Periodic orbit quantization of chaotic maps by harmonic inversion

@article{Weibert2001PeriodicOQ,
  title={Periodic orbit quantization of chaotic maps by harmonic inversion},
  author={Kirsten Weibert and Jorg Main and G{\"u}nter Wunner},
  journal={Physics Letters A},
  year={2001},
  volume={289},
  pages={329-332}
}
View PDF on arXiv
3 Citations

Figures from this paper

3 Citations

Deterministic diffusion in one-dimensional maps—calculation of diffusion constants by harmonic inversion of periodic orbit sums

Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals

Basics of Nonlinear and Chaotic Dynamics.- Phase Transitions and Synergetics.- Geometry and Topology Change in Complex Systems.- Nonlinear Dynamics of Path Integrals.- Complex Nonlinearity: Combining…

Quantization ambiguity, ergodicity and semiclassics

It is well known that almost all eigenstates of a classically ergodic system are individually ergodic on coarse-grained scales. This has important implications for the quantization ambiguity in…

References

SHOWING 1-10 OF 27 REFERENCES

Use of harmonic inversion techniques in the periodic orbit quantization of integrable systems

Abstract: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…

Periodic Orbit Quantization by Harmonic Inversion of Gutzwiller's Recurrence Function

Semiclassical eigenenergies and resonances are obtained from classical periodic orbits by harmonicinversion of Gutzwiller’s semiclassical recurrence function, i.e., the trace of the…

Periodic orbit theory for the quantized Baker's map

Periodic orbit quantization of Baker's map

We consider the resummation of the semiclassical Selberg zeta function for quantized maps on compact phase space, specifically the quantized Baker's map. In particular, we demonstrate that the…

Classical structures in the quantized baker transformation

Chaos in classical and quantum mechanics

Contents: Introduction.- The Mechanics of Lagrange.- The Mechanics of Hamilton and Jacobi.- Integrable Systems.- The Three-Body Problem: Moon-Earth-Sun.- Three Methods of Section.- Periodic Orbits.-…

High Resolution Quantum Recurrence Spectra: Beyond the Uncertainty Principle

Highly resolved recurrence spectra are obtained by harmonic inversion of quantum spectra of classically chaotic systems and compared in detail to the results of semiclassical {ital periodic orbit}…

Anatomy of the trace formula for the baker's map.

The structure of the trace formula for quantum maps on a compact phase space is analyzed. An explicit expression for the functional determinant in terms of a finite number of traces is derived which…

Periodic orbit action correlations in the Baker map

Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the…

Quantum signatures of chaos

The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2,…