Periodic Orbit Quantization beyond the Semiclassical Theory
نویسندگان
چکیده
منابع مشابه
Periodic Orbit Quantization beyond Semiclassics
A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher h̄ contributions to the spectral determinant. We apply the theory to billiard systems, and compare the periodic orbit quantization including the first h̄ contribution to the exact quantum mechanical results. Typeset using REVTEX
متن کاملBeyond the periodic orbit theory
The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory appr...
متن کاملPeriodic Orbit Quantization : How to Make Semiclassical Trace Formulae Convergent ∗
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of semiclassical recurrence functions. A band-limited periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. The frequencies of ...
متن کاملSemiclassical quantization by Padé approximant to periodic orbit sums
– Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Padé approximant to the periodic orbit sums. The Padé approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynam...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review Letters
سال: 1996
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.76.335