Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems

Details Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems

2000-05-22

arxiv.org/abs/nlin/0005045v1

Eur. Phys. J. D 12 (2000) 381

Nonlinear Sciences

Chaotic Dynamics

21 pages, 9 figures, submitted to Eur. Phys. J. D

Scientific paper

10.1007/s100530070001

Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the periodic orbit sum and the uncertainty principle of the usual Fourier analysis, thus yielding results of high resolution and high precision. Based on the close analogy between periodic orbit trace formulae for regular and chaotic systems the technique is generalized in this paper for the semiclassical quantization of integrable systems. Thus, harmonic inversion is shown to be a universal tool which can be applied to a wide range of physical systems. The method is further generalized in two directions: Firstly, the periodic orbit quantization will be extended to include higher order hbar corrections to the periodic orbit sum. Secondly, the use of cross-correlated periodic orbit sums allows us to significantly reduce the required number of orbits for semiclassical quantization, i.e., to improve the efficiency of the semiclassical method. As a representative of regular systems, we choose the circle billiard, whose periodic orbits and quantum eigenvalues can easily be obtained.

Affiliated with

Also associated with

No associations

Rating

Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-83089