We investigate two kinds of band random matrix ensemble (BRM) with differen
t time reversal symmetry, namely, BRM of complex and quaternion real (C-BRM
and QR-BRM) Hermitians. Their scaling behaviors of localization are numeri
cally studied. Results show that the removal of time reversal symmetry yiel
ds a multiplication of the localization length by a factor 2 (or, 1/2) in t
he absence (or, presence) of Kramers' degeneracy This leads us to expect a
simple and universal description of the effects of time-reversal symmetry b
reaking on localization that the localization length xi is given by xi = be
ta b(2)/4 where b is the band-width parameter and beta the universality par
ameter.