Semiclassical Spectra from Periodic-Orbit Clusters in a Mixed Phase Space
نویسندگان
چکیده
We calculate complete quasienergy spectra (rather than partial information thereon) from classical periodic orbits for the kicked top, throughout the transition from integrability to well-developed chaos. The standard error incurred for the quasienergies is a small percentage of their mean spacing, even though the effective Planck constant is not pushed to small values. The price paid is the inclusion of collective contributions of clusters of periodic orbits near bifurcations into Gutzwiller’s trace formula. [S0031-9007(97)03790-3]
منابع مشابه
Use of Harmonic Inversion Techniques in Semiclassical Quantization and Analysis of Quantum Spectra
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and to extract dynamical information from quantum spectra which has been unattainable before, such as bifurcations of orbits, the uncovering of hidden ghost orbi...
متن کاملSemiclassical Transition from an Ellipticalto an Oval
Semiclassical approximations often involve the use of stationary phase approximations. This method can be applied when h is small in comparison to relevant actions or action diierences in the corresponding classical system. In many situations, however, action diierences can be arbitrarily small and then uniform approximations are more appropriate. In the present paper we examine diierent unifor...
متن کاملSemiclassical interference of bifurcations
– In semiclassical studies of systems with mixed phase space, the neighbourhood of bifurcations of co-dimension two is felt strongly even though such bifurcations are ungeneric in classical mechanics. We discuss a scenario which reveals this fact and derive the correct semiclassical contribution of the bifurcating orbits to the trace of the unitary time evolution operator. That contribution has...
متن کاملSemiclassical quantization of the diamagnetic hydrogen atom with near-action-degenerate periodic-orbit bunches.
The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters. Orbits can be grouped already on the level of the symbolic dynamics by application of appropriate reconnection rules to the symbolic code in the ternary alphabet....
متن کاملOrbit bifurcations and spectral statistics
Systems whose phase space is mixed have been conjectured to exhibit quantum spectral correlations that are, in the semiclassical limit, a combination of Poisson and randommatrix, with relative weightings determined by the corresponding measures of regular and chaotic orbits. We here identify an additional component in long-range spectral statistics, associated with periodic orbit bifurcations, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997