• Transition from Poisson to circular unitary ensemble

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      https://www.ias.ac.in/article/fulltext/pram/073/03/0505-0519

    • Keywords

       

      Quantum chaos; random matrix; symmetry breaking; fluctuations; correlation functions; Brownian motion; contour integral.

    • Abstract

       

      Transitions to universality classes of random matrix ensembles have been useful in the study of weakly-broken symmetries in quantum chaotic systems. Transitions involving Poisson as the initial ensemble have been particularly interesting. The exact two-point correlation function was derived by one of the present authors for the Poisson to circular unitary ensemble (CUE) transition with uniform initial density. This is given in terms of a rescaled symmetry breaking parameter Λ. The same result was obtained for Poisson to Gaussian unitary ensemble (GUE) transition by Kunz and Shapiro, using the contour-integral method of Brezin and Hikami. We show that their method is applicable to Poisson to CUE transition with arbitrary initial density. Their method is also applicable to the more general $\ell$CUE to CUE transition where CUE refers to the superposition of $\ell$ independent CUE spectra in arbitrary ratio.

    • Author Affiliations

       

      Vinayak1 Akhilesh Pandey1

      1. School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India
    • Dates

       
  • Pramana – Journal of Physics | News

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