• Universality in the length spectrum of integrable systems

• # Fulltext

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

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

• # Pramana – Journal of Physics

Volume 96, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019