NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES

Authors

  • Sachin Kumar Bhabha Atomic Research Centre, Mumbai
  • Zafar Ahmed Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India

DOI:

https://doi.org/10.14311/AP.2017.57.0418

Keywords:

real symmetric matrices, Wigner surmise

Abstract

We investigate spacing statistics for ensembles of various real random matrices where the matrix-elements have various Probability Distribution Function (PDF: f(x)) including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derive the spacing distributions p(s) of adjacent energy eigenvalues. Nevertheless, they show the linear level repulsion near s = 0 as αs where α depends on the choice of the PDF. More interestingly when f(x) = xe−x2 (f(0) = 0), we get cubic level repulsion near s = 0: p(s) ~ s3e−s2.We also derive the distribution of eigenvalues D(ε) for these matrices.

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Published

2017-12-30

How to Cite

Kumar, S., & Ahmed, Z. (2017). NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES. Acta Polytechnica, 57(6), 418–423. https://doi.org/10.14311/AP.2017.57.0418

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Section

Articles