  We theoretically examine the validity of Matthiessen's rule caused by strong
dislocation-dislocation interaction using a fully quantized dislocation field,
where its degree of deviation is quantified at arbitrary electron energy,
dislocation-electron and dislocation-dislocation distances and interaction
strengths. Contrary to intuition, we show that the electron relaxation rate
deviates from the Matthiessen's rule in an oscillatory way as a function of
inter-dislocation distance, instead of monotonically. This study could serve as
a computational tool to investigate the electronic behavior of a
highly-dislocated system at a full quantum field theoretical level.
