Henning Schomerus and Martin Sieber 1997 J. Phys. A: Math. Gen. 30 4537 doi:10.1088/0305-4470/30/13/010
Bifurcations of periodic orbits and uniform approximations
Henning Schomerus
and Martin Sieber
We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiller's type would diverge at the bifurcation. New results for the tangent, the period-doubling and the period-tripling bifurcation are given. They are obtained by going beyond the local approximation and including higher-order terms in the normal form of the action. The uniform approximations obtained are tested on the kicked top and are found to be in excellent agreement with exact quantum results.
- PACS
- MSC
- Subjects
- Dates
-
Issue 13 (7 July 1997)
Received 27 January 1997, in final form 2 May 1997
-
Bifurcations of periodic orbits and uniform approximations
Henning Schomerus and Martin Sieber 1997 J. Phys. A: Math. Gen. 30 4537
-
Uniform approximation for bifurcations of periodic orbits with high repetition numbers
M Sieber 1996 J. Phys. A: Math. Gen. 29 4715
-
Secular determinants of random unitary matrices
Fritz Haake et al 1996 J. Phys. A: Math. Gen. 29 3641
-
Statistical mechanics of the knapsack problem
E Korutcheva et al 1994 J. Phys. A: Math. Gen. 27 L645
-
Separation of variables in the nonlinear wave equation
R Z Zhdanov 1994 J. Phys. A: Math. Gen. 27 L291
-
Differential calculus and gauge theory on finite sets
A Dimakis and F Muller-Hoissen 1994 J. Phys. A: Math. Gen. 27 3159
-
The Hausdorf dimension of the Apollonian packing of circles
P B Thomas and D Dhar 1994 J. Phys. A: Math. Gen. 27 2257
-
Coupled dynamics of fast spins and slow interactions in neural networks and spin systems
R W Penney et al 1993 J. Phys. A: Math. Gen. 26 3681
-
Noncommutative differential calculus and lattice gauge theory
A Dimakis et al 1993 J. Phys. A: Math. Gen. 26 1927
-
Exact solution of a 1D asymmetric exclusion model using a matrix formulation
B Derrida et al 1993 J. Phys. A: Math. Gen. 26 1493
Related review articles
What's this?- New integral representations of Whittaker functions for classical Lie groups
- The nonlinear Schrödinger equation with a random potential: results and puzzles
- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
, and Chern–Simons–Higgs solitons on 
: dimensional reduction of Chern–Pontryagin densities