Universality of S-matrix correlations for deterministic plus random Hamiltonians

Details Universality of S-matrix correlations for deterministic plus random Hamiltonians Universality of S-matrix correlations for deterministic plus random Hamiltonians

2000-08-02

arxiv.org/abs/cond-mat/0008027v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, no figure, REVTeX 3.1 with pLaTeX 2e. Minor corrections, references added. Accepted for publication in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.63.047102

We study S-matrix correlations for random matrix ensembles with a Hamiltonian which is the sum of a given deterministic part and of a random matrix with a Gaussian probability distribution. Using Efetov's supersymmetry formalism, we show that, in the limit of infinite matrix size of the Hamiltonian, correlation functions of S-matrix elements are universal on the scale of the local mean level spacing: the dependence of the deterministic part enters into these correlation functions only through the average S-matrix and the average level density. This statement applies to each of the three symmetry classes (orthogonal, unitary, and symplectic).

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