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Semi classical chaos in a 2-D exactly solvable system

Author:

A Nanayakkara

Institute of Fundamental Studies, Hanthana Road, Kandy, LK
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Abstract

The Chaotic behavior of the classical trajectories and the level spacing distributions of 2-D Pseudo Hermitian Hamiltonian H =½ (px2 + py2) + ½ x2x2 + ωy2y2) - igxy, where g is a real parameter are investigated. This Hamiltonian is separable and Lyapunov exponents are obtained analytically. All the trajectories of this system are found to be regular and Hamiltonian is Hermitian when ½(| ωx2 - ωy2|)≥|g| and trajectories become chaotic and Hamiltonian becomes Pseudo Hermitian when ½(| ωx2 - ωy2|) < |g|. The level spacing distributions are obtained for both real and complex eigen energies. It was interesting to find out that level spacing distributions of complex norm of the eigen energies which are corresponding to chaotic motion show Poisson like distribution rather than Gaussian ensamble statistics.

doi:10.4038/sljp.v5i0.192  

Sri Lankan Journal of Physics, Vol.5 (2004) 1-9

How to Cite: Nanayakkara, A., (2004). Semi classical chaos in a 2-D exactly solvable system. Sri Lankan Journal of Physics. 5, pp.1–9. DOI: http://doi.org/10.4038/sljp.v5i0.192
Published on 10 Dec 2004.
Peer Reviewed

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