# 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} }

## 3 Citations

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

- Mathematics
- 2001

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

- Physics
- 2008

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

- Physics
- 1999

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

- Physics
- 2000

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

- Physics
- 1997

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 quantization of Baker's map

- Mathematics
- 1994

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…

### Chaos in classical and quantum mechanics

- Physics
- 1990

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

- Physics
- 1997

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.

- MathematicsChaos
- 1992

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

- Physics
- 1999

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…