• Universality in the length spectrum of integrable systems

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/042/06/0447-0453

    • Keywords

       

      Length spectrum; periodic orbits; integrable systems; fluctuations; Poisson summation formula

    • Abstract

       

      The length spectrum of periodic orbits in integrable hamiltonian systems can be expressed in terms of the set of winding numbers {M1,…,Mf} on thef-tori. Using the Poisson summation formula, one can thus express the density, Σδ(TTM), as a sum of a smooth average part and fluctuations about it. Working with homogeneous separable potentials, we explicitly show that the fluctuations are due to quantal energies. Further, their statistical properties are universal and typical of a Poisson process as in the corresponding quantal energy eigenvalues. It is interesting to note however that even though long periodic orbits in chaotic billiards have similar statistical properties, the form of the fluctuations are indeed very different.

    • Author Affiliations

       

      Debabrata Biswas1

      1. Theoretical Physics Division, Bhabha Atomic Research Centre, Bombay - 400 085, India
    • Dates

       
  • Pramana – Journal of Physics | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.