2007)
[2] M. Mińkowski, M. A. Załuska-Kotur, J. Stat. Mech. P05004 (2013)
[3] M. Mińkowski, M. A. Załuska-Kotur, Appl. Surf. Sci. 304, 81 (2014)
[4] M. Mińkowski, M. A. Załuska-Kotur, sent to J. Stat. Mech. (2017)
[5] K. Mussawisade, T. Wichmann, K. W. Kehr, J. Phys.: Condens. Matter 9, 1181-1189 (1997)
[6] M. Mińkowski, M. A. Załuska-Kotur, Phys. Rev. B 91, 075411 (2015)
[7] M. Mińkowski, M. A. Załuska-Kotur, Surf. Sci. 642, 22 (2015)