Calculation of eigenvalues of a strongly chaotic system using Gaussian wavepacket dynamics

Abstract

We apply the approximate dynamics derived from the Gaussian time-dependent variational principle to the Hamiltonian $\hat{H}=1/2({\hat{p}}_x^2+{\hat{p}}_y^2)+1/2{\hat{x}}^2{\hat{y}}^2$, which is strongly chaotic in the classical limit. We are able to calculate, essentially analytically, low-lying eigenvalues for this system. These approximate eigenvalues agree within a few percent with the numerical results. We believe that this is the first example of the use of TDVP dynamics to compute individual eigenvalues in a non-trivial system and one of the few such computations in a chaotic system by any method. There is a short self-contained discussion on the validity of Gaussian approximations in the paper.

19 pages, Revtex + 1 ps fig , Phys. Rev. E, to appear (1997)

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