Browsing by Author "Hsieh, J"

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Conservation constraints on random matrices
(2003-02-07)
Ma, WJ
;
Wu, TM
;
Hsieh, J
;
物理研究所
;
Institute of Physics
We study the random matrices constrained by the summation rules that are present in the Hessian of the potential energy surface in the instantaneous normal mode calculations, as a result of momentum conservation. In this paper, we analyse the properties related to such conservation constraints in two classes of real symmetric matrices: one with purely row-wise summation rules and the other with the constraints on the blocks of each matrix, which underscores partially the spatial dimension. We show explicitly that the constraints are removable by separating the degrees of freedom of the zero-eigenvalue modes. The non-spectral degrees of freedom under the constraints can be realized in terms of the ordinary constraint-free orthogonal symmetry but with the rank deducted by the block dimension. We propose that the ensemble of real symmetric matrices with full randomness, constrained by the summation rules, is equivalent to the Gaussian orthogonal ensemble (GOE) with lowered rank. Independent of the joint probability distribution, the Jacobian contributed by the transformation from the matrix coordinates to the spectral coordinates, possesses the same spectral-variable dependence in these two cases. We verify numerically that the small-separation asymptotic in the nearest-neighbour level spacing distribution is indeed governed by the same symmetry power factor, beta = 1, as that of the GOE, under conservation constraints and other underlying spatial correlations.
Level statistics of Hessian matrices: random matrices with conservation constraints
(2003-04-01)
Ma, WJ
;
Wu, TM
;
Hsieh, J
;
Chang, SL
;
物理研究所
We consider the Hessian matrices of simple liquid systems as a new type of random matrices. By numerically comparing the distribution of the nearest-neighbor level spacing of the eigenvalues with the Wigner's surmise, we round that the level statistics is akin to the generic Gaussian Orthogonal Ensemble (GOE), in spite of the constraints due to the summation rules and the presence of the correlation among the components inherited with the underlying spatial configuration. The distribution is in good agreement with the Wigner's prediction if only the extended eigenstates are considered. Indeed, our theoretical analysis shows that the ensemble of real symmetric matrices with full randomness. but constrained by the summation rules, is equivalent to the GOE with matrices of the rank lowered by the spatial dimension. (C) 2002 Published by Elsevier Science B.V.
MOCVD growth of highly strained InGaAs : Sb-GaAs-GaAsP quantum well vertical cavity surface-emitting lasers with 1.27 mu m emission
(2004-12-10)
Kuo, HC
;
Yao, HH
;
Chang, YH
;
Chang, YA
;
Tsai, MY
1.27mum InGaAs:Sb-GaAs-GaAsP vertical cavity surface-emitting lasers (VCSELs) were grown by metalorganic chemical vapor deposition (MOCVD) with superior performance. The threshold current changes between 1.8 and 1.1 mA and the slope efficiency drops below similar to35% when the temperature is raised from room temperature to 70degreesC. With only 5 mA of bias current, the 3 dB modulation frequency response is measured to be 8.36 GHz which is suitable for 10Gb/s operation. The maximal bandwidth is estimated to 10.7GHz with modulation current efficiency factor MCEF) of similar to5.25GHz/(mA)(1/2). The results of InGaAs:Sb-GaAs-GaAsP VCSELs can reach a performance level comparable to GalnAsN VCSELs with better thermal stability and should be considered as a very promising candidate for 1.3 mum commercial applications. (C) 2004 Elsevier B.V. All rights reserved.