Effects of Time Reversal-Symmetry Breaking on Localization: Band Random Matrix Description

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Communications in Theoretical Physics ›› 1999, Vol. 31 ›› Issue (1) : 91-98.

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Effects of Time Reversal-Symmetry Breaking on Localization: Band Random Matrix Description

GONG Jiangbin, XU Gong'ou

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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 Icramers' degeneracy. This leads us, to expect a simple and universal description of the effects of time-riversal symmetry breaking on localization that the localization length ξ is given by ξ = βb²/4 where b is the band-width parameter and β the universality parameter.

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time reversal symmetry breaking / band random matrix ensemble

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GONG Jiangbin, XU Gong'ou. Effects of Time Reversal-Symmetry Breaking on Localization: Band Random Matrix Description[J]. Communications in Theoretical Physics, 1999, 31(1): 91-98

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