We numerically calculated the full capacitance matrices for both
one-dimensional (1D) and two-dimensional (2D) quantum-dot arrays. We found it
is necessary to use the full capacitance matrix in modeling coupled quantum dot
arrays due to weaker screening in these systems in comparison with arrays of
normal metal tunnel junctions. The static soliton potential distributions in
both 1D and 2D arrays are well approximated by the unscreened (1/r) coulomb
potential, instead of the exponential fall-off expected from the often used
nearest neighbor approximation. The Coulomb potential approximation also
provides a simple expression for the full inverse capacitance matrix of uniform
quantum dot arrays. In terms of dynamics, we compare the current-voltage (I-V)
characteristics of voltage biased 1D arrays using either the full capacitance
matrix or its nearest neighbor approximation. The I-V curves show clear
differences and the differences become more pronounced when larger arrays are
considered.Comment: 8 pages preprint format, 3 PostScript figure