Universal K-matrix distribution in β = 2 ensembles of random matrices
Universal K-matrix distribution in β = 2 ensembles of random matrices
复制标题
β = 2 随机矩阵系综中的通用 K 矩阵分布
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Nock
中科院分区：
文献类型：
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作者：
Y. Fyodorov;B. Khoruzhenko;A. Nock
K矩阵，也称为核散射中的“维格纳反应矩阵”或电磁波散射中的“阻抗矩阵”，本质上是由哈密顿量H的预解式（E-H）−1的M × M对角块给出。对于混沌量子系统，哈密顿量H可以用取自Dyson对称性指数β = 1，2或4的不变系综的随机Hermitian N × N矩阵来建模。对于β = 2，我们通过显式计算证明了Brouwer（1995 B-84）的一个普适性猜想，它等价于K的概率分布对于随机Hermitian矩阵H的一大类不变系综收敛于密度为P（K）<$[det（λ2+（K− <$）2）]−M？>在极限N → ∞中，假设参数M是固定的，谱参数E取在H的本征值分布的支集内。特别是，我们证明了一个广泛的一类酉不变的合奏随机矩阵，有限对角块的预解是柯西分布。β = 1和β = 4的案件仍未解决。
The K-matrix, also known as the ‘Wigner reaction matrix’ in nuclear scattering or the ‘impedance matrix’ in electromagnetic wave scattering, is given essentially by an M × M diagonal block of the resolvent (E − H)−1 of a Hamiltonian H. For chaotic quantum systems, the Hamiltonian H can be modelled by random Hermitian N × N matrices taken from invariant ensembles with the Dyson symmetry index β = 1, 2 or 4. For β = 2, we prove by explicit calculation a universality conjecture by Brouwer (1995 Phys. Rev. B 51 16878–84), which is equivalent to the claim that the probability distribution of K, for a broad class of invariant ensembles of random Hermitian matrices H, converges to a matrix Cauchy distribution with density P(K)∝[det(λ2+(K−ϵ)2)]−M?> in the limit N → ∞, provided the parameter M is fixed and the spectral parameter E is taken within the support of the eigenvalue distribution of H. In particular, we show that for a broad class of unitary invariant ensembles of random matrices, finite diagonal blocks of the resolvent are Cauchy distributed. The cases β = 1 and β = 4 remain outstanding.
影响因子：
3.5
作者：
Mehmet Akyol;Georgios Papadopoulos
通讯作者：
Mehmet Akyol;Georgios Papadopoulos