Abstract
We investigate two kinds of band random matrix ensemble (BRM) with different time reversal symmetry, namely, BRM of complex and quaternion real (C-BRM and QR-BRM) Hermitians. Their scaling behaviors of localization are numerically studied. Results show that the removal of time reversal symmetry yields a multiplication of the localization length by a factor 2 (or, 1/2) in the absence (or, presence) of Kramers' degeneracy. This leads us, to expect a simple and universal description of the effects of time-reversal symmetry breaking on localization that the localization length ξ is given by where b is the band-width parameter and β the universality parameter.
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